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U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

Environmental Effects

on Microphones and Type II Sound Level Meters
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3. 1901. The Bureau's overall goal is lo strengthen and advance the Nation's science and technology

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' Headquarters ami Laboratories .it Ciuiihcrshurg. Maryland, unless otherwise noted: mailing address Washington. I) C. 202.14.

- I ..cited at Boulder. Colorado RO302.
nal Bureau of Standards fern Environmental Effects on Microphones

and Type II Sound Level Meters y^ k , V.OO

*3

Edward B. Magrab, Editor

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

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U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward 0. Vetter, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued October 1976
National Bureau of Standards Technical Note 931

Nat. Bur. Stand. (U.S.), Tech. Note 931, 120 pages (Oct. 1976) CODEN: NBTNAE

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WASHINGTON: 1976

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TABLE OF CONTENTS

Page

1. INTRODUCTION ... 2

2. ATMOSPHERIC EFFECTS ... .. e •

2.1. Temperature and Humidity Effects on Microphone

Sensitivity by G. R. Hruska, E. B. Magrab, and

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2. 1. 1. Introduction 3

2. 1. 2. Test Method and Procedure 3

2.1.3. Discussion of Results 5

2. 1. 4. Conclusions . 22

2. 2. Static Pressure Effects on the Output Sound Level

of Microphone Calibrators by G. F. Kuhn ......... 23

2. 3. Temperature Effects on the Electrical Sensitivity

of Type II Sound Level Meters by W.B. Penzes and

tjo -Do lviagrao ...... ........ ............. ...... £* *

2.4. Attentuation of Aerodynamically Generated Noise by

Foam Windscreens by D. S. Blomquist 32

3. effects of the physical environment 38

3.1. Free-Field Response of Type II Sound Level Meters

by G.R. H rus ka 38

3.2. Random Incidence Response of Type II Sound Level

Meters by T. M. Proctor ....................... 38

3. 3. Effects of Ground Reflections on Sound Level Meter

Measurements by T.M. Proctor and E.B. Magrab. 44

3.4. Effects of Walls, Persons, and Tripods on Sound

Level Meter Measurements by T.M. Proctor ..... 54

4. PROCEDURES FOR THE ASSURANCE OF THE ADEQUACY

MEASUREMENTS by J. M. Cameron 63

4. 1. Introduction 63

4. 2. The Cross-examining of Measurement Data 63

4. 3. The Measurement Method . 65

4. 4. Measurement as a Production Process .......... 65

iii
Page

4. 5. The Concept of a "Repetition" of a Measurement. . 66

4. 6. Possible Offset of the Process 71

4. 7. Uncertainty 72

4. 8. Measurement Process Control 75

4. 9. Measurement Assurance 76

4. 10. An Example 76

4. 10. 1. Introduction 76

4. 10. 2. Initial Determination of Process

Parameters 77

4. 10. 3. Maintenance of Process 82

4. 11„ References 84

APPENDIX Af MICROPHONE CALIBRATION METHOD 85

APPENDIX B. MEASUREMENT ASSURANCE PROGRAM ... 92

APPENDIX C. SOME ELECTRICAL CHARACTERISTICS

OF SOUND LEVEL METERS by W. B. Penzes

and E. B. Magrab 97

LIST OF FIGURES

Fig. 1. Change in sensitivity of "l-incri* 1 condenser microphone No. 1 as a function of frequency and temperature.

The change in relative humidity introduces an uncertainty about the data points of less than ± 0. 15 dB. . . 6

Fig. 2. Change in sensitivity of "1-inch" condenser microphone No. 1 as a function of temperature for several

frequencies 7

Fig. 3. Change in sensitivity of "1-inch" condenser microphone No. 2 as a function of frequency and temperature.

The change in relative humidity introduces and uncertainty about the data points of less than ± 0. 15 dB. . . 8

Fig. 4. Change in sensitivity of "1-inch" condenser microphone No. 2 as a function of temperature for several

frequencies 9

IV
Page

Fig. 5a. Change in sensitivity of "1/2 -inch" electret

microphone No. 1 as a function of frequency and

temperature. The vertical bars indicate the

range of the data as a function of humidity 10

Fig. 5b. Change in sensitivity of "1/2-inch" electret

microphone No. 1 as a function of frequency and

temperature. The vertical bars indicate the

range of the data as a function of humidity 11

Fig. 6a. Change in sensitivity of "1/2-inch" electret

microphone No. 2 as a function of frequency and

temperature. The vertical bars indicate the

range of the data as a function of humidity . 12

Fig. 6b. Change in sensitivity of "1/2-inch" electret

microphone No. 2 as a function of frequency and

temperature. The vertical bars indicate the

range of the data as a function of humidity 13

Fig. 7a. Change in sensitivity of "1/2 -inch" ceramic

microphone No. 1 as a function of frequency and

temperature. The vertical bars indicate the

range of the aiata as a function of humidity 14

Fig. 7b. Change in sensitivity of "1/2-inch" ceramic

microphone No. 1 as a function of frequency and

temperature. The vertical bars indicate the

range of the data as a function of humidity 15

Fig. 7c. Change in sensitivity of "1/2-inch" ceramic

microphone No. 2 as a function of frequency and

temperature. The vertical bars indicate the

range of the data as a function of humidity 16

Fig. 8a. Change in sensitivity of "1/2-inch" ceramic

microphone No. 2 as a function of frequency and

temperature. The vertical bars indicate the

range of the data as a function of humidity 17

Fig. 8a. Change in sensitivity of "1/2-inch" ceramic

microphone No. 2 as a function of frequency and

temperature. The vertical bars indicate the

range of the data as a function of humidity 18
Page

Fig. 9. Experimental setup to determine the change in

calibrator level as a function of static pressure . . 25

Fig. 10. Change in the sound pressure level of calibrator A

as a function of static pressure ................. 26

Fig. 11. Change in the sound pressure level of calibrator B

as a function of static pressure 27

Fig. 12. Change in the sound pressure level of calibrator C

as a function of static pressure . 28

Fig. 13. Change in the sound pressure level of calibrator D

as a function of static pressure ................. 29

Fig. 14. Change in the sound pressure level of calibrator E

as a function of static pressure 30

Fig. 15. Change in the sound pressure level of calibrator F

as a function of static pressure 31

Fig. 16. Change in the electrical sensitivity of four different sound level meters at 1000 Hz as a function of

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Fig. 17. 1/3-octave band pressure levels for windscreens

of various diameters having a nominal linear

pore density of 800 pores /m and subjected to a wind speed of 40 km/hr blowing across the microphone grid at grazing incidence 35

Fig. 18. A-weighted sound levels as a function of windscreen diameter when windscreen has a 40 km/hr

wind blowing across the microphone grid at grazing incidence 36

Fig. 19. Random incidence insertion loss as a function of

frequency for windscreens of various diameters

and linear pore density 37

Fig. 20. Schematic of the instrumentation used to determine

the free-field response of sound level meters .... 39

Fig. 21. Free- field A-weighted response of SLM-Uas a function of several angles of incidence 40

Fig. 22. Free-field A-weighted response of SLM-V as a

function of several angles of incidence 41

vi
Page

Fig. 23. Free-field A-weighted response of SLM-W as a function of several angles of incidence .......... 42

Fig. 24. Free-filed A-weighted response of SLM-Y as a

function of several angles of incidence .......... 43

Fig. 25. Deviation of SLM-U from the ideal random

incidence A-weighting . 45

Fig. 26. Deviation of SLM-V from the ideal random

incidence A-weighting 46

Fig. 27. Deviation of SLM-W from the ideal random

incidence A-weighting ......................... 47

Fig. 28. Deviation of SLM-Y from the ideal random

incidence A-weighting 48

Fig. 2 9. Schematic of instrumentation used to measure

sound propagation over reflecting surfaces ...... 50

Fig. 30. Directivity patterns at several frequencies of

loudspeaker used in propagation studies . 51

Fig. 31. Difference between A-weighted levels of sound

propagating over grass and those over asphalt

as a function of sound level meter orientation

and its distance from the loudspeaker 52

Fig. 32. Difference between A-weighted levels of sound

propagating over grass and those over asphalt

as a function of distance of the sound level meter

from the loudspeaker 53

Fig. 33. Band pressure level of a 250-Hz 1/3-octave band

of noise propagating over grass and asphalt as a function of the distance between the sound level

meter and loudspeaker for the configuration shown

in the bottom of Fig. 31. Point source frequency is

250 Hz . 55

Fig. 34* Band pressure level of a 500-Hz 1/3-octave band

of noise propagating over grass and asphalt as a function of the distance between the sound level

meter and loudspeaker for the configuration shown

in the bottom of Fig. 31. Point source frequency

is 500 Hz 56

VII
Page

Fig. 35. Band pressure level of 1000-Hz 1/3-octave band

of noise propagating over grass and asphalt as a function of the distance between the sound level

meter and loudspeaker for the configuration shown

in the bottom of Fig. 31. Point source frequency

is 1000 Hz ............................. o . o ... . 57

Fig. 36. Band pressure level of a 2000-Hz 1/3-octave band

of noise propagating over grass and asphalt as a function of the distance between the sound level

meter and loudspeaker for the configuration shown

in the bottom of Fig. 31 ....................... 58

Fig. 37. 1/3-octave band analysis of the effects of people

and tripods on sound level meter measurements

of broadband noises. See text for description of

the cases A through D . . ............ ........... 59

Fig. 38. Experimental configuration used to determine the

effects of mutually perpendicular and adjacent

reflecting surfaces on sound level meter measurements ....................................... 61

Fig. 3 9. A-weighted sound levels as a function of the

distance of both the loudspeaker and sound level

meter from a vertical surface for the configuration shown in Fig. 38 ... 62

Fig. 40. Day-to-day variation in meter readings .......... 67

Fig. 41. Day-to-day variation in meter readings with

multiple values per day. (Coincident points indicated by numbers) ............................ 68

Fig. 42. Difference between readings by meters A and B

under a variety of conditions 69

Fig. 43. Difference between meter value with change in

Fig. 44. Difference between meter values with change in

orientation 74

vm
Page

Fig. A-l. Schematic of equipment required for the

voltage ratio measurements . 86

Fig. A-2. Schematic of equipment required for the

measurement of the capacitance of the source

microphone 87

Fig. C-l. Linearity of the meter scale of four different

sound level meters „ 103

Fig. C-2. Linearity of the range potentiometer or meter

scale of four different sound level meters 104

LIST OF TABLES

TABLE 1. Long-Term Stability of "1-inch" Condenser

Microphones at 20 6C and 44% RH 19

TABLE 2. Long-Term Stability of "1/2-inch" Electret

Microphones at 20 C and 44% RH 20

TABLE 3. Long-Term Stability of "1-inch" Ceramic

Microphones at 20 C and 44% RH 21

TABLE 4. Determination of Sound Level Meter x

Calibration Errors 77

TABLE 5. Determination of Sound Level Meter z Calibration Errors 78

TABLE 6. Determination of the Random Error of Two

Sound Level Meters 79

TABLE 7. Determination of the Random Error of a Sound Level Meter 81

TABLE 8. Determination of the Revised Process Parameters

for Sound Level Meters x and y 83

IX
Page

TABLE A-l. Estimated Magnitudes and Sources of

Errors in the Microphone Calibration

Data 91

TABLE B-l. Determination of Sound Level Meter

Calibration Errors 92

TABLE B-2. Determination of Sound Level Meter

Random Errors 93

TABLE B-3. Determination of Sound Level Meter

Systematic Errors 94

TABLE B-4. Determination of Process Control

Parameters 95

TABLE C-l. Difference between A t-Am for SLM-U as a

Function of Frequency and Crest Factor 98

TABLE C-2. Difference Between A t-Am for SLM-V as a Function of Frequency and Crest Factor 99

TABLE C-3. Difference Between A t-Am for SLM-W as a

Function of Frequency and Crest Factor 100

TABLE C-4. Difference Between A t-Am for SLM-Y as a

Function of Frequency and Crest Factor 101

TABLE C-5. Theoretical Crest Factor for a Tone Burst of

Various Frequencies when Passed through an

Ideal A-Weighting Network 106

x
ENVIRONMENTAL EFFECTS ON

MICROPHONES AND TYPE II SOUND LEVEL METERS

Edited by

Edward B. Magrab

For four different manufacturer's Type II sound level meters

numerous experimentally-determined data concerning the effects of frequency, temperature, angle of incidence of the sound, and types of

ground cover and reflecting surfaces on sound level meter readings are presented. Data are also given for the effects of ambient barometric

pressure on several manufacturers' acoustic calibrators, the effect of

frequency and crest factor on the sound level meters' detector circuit,

the linearity of the sound level meters' range potentiometer and meter

scale, and the precision of the A-weighted response in a randomly incident (diffuse) sound field. Additional data are given concerning the

effects of temperature and humidity on the sensitivity of electret,

condenser, and ceramic microphones. Finally, important statistical

concepts and recommended data-monitoring procedures are presented to

insure that the precision of repeated sound level measurements is known.

Key words: Acoustic calibrators; A-weighting; barometric pressure;

crest factor; ground cover; humidity; instrumentation; microphones;

sound level meters; statistical control processes; temperature;

windscreens.
INTRODUCTION

The objective of the results presented herein is to provide the reader

with a unified presentation from which an estimate of the magnitude of

the variations in Type II sound level meter readings as a function of numerous environmental conditions can be obtained. Much of the data were

obtained during the course of developing test methods at NBS for the evaluation of sound level meters. These data were also presented in a NBSspcrsored course entitled "Workshop on Sound Level Meters," which was held at NBS on November 20 and 21, 1975.

The information is presented in the following three chapters, with supplemental information appearing in the appendices. Each section or chapter

describing a particular environmental effect consists of a brief discussion

of the experimental technique used to obtain the data and a discussion of

the results. Appendices A and B relate to Section 2.1 and Chapter 4, re- spectively, whereas Appendix C presents additional information that is not

directly related to the theme of the report, but is included because it

provides information regarding the magnitudes of electrical errors that are

of considerable importance in certain applications.

Chapter 2 presents results illustrating the effects of temperature, wind,

humidity, and static (barometric) pressure on the various components of a sound level meter. Chapter 3 presents typical variations in the meter

readings as a function of the physical environment; namely, the presence

or absence of reflecting surfaces. The last chapter presents a detailed

outline of a method whereby one can determine both an estimate of the precision of the sound level meter readings and whether or not this precision

is, at all times, within acceptable limits; that is, whether or not the

measurement process is in control. It is felt that the material in this

chapter will be of great importance to those enforcing noise regulations.

Finally, Appendix C presents some additional data concerning certain electrical properties of sound level meters: meter scale linearity and the

crest factor capability of the detector circuits.
2. ATMOSPHERIC EFFECTS

2.1. Temperature and Humidity Effects on Microphone Sensitivity*

2.1.1. Introduction

The introduction of federal regulations stipulating the permissible noise

levels in the environment has made it necessary for many acoustic measurements to be performed over extended periods of time during which the temperature and humidity vary markedly. These changes in the environmental

conditions could affect the sensitivity of the microphones. There exist

some published data 1-5 concerning the effects of environmental conditions

on microphones of various construction. However these data appear in abbreviated form, usually in terms of frequency-independent temperature co- efficients. Furthermore the experimental techniques employed to obtain

this information are rarely stated. It was felt therefore that a reasonably thorough investigation, which determined the changes in the pressure

sensitivity of those commercially available microphone constructions most

frequently found in noise-measuring and noise-monitoring systems and

which used a consistent and standardized measurement procedure, would provide useful and meaningfully-comparable data.

Six commercially-available microphones were measured: two "1/2-inch"

electret, two "1-inch" ceramic, and two "1-inch" condenser microphones.

The condenser microphones had their pressure equalization port back-vented

through a dehumidifier containing silica gel.** The sensitivity was measured (where physically possible) at the following combinations of frequency,

temperature, and relative humidity: frequency: 0.1, 0.2, 0.5, 1, 2, 3, 4,

and 5 kHz; temperature: every 10 °C from -20 to +50 °C; and (nominal) relative humidity: every 10% RH from 25 to 95% RH.

2.1.2. Test Method and Procedure

The sensitivities of the microphones were measured using the procedures

specified in the ANSI Standard. 6 The NBS facility used to calibrate microphones was essentially duplicated, except that the 3-cm 3 coupler, the

microphones and the microphone preamplifiers were placed in an environmental chamber having wet and dry bulb temperature control and spatial uniformity to within ± 0.2 °C. So that the microphone could be inserted into

the coupler, several different size adapter rings, which are used to electrically isolate one of the microphones in the coupler, were required to

*This section is identical to "Environmental Effects on Microphones of

Various Constructions" by G. R. Hruska, E. B. Magrab , and W. B. Penzes

,

NBSIR 76-1090 (July 1976).

**By their very nature the small enclosed volumes in the electret and

ceramic microphone cartridges are unaffected by humidity in the same way

that condenser microphones are and therefore do not require a desiccant.

However, certain electret or ceramic configurations protect their electronics from the effects of humidity with a desiccant.
compensate for thermal expansion and contraction over the temperature

range. The microphone preamplifiers, having insert voltage capabilities,

provided a means whereby the effects of the environmental conditions on

the preamplifiers were eliminated.

The coupler, the preamplifiers and the six microphones (plus an additional

"1-inch" condenser microphone required for the reciprocity calibration)

were placed in the environmental chamber. The desired temperature and

relative humidity were set and then two hours were allowed for the chamber

to reach equilibrium. Then the "source" microphone was placed in the

coupler and the "receiver" microphone connected to the preamplifier but

not placed in the top of the coupler. An additional fifteen minutes were

allowed for the chamber to return to equilibrium at which time the receiver

microphone was rapidly placed into the coupler. After equilibrium had

again been established, the measurements were started by first determining

the resonance frequency of the lowest longitudinal mode of the coupler

volume. Then the voltage ratio measurements were made in the following

order: 5, 0.1, 0.2, ...4, and 5 kHz. Then the resonance frequency measurement was repeated. By examining the first and final measurements at

5 kHz and the two resonance frequencies, it was possible to check that

equilibrium conditions had existed during the course of the measurements.

The sequence of measurements was as follows: For a given temperature and

humidity the three condenser microphones, labeled A, B, and C, were interchanged after each frequency run, as shown in the table below:

Frequency Run

1

23

Runs 1 and 2 gave the ratio of the responses of the microphones B and C. Using the results of Run 3 plus the measurement of the capacitance of

microphone B, the absolute pressure response levels of microphones A, B,

and C were calculated. The pressure response of the remaining four microphones was determined using microphone B as the source, with the measurements on the electret microphones preceding those on the ceramic microphones. More specific details of t,he procedure are given in Appendix A

along with a discussion of the uncertainties in the measurement. The

total time, after warm-up, to perform the reciprocity and comparison

measurements on all six microphones at a given temperature and humidity

was approximately 6 hours. The temperatures were changed in the following

order: 20, 30, 40, 10, 0, -10, -20, 50, and 20 °C. At each temperature

the humidity was incrementally increased from the lowest to the highest

obtainable humidity. The lowest humidity depended on the temperature,

with this minimum value increasing with decreasing temperature. Below

°C the relative humidity could not be determined with good precision

and only one set of microphone calibrations was made at these temperatures.

The repeated calibration at 20 °C was only performed at 44% RH.

Source Receiver

A B

A C

B C
.

2.1.3. Discussion of Results

he changes in sensitivity of the six microphones normalized to their

respective pressure sensitivities at 1 kHz and 20 °C are shown in Figs. 1

through 8. Figures 1 and 3 show the change in sensitivity of the "1-inch"

condenser microphones as a function of frequency for the various temperatures. These figures are replotted in Figs. 2 and 4, respectively, as a function of temperature for selected frequencies. The data points shown

in these four figures are the mean values of the sensitivity changes for

the range of humidities tested. The spread of the data at virtually every

one of the points is less than ± 0.15 dB. These figures show that the two

"1-inch" condenser microphones exhibited small temperature coefficients

(change in microphone sensitivity per change in temperature) of approximately -0.003 and +0.005 dB/°C, respectively, from -20 tc 50 °C and for

frequencies below 1000 Hz. At frequencies above 1000 Hz the temperature

coefficient increased, such that at 5000 Hz they become approximately

-0.02 and -0.03 dB/°C, respectively. This variation in the temperature

coefficient as a function of frequency is due to the relatively large

amount of viscous damping introduced by the particular backplate design

of these microphones, that is, by the distance between the diaphragm and

the backplate and the location, number, and size of the holes in the backplate. Since the viscous losses greatly affect the sensitivity near resonance, smaller microphones could be expected to show less sensitivity

change at high frequencies.

The changes in sensitivity for the electret microphones are shown in Figs.

5 and 6 and for the ceramic microphones in Figs. 7 and 8. In these figures the vertical bars indicate the range of the data as a function of

humidity. The absence of those vertical bars indicates that those data

were only taken at a single relative humidity. The data are presented

in this form because no meaningful relation can be established for the

change in sensitivity of these microphones as a function of either frequency, temperature or humidity. This type of behavior can be explained

if the systematic changes due to temperature and humidity are much smaller

than the inherent instability of the microphone itself. Consequently, it

is not possible to obtain from these measurements the temperature coefficients of the electret and ceramic microphones.

If the electret and ceramic microphones are subject to these instabilities

they will exhibit similar behavior at standard conditions, 20 °C and 44%

RH. As can be seen from Tables 1-3 the condenser microphones are within

± 0.2 dB of their original sensitivities whereas the electret and ceramic

microphones show relatively large variations. These tables give an indication of the moderately long-term stability of these types of microphone

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TABLE 1

Long-Term Stability of "1-inch" Condenser Microphones

at 20 °C and 44% RH

Change in Sensitivity

(dB re value on May 21, 1975)

Frequency (Hz) June 17

,

1975 July 22, 1975 September 9, 1975

Cartridge #1

100 0.17 -0.11 -0.04

200 0.07 -0.12 -0.09

500 0.04 -0.15 -0.09

1000 0.06 -0.12 -0.05

2000 0.07 -0.03 +0.01

3000 0.08 +0.11 +0.11

4000 0.08 +0.17 +0.19

5000 0.07 +0.21 +0.22

Cartridge //2 100 +0.18 +0.18 -0.11

200 +0.17 +0.12 -0.16

500 +0.18 +0.06 -0.15

1000 +0.12 +0.06 -0.12

2000 +0.01 +0.03 +0.01

3000 -0.09 +0.05 +0.13

4000 -0.15 +0.02 +0.18

5000 -0.17 +0.03 +0.26

19
TABLE 2

Long-term Stability of "1/2-inch" Electret Microphones

at 20 °C and 44% RH

Change in Sensitivity

(dB re value on May 21, 1975)

Frequency (Hz) July 23, 1975 September 9, 1975

Cartridge #1

100 -1.22 +1.53

200 -0.51 +1.33

500 -0.30 +1.25

1000 -0.34 +1.24

2000 -0.34 +1.17

3000 -0.38 +1.05

4000 -0.40 +0.97

5000 -0.32 +0.93

Cartridge #2

100 +0.26 +2.47

200 -0.02 +1.26

500 -0.11 +0.88

1000 -0.12 +0.88

2000 -0.12 +0.88

3000 -0.14 +0.84

4000 -0.16 +0.70

5000 -0.17 +0.59

20
TABLE 3

Long-Term Stability of "1-inch" Ceramic Microphones

at 20 °C and 44% RH

Change in Sensitivity

(dB re value on May 21, 1975)

Frequency (Hz) July 23, 1975 September 9, 1975

Cartridge #1

100 -1.51 0.19

200 -1.47 0.04

500 -1.44 0.04

1000 -1.45 0.04

2000 -1.40 0.31

3000 -1.40 0.81

4000 -1.56 1.16

5000 -3.90 0.70

Cartridge #2

100 0.23 0.73

200 0.24 0.12

500 0.26 0.00

1000 0.30 0.05

2000 0.49 0.57

3000 0.78 1.08

4000 0.52 1.25

5000 0.07 0.36

21
2.1.4. Conclusions

From the data presented the following conclusions are reached:

1. The back-vented condenser microphones with a dehumidifier were

largely insensitive to relative humidity.

2. At frequencies far below the condenser microphone's resonance frequency the temperature coefficient was extremely small (^ ± 0.005

dB/°C).

3. Condenser microphones having a large amount of viscous damping

could have a greatly increased (by a factor of 4) temperature coefficient

in the vicinity of the microphone's resonance frequency.

4. The electret microphones which were tested exhibited short-term

sensitivity instabilities of the order of ± 0.5 dB. The ceramic microphones examined showed short-term instabilities of the order of ± 1 dB or larger, at some frequencies. The magnitudes of these instabilities made

it impossible to determine the changes in sensitivity as functions of temperature or relative humidity.

5. The condenser microphones exhibited long-term instabilities (i.e.. over a period of about sixteen weeks) of the order of ± 0.2 dB. The electret and ceramic microphones showed long-term instabilities of up to ± 1.5

dB , with larger values at a few frequencies.

From the data which were taken, it is not possible to predict with assurance what uncertainties would occur if the ceramic and electret microphones

were used for outdoor noise measurements. It seems reasonable, however, to assume that if significant changes in temperature and relative humidity

occur between system calibrations, then the uncertainties in the measured

sound levels could be at least of the magnitude of the short-term instabilities already mentioned. Furthermore, in actual sound measuring systems,

changes in temperature and relative humidity could affect the electronics

thus introducing additional changes in overall system sensitivity.

2.1.5. References

1. G. M. Sessler and J. E. West, "Electret Transducers: A Review," J. Acoust. Soc. Amer. 5_3, 1589-1600 (1973).

2. L. L. Beranek, Ed., Noise and Vibration Control (McGraw-Hill Book Co.,

New York, 1971), pp. 48-49.

3. G. Rassmussen, "Reliability of Measurement Microphones Under Outdoor

Conditions," Seventh International Congress oh Acoustics, Budapest,

1971, pp. 289-292.

22
4. G. Rassmussen, "Measurement Microphones," Inter-Noise 74 Proceedings,

International Conference on Noise Control Engineering, Washington,

D.C. (September 1974), pp. 55-60.

5. A.P.G. Peterson and E. E. Gross, Jr., Handbook of Noise Measurement , 7th Edition (General Radio Co., Concord, Mass., 1972), pp. 172-173.

6. "Method for the Calibration of Microphones," SI. 10-1966, American

National Standards Institute, New York, N. Y.

7. R. K. Cook, "Measurement of Electromotive Force of a Microphone," J.

Acoust. Soc. Amer. 19, 503 (1947).

2.2. Static Pressure Effects on the Output Sound Level of Microphone

Calibrators

A microphone calibrator consists of a transducer that drives a piston or

a diaphragm inside a small cavity to generate a known sound pressure

level at a fixed frequency. The microphone is inserted into this cavity.

The calibrator's transducer may be electrodynamic , mechanical, piezoelectric, magnetostrictive , or some other type. From the known pressure

generated by the calibrator and the measured output voltage of the microphone, the microphone sensitivity, defined as the ratio of the microphone

output voltage to the input sound pressure, is determined.

The output sound pressure level of the calibrators changes with changes

in the static (barometric) pressure. This effect on the sound pressure

level output of a calibrator as a function of static pressure is most

easily demonstrated if one considers a constant (volume) displacement of a piston in a cavity. For an ideal gas under adiabatic conditions it can

be shown that

p

AP

Y

AV m

v" (1)

o o

where P is the static pressure, V is the undisturbed volume, AP is the

o o acoustic pressure resulting, in this instance, from the change in volume

AV, the volume displacement of the piston. The quantity y is the ratio

of specific heats of air at constant pressure and constant volume. The

acoustic pressure is, therefore

AP = P = - Y P

^

(2) acoustic o V

o

It is apparent that a calibrator with a constant displacement transducer

generates an acoustic pressure proportional to the static pressure of the

environment

23
Microphone calibrators that do not use transducers of the constant displacement type are not easily described analytically and their output

sound pressure level versus static pressure must be determined experimentally. (Each manufacturer of microphone calibrators provides a calibration graph of the calibrator's sound pressure level versus static

pressure.

)

Calibrators from several manufacturers were checked for their sound pressure level output as a function of static pressure. The experimental

setup for measuring the effect of static pressure on the sound pressure

level of the calibrator and on the microphone is shown in Fig. 9. First,

the change in the (condenser) microphone sensitivity as a function of

static pressure is measured with an electrostatic actuator by placing the

microphone and the calibrator inside a bell jar. The microphone output

voltage is then recorded as a function of the static pressure. The

change in the calibrator's sound pressure level, A

p

, is determined from

A SpL

= 20 log 10 [(R/Ro)/(S/So )J dB (3)

where R/RQ and S/S are the ratios of the microphone output voltages and

sensitivities, respectively, at any given static pressure to the output

voltage and sensitivity at a reference static pressure.

Figure 10-14 show both the measured AgPL and the Agp^ specified by the

manufacturer as a function of pressure. Figure 15 compares the measured

AgpL to that predicted by Eq. (1), since this particular calibrator uses

a constant displacement transducer. The vertical bars on the experimentally determined curve shows the spread in the measurement when repeated

several times.

It is apparent from these results that certain calibrators deviated con- siderably from the manufacturer's specification, whereas others followed

the predictions or specifications very closely.

2.3. Temperature Effects on the Electrical Sensitivity of Type II SoUnd

Level Meters

Tests were conducted on several sound level meters in an environmental

chamber to determine the change in the electrical sensitivity of the

sound level meters as a function of temperature. The sound level meter

was placed in an environmental chamber wherein a constant relative humidity

of 70% was maintained. The sound level meter's microphone was removed and

an electrical signal at 1000 Hz was inserted at the same location that the

microphone's output voltage normally would be found. The sound level meter

was left at the desired temperature for one hour, during which time thermal

equilibrium was reached. The amplitude of the input signal was kept con- stant for each temperature considered. The output voltage of the sound

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level meter at each temperature was compared to the sound level meter's

output voltage at 20 °C. The results* are shown in Fig. 16. In addition,

the entire A-weighting curve was checked from 100 to 10 '000 Hz at each

temperature. However, since the shape of this curve remained virtually

constant over the range of temperatures considered only the change in

level at 1000 Hz is shown.

It is seen that when the sound level meter is used in a changing temperature environment one can often expect relatively rapid changes in the

sound level meter's sensitivity. However, when the sound level meter is

used in a uniform temperature environment these electrical sensitivity

changes due to temperature can be accounted for with the use of a sound

level calibrator just before a measurement.

2.4. Attenuation of Aerodynamically Generat-ed Noise by Foam Windscreens**

Various configurations of microphone windscreens are used to reduce windgenerated noise, which allow the acoustic signal to be measured without

excessive attenuation while keeping the turbulent eddies away from the

microphone sensing element. Since the direction of the wind usually is not

known a priori and it is often desired that the directional characteristics of the microphone not be changed, a spherical-shaped windscreen is

most commonly used. Previous investigators 1-3 frequently have used a light wire framework covered with cloth. A reduction of wind-generated

noise by 20 dB has been reported using a cloth screen 12 cm in diameter.

Recently spheres of open-cell polyurethane foam have been used as windscreens. The spheres are solid except for a cylindrical hole in which

the microphone is placed. These windscreens have the advantage of not

degrading the directional characteristics of the microphone over most of

the frequency range and are inexpensive compared to cloth windscreens.

However, no specific information regarding the effects of sphere size and

pore size of these open-celled materials appears to be available in the

literature. Consequently, an investigation was conducted to determine,

as a function of frequency for four different pore sizes and various diameters of spheres, the amount of reduction in wind-generated noise and the

amount of acoustic attenuation of the signal.

Since available wind tunnels are too noisy for windscreen testing, the

measurements of wind-generated noise were made by mounting the microphone

and windscreen combination at the end of a rotating arm in a large (452

m

3

) anechoic room. An aerodynamically-smooth radial arm of 1.57 m radius was mounted on a variable-speed turntable. The table had slip rings to

*The four different manufacturers' sound level meters are denoted SLM-U,

SLM-V, SLM-W, and SLM-Y . This denotation, where appropriate, is employed

throughout the report.

**Based on material previously reported in a paper entitled "An Experimental Investigation of Foam Windscreens" presented at INTER-NOISE 73,

Copenhagen, Denmark (August, 1973).

32
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bring the microphone signal out to the measuring instrumentation. The

microphone was mounted at the top of a 0.75 m vertical support (also aero dynamic ally smooth) at the end of the rotating arm so that the air

flow passed across the microphone diaphragm at grazing incidence. The

turntable was rotated at angular speeds corresponding to microphone speeds

of 24, 32, and 40 km/hr. For the measurements reported here a "1-inch"

condenser microphone was used. The output of the microphone was analyzed

in 1/3-octave bands.

The results of the measurements of wind-generated noise are shown in Figs.

17 and 18. Figure 17 shows the 1/3-octave band sound pressure levels for

10-cm, 17.8-cm, and 25.4-cm diameter windscreens, fabricated from foam

having a nominal linear pore density of 800 pores/m, subjected to a wind

speed of 40 km/hr. A-weighted sound pressure levels are shown in Fig. 18

where these levels, corresponding to a speed of 40 km/hr, are plotted as

a function of windscreen diameter for four different linear pore densities.

In order to measure the sound attenuation due to the windscreens, the insertion losses under random incidence conditions were measured in a large

(425 m

3

) reverberation room. With the room excited with broad-band pink

noise, the signal from the condenser microphone was measured in 1/3-octave

bands with and without the various windscreens in place. Figure 19 shows

the attenuation (insertion losses) as a function of frequency for the different linear densities and sphere diameters tested.

As a result of this investigation it is recommended that (1) for maximum

reduction of wind noise, where the main frequency of interest is less than

1 kHz, an 18-cm diameter windscreen with 1600 pores/m should be used, and

(2) for other uses an 18-cm diameter windscreen with 800 pores/m should be

used.

References J

1. Per V. Briiel, "Aerodynamically Induced Noise of Microphones and Windscreens," Briiel & Kjaer Technical Review No. 2, 1960, pp. 3-27.

2. J. C. Bleazey, "Experimental Determination of the Effectiveness of

Microphone Wind Screens," J. of the Audio Eng. Soc. _9, No. 1, 48-54

(1961).

3. F. Sk^de, "Windscreening of Outdoor Microphones," Briiel & Kjaer

Technical Review No. 1, 1966, pp. 3-9.

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37
3. EFFECTS OF THE PHYSICAL ENVIRONMENT

3.1. Free-Field Response of Type II Sound Level Meters

Sound level meters are often used in nonreverberant environments wherein

their A-weighted frequency response as a function of the angle of incidence of sound can deviate markedly from the ideal response. The amount

of deviation permitted is stipulated in the appropriate standards document.* To obtain an estimate of the actual deviation from the ideal Aweighted frequency response that one could encounter, the free-field frequency response for five angles of incidence of sound was measured on one Type II sound level meter from each of four manufacturers from 400 to

10 000 Hz in a large (452 m^) anechoic room.

The deviations from the ideal A-weighted response were obtained in the

following manner. A "1/2-inch" condenser microphone, which had a uniform

frequency response at normal sound incidence over the frequency range of

interest, was placed 68 cm from the loudspeaker while the second sound

level meter was placed 233 cm away. Both the microphone and the sound

level meter were oriented, with respect to each other, such that the axes perpendicular to the center of each microphone diaphragm were coincident.

The sound level meter was suspended from the ceiling of the room by thin

wires. The "1/2-inch" microphone was used in a feedback loop so that the

output sound level of the loudspeaker was uniform within ± 1 dB over the

frequency range. The interconnection of the instrumentation used to perfrom the experiment is shown in Fig. 20.

The results, retraced and slightly smoothed, are shown in Figs. 21-24.

From these figures it is seen that the deviation from the ideal A-weighted

response at frequencies below 1000 Hz is relatively small for most of the

meters compared to the deviation above 1000 Hz where the diffraction of

sound by the microphone and the sound level meter cause the deviations to

be larger and, except for SLM-Y , to vary irregularly as a function of both

angle of incidence and frequency.

3.2. Random Incidence Response of Type II Sound Level Meters

The A-weighted frequency response of sound level meters is specified only

for a very specific acoustic environment; namely, a spatially homogeneous

sound field.** This environment is very closely approximated in properly

configured reverberations rooms, provided that sufficient spatial and temporal sampling is employed. All other specified acoustic and electrical

characteristics of sound level meters are referred to the A-weighted re- sponse. Consequently, the actual deviation of the A-weighted response

from its idealized response is an important indicator of a sound level

meter's precision. Therefore, the actual deviations from the ideal

*See, for example, American National Standard SI. 4-1971, "Specification

for Sound Level Meters," American National Standards Institute, New York.

**More commonly referred to as a diffuse or random incidence sound field.

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A-weighting, as specified in the American National Standard SI. 4-1971,*

of three Type II sound level meters from each of four manufacturers was

determined in a 425-m3 reverberation room. : ; .

A close approximation to the random incidence A-weighted sound pressure

level existing in the room was obtained by measuring the space-time averaged

sound level in each 1/3-octave band with a "1/2-inch" condenser microphone

having a uniform random incidence frequency response from 100-10 000 Hz

and adding to its electrical output the appropriate A-weighting as defined

in the standard. The sound field in the reverberation room was generated

by a loudspeaker excited by broadband white noise at a constant rms voltage. The "1/2-inch" microphone was placed on a cart at a height of 2.06 m

from the floor of the room and pulled across the room a distance of 6.4m

along a line connecting two diagonally opposed trihedral corners. The microphone was never closer than 1 m to any room surface during this traverse. The time to traverse this distance was 1920 s (32 min) . During

this traverse the microphone's electrical signal was analyzed in 1/3-

octave bands from 100-10 000 Hz using 1920 s of rms averaging in each of

the 21 bands.

The cart was returned to its original position and the microphone was re- placed by one of the sound level meters. The A-weighted electrical output of the sound level meter was analyzed in the same manner as the output

of the "1/2-inch" microphone, except that no conversion to A-weighting was

required. The resulting 1/3-octave levels from the two traverses were subtracted from each other and normalized (referenced) to 1000 Hz. The re- sults are shown in Figs. 25-28.

Examination of these figures indicates that each set of three sound level

meters yields fairly consistent deviations of their A-weighted response as

a function of frequency. However, the actual magnitudes of the deviations

from manufacturer to manufacturer vary widely depending on the frequency.

It should be noted that units designated SLM-U have a deviation that is

within ± 1 dB over almost the entire frequency range whereas units designated SLM-V have deviations that vary widely as a function of frequency.

However all units tested meet the SI. 4-1971 specification for Type II

sound level meters.

3.3. Effects of Ground Reflections on Sound Level Meter Measurements

Measurements made with sound level meters are usually performed in the

presence of a large (nominally) flat reflecting surface, namely the ground.

The acoustical reflecting properties of such a surface can alter the sound

pressure level recorded by the sound level meter. The degree to which

such a surface affects the measurement depends on the reflection coefficient of the ground cover as a function of frequency, the location of the

sound source relative to the ground, the frequency spectrum of the sound

source and its directivity, the location of the sound level meter relative

*Loc. cit.

44
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Figure 25, Deviation of SLM-U from the ideal random incidence

A-WEIGHTING,

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46
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A-WEIGHTING.

48
to both the surface and the source, and the directional characteristics

of the sound level meter. To obtain some idea of the .possible variations

one can expect from the numerous combinations of the above-mentioned

variables the following parametric tests were conducted at NBS. A loudspeaker was excited by broadband noise. A sound level meter was placed

a distance varying from 1 to 12 m from the loudspeaker. Both the loudspeaker and the sound level meter were held at various heights relative

to the ground and to each other. Each of these combinations was investigated over an asphalt surface and over a grass-on-earth surface.

The two sites chosen for these investigations were a flat asphalt parking

lot 33 m by 21 m and a large, fairly smooth grass area. The nearest

vertical obstruction from the measurement area was more than 20 m away.

The subsoil of the grass was hard-packed clay. The grass height varied

during the tests from 6 cm (freshly cut) to approximately 10 cm. The

background noise during the daytime was an A-weighted level of 55 dB re- quiring certain runs to be made in the late evening/early morning hours.

No measurements were made when the wind velocity exceeded 15 km/hr.

The instrumentation used in the experiment is shown in Fig. 29. The loudspeaker's directivity patterns were measured in a large (452 m

3

) anechoic

room and are shoWn in Fig. 30. The electrical broadband noise signal to

the loudspeaker was kept at a constant value throughout the experiment

and was monitored by an AC ammeter. Since the signal-to-noise ratio at

frequencies below 200 Hz was relatively poor, the output signal from the

sound level meter was analyzed in 1/3-octave bands from 80 to 10 000 Hz

for both the background noise and for the loudspeaker's output. The background noise levels were subtracted in the appropriate manner from those

levels obtained from the loudspeaker's output in each 1/3-octave band and

then recombined to obtain the A-weighted levels. The signal in each 1/3-

octave band was averaged over a period of 320 s (5-1/3 min) . This long

averaging time was sufficient to reduce the influence of the fluctuations

in the sound levels due to any transient acoustic disturbances.

To determine the effects of the ground on the sound level meter measurements, the difference between the A-weighted level measured over asphalt

and that over grass is presented in Figs. 31 and 32 for various combinations of orientations and distances of the sound level meter relative to

the loudspeaker and to the ground. From Fig. 31 it is seen that for the

particular sound level meter used (SLM-Y) the orientation of the meter

with respect to the source caused differences in the A-weighted readings

of more than 1 dB at separations from 4 to 9 m. If the response of the

sound level meter were truly omnidirectional these differences for the

two orientations would have had virtually the same values. This figure

clearly shows that for precision measurements in the presence of a re- flecting surface sound level meter orientation is important.

Figure 32 shows the effects that the ground reflections can cause for two

placements of the sound level meter and the loudspeaker relative to each

other and relative to the ground. At relatively large distances from the source for the case where the loudspeaker is placed on the ground, the

49
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differences in the A-weighted levels due to differences in ground reflection properties can be as large as 9.5 dB. For the loudspeaker off the

ground a distance of 1.3 m the differences do not exceed 4 dB. This figure indicates the complex nature by which the ground affects the sound

level meter readings. Also, it is seen that at microphone distances less

than 2 m these results are independent of the relative locations of the

sound level meter and the loudspeaker.

Figures 33 to 36 give the actual 1/3-octave band pressure levels, for

several selected bands, as a function of the type of ground cover and the

separation distance between the sound level meter and the loudspeaker when

they are both 1.3 m from the ground. In addition, Figs. 33 to 35 give the

results for a point source over a perfectly reflecting plane when the source is oscillating at the center frequency of the respective 1/3-octave

band. From Fig. 33 it is seen that the idealized model and the test re- sults agree fairly well for sound propagating over asphalt. This agreement

is, in part, due to the omnidirectional characteristics of the loudspeaker

at this particular frequency. Further comparisons with other theoretical

models are difficult because the source is not omnidirectional at the

higher frequencies and the impedances of the ground covers are not known.

These figures indicate that at distances large compared to the wavelength

of sound from the source the interference caused by reflections from the

surface can cause large variations in the band pressure levels, especially

for propagation over asphalt.

3.4. Effects of Walls, Persons, and Tripods on Sound Level Meter

Measurements

To obtain an estimate of the magnitude of the effects that certain frequently-encountered obstacles have on sound level meter measurements two

separate experiments were conducted. The first set of experiments were

conducted in an anechoic room. A "1-inch" microphone with a uniform

frequency response over the frequency range was placed in a metal stand

3 m from the source. The output of the "1-inch" microphone was analyzed

in 1/3-octave bands. The "1-inch" microphone was then replaced by a sound

level meter and its output analyzed in 1/3-octave bands for the following

four configurations:

Case A: The sound level meter is placed on a metal stand with the

microphone diaphragm facing the sound source.

Case B. Same as Case A except a person is standing 20 cm behind the

sound level meter. (The sound level meter is 1.49 m above

the wire grid.

)

Case C: Same as Case B except the sound level meter is resting

against the person and the metal stand has been removed.

Case D: Same as Case C except the sound level meter is 55 cm (arm s length) from the person.

These results are shown in Fig. 37.

54
a PROPAGATION OVER GRASS

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Figure 33, Band pressure level of a 250-Hz 1/3-octave band of

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Figure 34. Band pressure level of a 500-Hz 1/3-octave band of

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NOISE PROPAGATING OVER GRASS AND ASPHALT AS A FUNCTION OF THE DISTANCE BETWEEN THE SOUND LEVEL METER

AND LOUDSPEAKER FOR THE CONFIGURATION SHOWN IN THE

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As can be seen from Fig. 37 the differences in the 1/3-octave band levels

are usually within ± 2 dB except in two frequency regions, 315 to 500 Hz

and above 3150 Hz, where the deviations increase markedly. At 400 Hz it

appears that the presence of a person within 0.5 m of the sound level

meter greatly increases the sound pressure recorded by the meter. At

frequencies above 3150 Hz both the presence of a person and the metal

stand greatly affect the sound field.

The second set of experiments, using the previously described source, signal, and data reduction techniques, determined the effects of two adjacent

and perpendicular reflective surfaces on sound level meter measurements.

The experimental set-up is shown in Fig. 38. The differences between the

A-weighted levels as both a function of distance from the source, and the

distance of the source and sound level meter from the vertical wall, to

those levels obtained at 1 m are shown in Fig. 39. As seen from this figure, as the distance from the source increases the attenuation that would

normally be obtained from the spherical spreading of sound decreases, the

magnitude of the decrease being greater when the meter and source are closer to the vertical wall. For a simple broad-band source near the corner of the two surfaces, the increase in sound pressure level is expected

to be about 6 dB at locations near and along the corner. This 6-dB increase

is evident when the source and meter are 1.3 m from the wall.

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62
4. PROCEDURES FOR THE ASSURANCE OF THE ADEQUACY OF SOUND LEVEL

MEASUREMENTS

4.1. Introduction

There is an obvious need that measurements in the fields of health,

safety, environmental control, or governmental regulatory actions be adequate for their intended purpose - that their uncertainty be small enough

to only negligibly affect the decisions and performances of the processes

of which they are a part. But this is no less true for all other measurements in science and industry and even though legal action may not be

involved, the validity of scientific inference, the effectiveness of process

control, or the quality of production may depend on adequate measurements.

Attention must therefore be focussed on the question of what constitutes adequate measurement from the point of view of the intended use of

the measurement. For this reason, procedures will be needed by which one arrives at the uncertainty of an individual measurement and maintains

assurance on a continuing basis that the quality of one's measurements

stays "in control." This emphasis on the uncertainty to be attached to

the measured value comes naturally in legal proceedings - the cross- examination seeks to develop the width of the shadow of doubt around the

value. The same type of scientific evaluation has to be carried out to

determine whether the uncertainty of one's measurement is less than some allowable amount. The error allowance is determined by program needs such

as, for example, the physiological tolerances on noise pollution, radioactivity dosage, and similar quantities in matters of health and safety.

In cases where the measurement relates to only a component of the

system, there may be an arbitrariness about what is "good enough," but in

any case the requirement on measurement will be in the form of a limit on

the allowable uncertainty.

This section gives procedures for describing the measurement process in

such a manner that valid statements about the uncertainty of individual

measurements can be made. To do this, the term "uncertainty" needs to be

given an operational meaning. One then can discuss method of monitoring

the measurement effort to assure that it remains in a state of statistical

control, so that the uncertainty statement can be applied to each measurement

4.2. The Cross-Examining of Measurement Data

One of the central problems of measurement is that of demonstrating

that the number one assigns to a phenomenon measures uniquely that phenomenon and does not depend on the instrument used, the environmental con- ditions, or the procedures involved. In a single isolated experiment one

is prepared to go to some lengths to develop the necessary evidence that one has, in fact, a valid measurement. The amount of work one does to

obtain the supporting evidence will depend on factors related to time, cost,

accuracy needs, etc.

63
It is instructive to consider this question in terms of the cross- examination of measurement data that might be expected in a scientific

review as part of a legal contest.

The question to be addressed is: What region of doubt would surround,

for example, a single value of noise level when used in a regulatory action?

For the regulatory agency, the objective is to be able to defend a single measurement. It must be able to withstand cross-examination. Particularly when repeated measurements of the same quantity disagree by an amount of practical significance, one needs some assurance that his measurements are correct enough for his purpose.

The key word in this discussion is "repetition." There are many

levels of repetition as illustrated by the following questions.

Within what limits would an additional measurement

by the same instrument agree when measuring some

stable quantity?

Would the agreement be poorer if the time interval

between repetitions were increased?

What if different instruments from the same manufacturer were used?

If two or more types (or manufacturers) were used,

how much disagreement would be expected?

To these can be added questions related to the conduct of the

measurement.

What effect does geometry (orientation, etc.) have

on the measurement?

What about environmental conditions - temperature,

moisture, etc.?

Is the result dependent on the procedure used?

Do different operators show persistent differences

in values?

Are there instrumental biases or differences due

to reference standards or calibrations?

It should be obvious that one needs additional evidence beyond that of

the measurement itself to demonstrate that one's measurements are "in

control." To do this one needs a perspective from which to view measurement

so that one can arrive at an uncertainty to be attached to a measurement - an uncertainty that will "stand up in court."

64
4.3. The Measurement Method

One begins with the objective of the measurement - for example, the

protection of the individual from noise pollution. One of the important

components of this problem is sound level and one can use the accepted

physical theory and measurement methods to set regulatory limits and to

monitor various noise sources. In general, however, there are several

measurement approaches possible.

One thus begins with the specification of a measurement method - the

detailed description of apparatus, procedures and conditions by which one will measure some quantity.

The current understanding of this process or any other scientific or industrial process is embodied in a physical model which explains the interactions of various factors, corrections for environmental or other effects,

and the probability models necessary to account for the fact that repetitions

of the same event give rise to nonidentical answers. For example, in noise

level measurement one is involved with assumptions regarding frequency

response, weighting networks, influence of procedures and geometry, and an accepted theory for making corrections for temperature and other environmental factors.

In this conceptual framework one speaks of the "true value," t, of the

measurements x. x. . . . having "errors" of e, = x. - t, e~ = x - t, . . . , but one must keep in mind that t (and also the e

l s) are unknowable so that one must replace these theoretical constructs by operationally defined

quantities. (It will turn out that one need not refer to "true value" in

practice.) Once the apparatus is assembled and checked out, one has a measure- ment process whose output can be studied to see if it conforms to the requirement for which it was created.

4.4. Measurement as a Production Process

Measurement, like history, can be looked at from a number of perspectives. A number in isolation is like a single event in history - its meaning

depends on the context in which it occurred. To arrive at a meaningful

perspective, several properties of measurement can be noted: First, that

repeated measurements of the same quantity disagree but after sufficient

work to remove the larger sources of systematic error and correlation among

the measurements have the properties and predictability of random variables

from a probability distribution. Second, that the parameters of the distribution still depend on the apparatus, procedures, or environment and only by

careful experimentation can the effect of changes on the parameters of the

process be evaluated.

This idea of measurements as the output of a process, analogous to an industrial production process, is the unifying concept that enables one to

discuss the adequacy of measurement. The output of measurement processes are

the numerical values for industrial, medical, scientific or other use. These

values pass on to the user but the measurement process remains and one must

build in some redundancy in order to determine the properties of the process.

65
As an example, a sequence of measurements was made using two sound level

meters to measure a sound of nominally 90 dB re 20 uPa. The sound was generated by a loudspeaker fed broadband noise. On 16 different days measurements were made outdoors and over grass with the loudspeaker in the same orientation and location relative to a building 2 m behind the loudspeaker. The sound level meter was always the same distance (10 m) from

the loudspeaker and on a line perpendicular to the face of the loudspeaker.

Other than the grass, the person holding the sound level meter, and the

building to the rear of the loudspeaker, there were no other reflecting

surfaces or obstacles within 50 m. No measurements were made in the rain

or in winds exceeding a few km/hr. The results from these 16 repetitions

are shown in Fig. 40. Typically, had duplicate measurements been made on

the same day they would have given results as shown in Fig. 41.

One now faces the question of how to describe the variation that exists.

Obviously there will be a different level of agreement expected between

pairs on the same day, but this variation in no way predicts that encountered

from day-to-day. The issue is not so much the statistical procedures to be

used - these will follow after one defines the set of repetitions over which

his conclusions must apply. For measuring the short term change in noise

level, the difference between duplicates would apply; for any regulatory

action, the day-to-day variation would have to be considered.

The crucial step in assessing the effects of random error is that of

defining the set of repetitions over which the measurement is to apply. In

the context of legal proceedings, one arrives at the degree of credibility

of evidence by questions designed to find out how far the statement could be

in error. In measurement, the uncertainty is arrived at by determining the

amount of disagreement expected in the set of repetitions that would be

appropriate in the context of the intended use of the measurement.

4.5. The Concept of a "Repetition" of a Measurement

Every measurement has a set of conditions in which it is presumed

to be valid. At a very minimum, it is the set of repeated measurements with

the same instrument-operator procedure-configuration. (This is the type of

repetition one would envision in some process control operations.) If the

measurement is to be interchangeable with one made at another location, the

repetition would involve different instrument-operator-procedure-environment

configurations. (This type of repetition is involved in producing items to

satisfy a specification and of manufacturing generally.) When the measurement is to be used for conformance to a health, safety, or environmental

regulation even different methods may be involved in a "repetition."

In Fig. 40 the difference between meters is small relative

to the day-to-day variation. When the difference between the meters on the same condition on the same day is examined (see Fig. 42), one finds that

the variation is somewhat reduced. However, with differences one would

expect an increase in variation (by a factor of /2) leading one to suspect

that the signal was not constant. (This was confirmed by determinations with

a much more accurate meter, a condition not usually available in routine

~°surements .

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This example brings out two important points: First, that some redundancy must be introduced into the system to determine the process parameters;

and second, that the values used to evaluate or monitor the process should

be representative (or a sample in some sense) of the set of repetitions with

respect to which the uncertainty is to apply.

In NBS's measurements of mass, a check standard is measured in parallel with

the unknowns submitted for calibration. One thus generates a sequence of

measurements of the same object covering an extended time period. From these

results one can answer questions relating to the agreement expected in a recalibration and the operating characteristics of the measurement process.

In this simple case the check standard is treated exactly the same way as the unknowns so that the properties of the process related to it are transferable to the unknown.

The essential characteristic in establishing the validity of measurement

is predictability that the variability remains at the same level and that

the process has not drifted or shifted abruptly from its established values.

One must build in redundancy in the form of a control - the measurement of a reference quantity of known value - or by remeasuring some values by a reference method (or by an instrument with considerably smaller uncertainty).

In cases where the phenomenon can be repeated, one can learn about random

errors by remeasuring at a later time sufficiently far removed to guarantee

independence.

In measuring an "unknown" one gets a single value, but one still is

faced with the need to make a statement that allows for the scatter of the

results. If we had a sufficiently long record of measurements, we could

set limits within which we were fairly certain that the next measurement would

lie. Such a statement should be based on a collection of independent determinations, each one similar in character to the new observation, that is

to say, so that each observation of the collection and also the new observation

can be considered as random drawings from the same probability distribution.

These conditions will be satisfied if the collection of points is from a sufficiently broad set of environmental and operating conditions to allow

all the random effects to which the process is subject to have a chance to

exert their influence on the variability. Suitable collections of data can be obtained by incorporating an appropriate reference measurement into routine

measurement procedures, provided they are representative of the same variability to which the "unknown" is subject. The statistical procedures for

expressing the results will depend on the structure of the data but they

cannot overcome deficiencies in the representativeness of the values being

used.

The results from the reference item provide the basis for determining

the parameters of the measurement process and the properties are transferable.

One is saying, in effect, if we could have measured the "unknown" again and

again, a sequence of values such as those for the reference item would have

been obtained. Whether our single value is above or below the mean we cannot

say, but we are fairly certain it would not differ by more than the bounds

to the scatter of the values on the reference item.

70
The bound, ±R, to be used for the possible effect of random errors may

be as simple as ±3 (standard deviation), or may involve the combination of

many components of variance. Once the set of repetitions over which one's

conclusions must apply is defined, the structure of the random error bound

can be determined.

4.6. Possible Offset of the Process

Once one has established that his measurement process is "in control"

from the point of view of random variation, there remains the question of

the possible offset of the process relative to other processes. It is not

helpful to speak of the offset from a "true value" which exists only in the

mathematical or physical model of the process. The usefulness of considering

measurement in the context of legal proceedings helps clear away some of the

classical confusion about errors of measurement. In a legal or regulatory

setting, one is forced to state what would be accepted as correct such as comparison (by a prescribed process) with national standards or with the

results from a designated laboratory or concensus of many laboratories.

The idea of defining uncertainty as the extent to which a measurement

is in doubt relative to a standard or process defined as correct finds ex- pression in the recent Nuclear Regulatory Commission statement:

70.57Ca) (4) "Traceability" means the ability to relate

individual measurement results to national standards or nationally accepted measurement systems . . . (italics added)

The logic of this approach seems unassailable - if one cannot state what

measurement system would be accepted as "correct," then one would have no defensible way of developing specifications or regulations involving such

measurements

.

One could measure the offset of his process relative to the accepted

process, and make suitable corrections to eliminate the offset. However,

for most processes, one is content with setting bounds to the possible offset

due to factors such as:

errors in the starting standards

departures from sought-after instrumentation (e.g.,

geometrical discrepancies)

errors in procedures, environment, etc.

and other effects which are persistent. From properly designed experiments,

one can arrive at a limit to the possible extent of errors from these sources

in answer to the question, "If the process were set up ah initio , how large a difference in their limiting means would be reasonable?"

71
A bound to a number of factors can be determined as part of regular

measurement. For example, the effect of elevation could be evaluated by

occasionally duplicating a measurement at a different height and taking an appropriate fraction of the observed difference as the limit to the possible

offset due to any error in setting elevation. Figure 43 shows some results

from sound level meters at two heights with the source at a constant height.

Even if one has a functional relation, y

~ f(hl, expressing the dependence of the result, y, on height, h, one still has to carry out these

measurements. The usual propagation of error approach involving partial

derivatives, etc., implies that all instruments are equally dependent on

the parameter under study, that there are no effects related to the factor

except that contained in the formula. This can be verified for a particular

instrument by actually measuring its response.

A similar comparison was made for a different orientation of the instrument

with respect to this signal source and is shown in Fig. 44. The effect of

orientation is negligible and one would not be justified in adding an allowance for possible systematic error from this source based on a theoretical

calculation.

From these measurements, one will have a set of bounds E , E„, E_, ... to the possible offset or systematic error from the various factors. The

question as to how to combine these to a single bound to the possible offset

depends on knowledge of the joint effects of two or more factors and on the

physical model assumed for the process. For example, if the bounds E. and E.

arise from independent random erro r bounds , then it would be appropriate to

combine them in quadrature, i.e., /E? + E? . An error in the model e.g.,

assumed linearity even when nonlinearity exists) would act as an additive

error. The properties of any combination rule can be evaluated and a selection made of the most appropriate. The result will be an overall value, E,

for the possible offset for the limiting mean of the process from that of the

nationally accepted process.

4.7. Uncertainty

What can one say about the uncertainty of a measurement made by a process

that may be offset from the nationally accepted process by some amount ±E,

and is subject to random errors bounded by ±R. How should these values be

combined? To begin with, one could raise the question, "If the random error

could be made negligible, what uncertainty would one attach to a value from

the process?" Clearly the answer is ±E. The next question, "If, in addition,

a random error of size R is possible, what do we now say about the uncertainty?"

The answer seems obvious - E and R are added to give an uncertainty of ±[E + R]

.

But what if E were itself the result of only random errors? The answer

depends on what one calls a repetition. By the way E is defined, it is the

bound for the systematic offset of the process and although it may be arrived

at from consideration of random errors, the factor involved keeps the same

(unknown) value throughout. Our ignorance does not make it a random variable.

72
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74
Consider the case of a mass standard. NBS's certificate states that the un- certainty is based entirely on random variation, the effects from systematic

errors being negligible. But unless one recalibrates, the error due to

calibration remains fixed.

The uncertainty of a measurement - the width of its "shadow of doubt" in a legal proceeding - must therefore be the sum of the random error and systematic error limits.

There are some who suggest that the uncertainty should be /E z + R

z

. Let

us consider the cas e where both are the same size (i.e., E = R) , then the un- certainty becomes /E z + E

z = E/2 by this rule. One is thus able to reduce

that part of the uncertainty due to the systematic offset to 40 percent of its

actual value on the grounds that it is unlikely in repetitions involving

setting up the process ab initio that the random and systematic effects

will always add up to this extreme. This is fallacious because we are not

talking about repetitions, otherwise all of the systematic error would already

be in the random error.

4.8. Measurement Process Control

The essential feature for the validity of the uncertainty statement is

that the process remain in a state of statistical control. Once an out-ofcontrol condition occurs, one has lost predictability and the previous un- certainty statements are no longer valid.

To monitor the process some redundancy has to be built into the system.

A variety of techniques can be used to give assurance of continued control.

For example, one could periodically measure the same reference item or artifact or one could make duplicate measurements on some production items

with enough delay to guarantee independence. The American National Standards

Institute Standard N15.18 for mass measurement 2 is an example where this

approach is worked out in detail. But one has to verify more than just

those parameters related to random variations. One needs to build in tests

of the adequacy of the physical model by a variety of tests on the process

(e.g., by repeating measurements under different conditions to verify the

adequacy of the corrections for such changes) as well as periodic redetermination of the bounds for systematic error. One thus tests that the assumed

model is still acceptable and that the parameters assigned to that model have

not changed.

An excellent example of the efficacy of this approach is given by the

recent announcement of discrepancies of 1 mg in the assignment of mass

to aluminum kilogram standards. The mass measurement system has long been

shown to be nearly perfect for the usual standards. To check up on the performance of the system at densities nearer to that of most objects involved

in practical measurement, an aluminum kilogram was sent to laboratories including several at high elevations. It turns out that the difference between

the mass of a stainless steel and an aluminum kilogram is significantly different at different elevations. This unsuspected property of the real measurement system is now the subject of considerable study.

75
4.9. Measurement Assurance

All measurements have some form of measurement assurance program associated with them although, as with quality control, we usually reserve the term

for a formal program. In a formal measurement assurance program one treats

the whole process - beginning with a study of the need, the development of

a measuring process and a procedure for determining and monitoring its performance, and an evaluation of the effectiveness of the whole effort.

One needs a criterion of success to be able to determine whether more

of one's current activity or perhaps some alternative would contribute most

to the overall program, and this is not necessarily provided by the smallness

of the uncertainty for a measurement.

When the measurement requirements are stated in terms of the needs of

the system (protection of the individual, process control, etc.), one can measure success of the measurement effort in terms of closeness to meeting

those goals. Measurement efficiency is thus judged in terms of the output of

the organization rather than by the count of the number of significant digits,

Also, one needs this measure of performance of the measurement effort to be

able to identify those areas which need improvement.

The emphasis in measurement assurance is on the properties of the measurements relative to their use. (This is in contrast to the traditional

approach which concentrated on the properties of instruments. Accuracy

statements were regarded as descriptive of the equipment and by restricting

^the conditions more severely at each step an echelon system of instrument

calibration became the accepted practice.) One builds into the measurement

process redundancy sufficient to enable each measurement to withstand the

kind of "cross-examination" which it will encounter whether it be a scientific evaluation or in a formal legal proceeding.

4.10. An Example

A detailed example is now presented to illustrate the concepts given in

this section. The numerical values appearing in this example are based on actual measurements. The details of the formulas used below are given in

Appendix B.

4.10.1. Introduction

Two Type II sound level meters, one from each of two manufacturers, are

to be used to measure vehicular passby noise. The laboratory has a Type I reference sound level meter which has been calibrated by NBS and has un- certainties relative to NBS standard microphones of ± 0.75 dB. It is

regularly compared against a second reference which is a "1/2-inch" microphone. The largest difference ever recorded between these two standards

has been 0.08 dB.

76
4.10.2. Initial Determination of Process Parameters

A. Errors in Meter Calibration

Meter: SLM-A

Factors: Broad band noise signal generated by a company Q loudspeaker.

Sound level meter oriented 90° with respect to the loudspeaker

at a height of 1.3 m from the ground.

TABLE 4.

Determination of Sound Level Meter x Calibration Errors

Low Level Middle Level High Level

Reading

from Reading

Type 1 from

Reference Type 2 Standard Meter Difference

Me asDate y X b=x-y

No. (1975)

8/12

(dB) (dB)

89.6

(dB)

1 90.3 - 0.7

2 13 90.4 89.5 - 0.9

3 14 90.5 90.8 0.3

4 15 90.5 89.8 - 0.7

5 18 90.3 89.8 - 0.5

6 19 90.3 89.9 - 0.4

7 20 Data 90.4 89.8 - 0.6 Data

8 21 Not 90.6 89.5 - 1.1 Not

9 25 Given 90.3 89.7 - 0.6 Given

10 26 90.3 89.5 - 0.8

11 27 90.6 90.0 - 0.6

12 28 90.6 89.4 - 1.2

13 29 89.8 90.2 0.4

14 9/2 91.1 90.0 - 1.1

15 3 91.1 90.0 - 1.1

16 4 91.1 89.6 - 1.5

me

average; b = - 0.69375 dB

standard deviation; a, = 0.5026 dB

b uncertainty in reference standard; U 0.75 dB

s ter calibration error limit; U + lb| + 3a, //m= 1.8027 dB

77
Meter: SLM-B

Factors: Broad band noise signal generated by a company Q loudspeaker.

Sound level meter oriented 90° with respect to the loudspeaker

at a height of 1.3 m from the ground.

TABLE 5.

Determination of Sound Level Meter z Calibration Errors

Me as

.

Date

No. (1975)

1 8/12

2 13

3 14

4 15

5 18

6 19

7 20

8 21

9 25

10 26

11 27

12 28

13 29

14 9/2

15 3 16 4

Low Level Middle Leve 1 High Level

Reading

from Reading

Type 1 from

Reference Type 2 Standard Meter Difference

y z b=x-z

(dB) (dB)

90.2

(dB)

90.3 - 0.1

90.4 90.2 - 0.2

90.5 90.7 0.2

90.5 90.5 0.0

90.3 89.7 - 0.6

90.3 90.2 - 0.1

Data 90.4 90.0 - 0.4 Data

Not 90.6 90.2 - 0.4 Not

Given 90.3 89.9 - 0.4 Given

90.3 89.5 - 0.8

90.6 90.4 - 0.2

90.6 90.2 - 0.4

89.8 89.9 0.1

91.1 90.4 - 0.7

91.1 90.4 - 0.7

91.1 89.5 - 1.6

average; b = - 0.39375 dB

standard deviation; a. = 0.4358 dB

b uncertainty in reference standard; U 0.75 dB

s meter calibration error limit; U + bl + 3a, //m = 1.4706 dB

s ' ' b

78
B. Meter Random Errors

Meter //l: SLM-A

Meter #2: SLM-B

Factors: Broad band noise signal generated by a company Q loudspeaker.

Sound level meter is oriented normal (pointing) to the loudspeaker and 85 cm from the ground.

TABLE 6

Determination of the Random Errors of Two Sound Level Meters

Reading from Reading from

Meter #1 Meter #2 Difference

X z x-z=d

Me as. No. Date (1975)

8/12

(dB) (dB) (dB)

1 90.2 90.3 - 0.1

2 13 90.2 90.5 - 0.3

3 14 90.7 90.8 - 0.1

4 15 90.2 90.4 - 0.2

5 18 90.1 90.1 0.0

6 19 89.1 89.3 - 0.2

7 20 90.3 90.4 - 0.1

8 21 90.2 90.6 - 0.4

9 25 90.5 90.6 - 0.1

10 26 89.9 90.0 - 0.1

11 27 90.6 90.9 - 0.3

12 28 90.5 91.1 - 0.6

13 29 90.8 91.1 - 0.3

14 9/2 90.8 91.4 - 0.6

15 3 90.6 90.7 - 0.1

16 4 90.3 90.4 - 0.1

standard deviation of differences; a, = 0.1807

a standard deviation of single measurement; a = a,//2 = 0.1271

d

average; d = - 0.225

standard deviation of d; a .//l6 = 0.0452

d

79
The measured value for the difference between the two meters is, from

Tables 4 and 5, d* = - 0.69375 - (- 0.39375) = - 0.3. The difference,

|d - d'| is equal to | (- 0.225) - (- 0.3) | = 0.075 which is less than

three times the standard deviation of the difference, i.e., 0.075/0.0452

< 3, so that one would regard the meters as having the same relative bias

as that found in the meter calibration experiment.

The standard deviation, a, of a single measurement should be in agreement

with that found in subsection A. The combined value for the standard deviation a, is

b

a^ = /[0.4358) 2 + (0.5026) 2 ]/2 = 0.4704

o I

whereas the value for a is only 0.1278. The ratio of the squares of these

standard deviations (placing the larger in the numerator) is

F = (0. 4704/0. 1278) 2 = 13.6

which exceeds the critical value corresponding to the 0.01 probability

value for the F distribution. The proper value for the standard deviation

to account for the process random errors will therefore be a, and the

value used for a_ will be a_ = 0.4704.

R R

If paired measurements by two meters are used to maintain process control, then oj = 0.1807 (or a = 0.1278) would be used as the initial

value for this process parameter.

C. Meter Systematic Errors

Meter: SLM-A

Factors: Broad band noise signal generated by a company Q loudspeaker.

Sound level meLer oriented normal (pointing) to the loudspeaker.

80
TABLE 7 Determination of the Random Error of a Sound Level Meter

Height = 85 cm Height = 130 cm

Test No. Date (1975)

1 8/12

2 13

3 14

4 15

5 18

6 19

7 20

8 21

9 25

10 26

11 27

12 28

13 29

14 9/2

15 3

Reading Reading

x

l x

2 (dB) (dB)

90.2 89.8

90.2 89.5

90.5 90.0

90.2 89.8

90.2 89.8

89.9 89.9

89.9 89.8

90.2 89.5

90.3 90.0

89.9 89.5

91.0 90.8

90.5 89.4

90.3 89.9

90.8 90.0

90.5 89.6

Average; Xj = 90.3375 dB x

2 = 89.8625 dB

In the absence of an assumed physical model (i.e., functional) the difference will be taken as the limit E to the possible systematic error

for this factor, i.e., E = x - x . = 0.475 dB.

max mm

D. Uncertainty

The uncertainty, U, of a single determination is given by

U = U + lb I + 3a. //m + E E. + 3an

s '

' b i R

where the numerical values for b are obtained from Tables 4 and 5

a, is obtained as shown after Table 6.

b SLM-A SLM-B

U + b + 3a, //m

s '

' b

E

Uncertainty, U

1.8201 1.4706

0.475 0.475

1.4112 1.4112

3.71 3.36

81
If the height of the sound level meter were specified the allowance of

0.475 could be dropped to give

Uncertainty

(with fixed height)

SLM-A

3.23 dB

SLM-B

2.88 dB

If the calibration factor, b, were applied to each determination, the

uncertainty would be reduced by |b | to give

Uncertainty

(fixed height, meter

calibration used)

SLM-A

2.54 dB

SLM-B

2.49 dB

4.10.3. Maintenance of Process

The process parameters were found in subsection B to be: d = 0.30, a ^ = 0.1807 with 9 degrees of freedom, and a^ = 0.4708 with 18 degrees of

freedom.

A. Duplicate Measurements

Duplicate determination by two meters gave values as shown Table 8. They

are spread far enough apart in time so that successive results should be

statistically independent. The results in Table 8 show that for the two

groups shown both t and F are less than their critical values , and therefore the process is accepted as being "in control."

B. Revised Process Parameter Values

The following are the updated values for the process after the first two

groups

:

d - 10C-0.30) +M-0.14) +5(-0.24) = _ Q>245 dB

9(.18Q7) + 4(.27Q2) + 4(.3362)

9 + 4 + 4 = 0.2471 dB ; degrees of freedom = 17

a = 0.4704 dB ; degrees of freedom = 18

K

These parameters are to be used to determine the uncertainty limits for

measurements by the process as long as the process is "in control" relative to its parameters. Once an out-of-control condition occurs it is

necessary to determine a new set of process parameters. Without this

predictability the validity of its uncertainty statement is in doubt.

82
TABLE 8

Determination of the Revised Process Parameters

for Sound Level Meters x and y

Meter Meter

Reading Reading D if f erence

Number Date (1975)

X

(dB)

Group I

y

(dB)

d=x-y

(dB)

1 9/8 90.2 90.5 - 0.3

2 9 90.0 90.5 - 0.5

3 10 90.5 90.6 - 0.1

4 11 90.5 90.5 0.0

5 12 90.2 90.0 0.2

average; d

& = - 0. 14 dB

standard deviation; s,. = 0.2702 dB

~C „~„~,-. . t- — w — d| 16 - n ^Q < -\ aj/5 0.1807//5

d

test of variability; F = 0.2702 2

0.1807 2 = 2.23 < Critical F

Group II

6

78

9 10

15

16

17

18

19

90.0 90.2

90.5 90.4

90.2 90.4

89.8 89.9

89.5 90.3

average; cL = - 0.24 dB

standard deviation; s

5 = 0.3362 dB

test of average; t = 1.42 < 3 test of variability; F = 3.46 < Critical F

Group III

- 0.2

0.1

- 0.2

- 0.1

- 0.8

83
4.11. References

1. "Measurement Control Program for Special Nuclear Materials Control

and Accounting (10 CFR 70.57)," Federal Register , Vol. 40, No. 155

August 11, 1975, pp. 33651-33653.

2. "Mass Calibration Techniques for Nuclear Material Control," N15.18-

1975, American National Standards Institute, New York, N. Y.

3. P. E. Pontius, "Mass Measurement: A Study of Anomalies," Science 190 , 379-380 (Oct. 24, 1975).

84
APPENDIX A

MICROPHONE CALIBRATION METHOD

A.l. Introduction

The microphone calibration procedure is performed in two stages. The

first stage employs a reciprocity calibration of the two condenser microphones. The second stage uses one of these microphones as a source from

which the response of the electret and ceramic microphones are obtained.

The reciprocity method is used to calibrate the reference (source) microphone at a particular temperature, humidity, and frequency. The reciprocity technique requires three microphones . One of these microphones

must be reversible, that is, it must perform according to certain relationships between the acoustic pressure and velocity on the surface of

the microphone diaphragm and the current and voltage produced by the micorphone. A third microphone is used as a source. After the reference

microphone has been calibrated it is used as a source to generate a known

sound pressure from which the other microphone responses are determined.

The details and theory of how one performs these calibrations are presented in Ref. 1. The purpose of this appendix is to describe how NBS

performed these measurements.

A. 2. Reciprocity Method

Two different types of measurements are made in the NBS reciprocity method

of calibration: voltage ratio and capacitance. The voltage ratio measurement is performed as shown in Fig. A-l. With the switch in position 1 the oscillator excites the source microphone. The receiving microphone,

acoustically coupled to the source through a 3-cm 3 plane-wave coupler,

converts the acoustic signal into a voltage, which is filtered and amplified. The magnitude of the signal is read on the meter and is denoted A. The switch is then placed in position 2 disconnecting the oscillator from

the source microphone and connecting it to an attenuator calibrated in

hundredths of a decibel. The output of the attenuator is connected across

the resistor R , which is in series with the receiving microphone. The

attenuator is varied until the meter indicates a value equal to A. The

resulting attenuation reading, denoted A (dB) , gives the logarithm of the

ratio between the open circuit voltage of the oscillator driving the source microphone to the open circuit voltage of the receiving microphone. Consequently the voltage ratio V is given by

K

V

R

= 10 (-Aa /20)

Measurements of the capacitance of a microphone are made according to the

method as applied by Koidan2 and is shown in Fig. A-2. The source and re- ceiving microphone are placed in the coupler in the same manner as in the

voltage ratio measurement in order that the source microphone be subjected

to the same acoustic impedance. When the two switches are in position 1

85
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a voltage is placed across the source microphone, which is in series with

a resistance R. The reading, denoted Mj , of the meter that is connected

across the resistance R is recorded. The two switches are now placed in

position 2 and the attenuator, which is calibrated in hundredths of a decibel, is adjusted so that the meter again reads M, . If the microphone

is assumed to be purely capacitive with an impedance at the given frequency that is much larger than R, the capacitance of the microphone, C,

is given by

c '• tkr3(A- 1J

where f is the frequency of the oscillator (Hz) , V3 = 10 c and A is

the attenuator reading in dB.

The reciprocity calibration method used three microphones denoted #0, #1,

and #2, and the two types of measurements discussed above to determine

the pressure response of two of them (#1 and #2). Microphone #0, which

will not be calibrated, is used as a source. With microphone #0 as the source and microphone //l as the receiver the voltage ratio V.. is obtained.

With microphone #0 as the source and microphone #2 as the receiver a voltage ratio V2 is obtained. Lastly, with microphone #1 used as a source and

microphone #2 as the receiver a quantity V21 , defined as the ratio of the

output voltage of microphone #2 to the input voltage to microphone #1, is

obtained. These three sets of measurements and some correction factors

described below, will yield the pressure response of microphones #1 and #2.

From Section 4 of Ref. 1 the expressions for the pressure response of microphones #1 and #2, denoted r, and r„ , respectively, are

r

1 K^ = K/G(fT \hr^ , V/Pa ( A"2)

where

and

r

2 = K/GiU t/Y'. V

21 V/Pa (A-3)

G(f) = jr£ A(f ,f

Q

) (A-4)

s

sin(-rrf/f ) i(f > f o> (.f/f

o )° < A~5 >

88
In Eqs. (A-2) to (A-4) f and R are defined as in Eq. (A-l) , P

s is the

ambient barometric pressure, fQ is the first longitudinal natural frequency

of the coupler, and K is a constant. For the setup used in this experiment

the value of f was the frequency at which the first maximum value of the

output of the receiving microphone was obtained when the frequency was varied with a constant voltage applied to the source microphone. The quantity K is a function of the volume of the coupler and the equivalent volumes of the microphones, adjustments for the heat conduction effects at

the walls of the cavity and the presence of the capillary tubes in the

coupler, and the ratio of the specific heats of air. The latter is virtually independent of temperature over the range considered, and while the

volumes and capillary correction change very slightly with temperature,

they have been assumed to remain constant. The constant K has been eliminated from the final results by referencing the r. to their respective

values at a given frequency and temperature.

A. 3. Comparison Method

Comparison calibrations used microphone #1 as the source and the electret

and ceramic microphones as the receiving ones. The pressure response of

these microphones is then determined from the expression

K 6A(f,f ) P =

a

- - V/Pa (A-6)

a P V

s a

where f a is the first longitudinal natural frequency of the coupler with

the microphone a as the receiver, Va is the voltage ratio, Ka

is assumed

constant,

K

r

i C

(A-7)

and r, is given by Eq. (A-2) and C by Eq. (A-l). The constant K is eliminated by referring the pressure response to its response at a given frequency and temperature.

In arriving at Eqs. (A-l) through (A-7) several assumptions were made re- grading the effects of temperature on some of the constants in Eqs. (A-2),

(A-3) and (A-6). Furthermore, there may be inaccuracies in the measurements themselves. The estimated maximum value of the errors introduced

by these two factors is tabulated in Table A-l which indicates that the

total maximum absolute error that exists in the results presented is

probably less than 0.2 dB.

89
A. 4. References

1. "Method for the Calibration of Microphones," SI. 10-1966, American

National Standards Institute, New York, N. Y.

2. W. Koidan, "Method for Measurement of |E'/I'| in the Reciprocity

Calibration of Microphones," J. Acoust. Soc. Amer. 32, 611 (1960),

90
TABLE A-l

Estimated Magnitudes and Sources of Errors

in the Microphone Calibration Data

Source of Error

Assumptions that the following are independent

of temperature:

1. Volume of coupler

2. Coupler capillary corrections

3. Heat conduction correction

4. Equivalent volumes of microphones

Estimated

Maximum Error

(dB)

0.02

0.02

0.06 dB @ 100 Hz

(less at higher freq.)

Unknown

Accuracy of measurement

6. Resonance frequency

7. Attenuator readings (combined)

8. Barometric pressure

0.02

0.04 (reciprocity)

0.05 (comparison)

0.01

91
APPENDIX B MEASUREMENT ASSURANCE PROGRAM

B.l. Introduction

This appendix presents a detailed outline of a method whereby one can determine both an estimate of the precision of the- sound level meter readings and whether or not this precision is, at all times, within acceptable

limits; that is, whether or not the measurement process is in control.

B.2. Initial Determination of Process Parameters (to be done for each

meter)

B.2.1. Errors in Meter Calibration

For: (Description of sound level meter)

Use: (Truck tire noise, factory noise, ...)

Meter:

Factors: (orientation, height from ground, sound source, etc.)

TABLE B-l

Determination of Sound Level Meter Calibration Errors

MethodI of Signal Middle High

Generation3 Low Level Level Level

Reading

from Reading . . Reference from

Standard*5 Meter Difference

Meas

.

y X b=x-y y X

Date Time No.

* 1

(dB) (dB)

*

(dB) (dB) (dB)

* * *

* * 2 * * *

* * 3 * * *

* * m-1 * * *

* * m * * *

average; b = standard deviation; a^ = ainty in reference standard Us

: calibration error

uncert

meter

limit

us + |b| + : ~iau//m =

ihe signal should have characteristics nearly like the quantity to be

measured.

Reference standard should itself have a history of stability, relative

immunity to environmental changes or signal characteristics, etc.

If |b| is large, it should be applied as a correction to the meter and

jb| should be omitted from this error limit.

92
B.2.2. Meter Random Errors

Meter #1

Meter #2

Factors: (orientation, height from ground, sound source, etc.)

TABLE B-2

Determination of Sound Level Meter Random Errors

Reading Reading

from from

Meter #1 Meter #2 Difference

Meas. x z d=x-z

Event No. (dB) (dB) (dB)

(A series of measurements which 1

"sample" the type, level and ex- 2

ternal conditions of practical 3

measurements. If more than one measurement per day is taken, the

full set of procedures used to n-1

start a new day should be done n between measurements .

)

average; d = standard deviation; a^ =

a = a d //2 =

If —— > 2.59, an explanation should be sought in the bias in the meter

<*d calibration (values of b as determined in Table B-l) . If this is not sufficient, presumably some procedural difficulty exists. The process should

not be implemented for practical measurements until changes have been made

to eliminate this bias between instruments.

A plot of d versus x should be made to see if the variability is a function of noise level. If a dependence exists, the data should be collected

for each of a number of groups within each of which the variation can be

regarded as homogeneous.

The standard deviation a^ , obtained from Table B-l, and a, obtained from

Table B-2, should be the same except for the effects of random error. If

afc/a > F (.01, m-1, n-1) where F is the critical value of the F distribution for (m-1) and (n-1) degrees of freedom exceeded with probability .01,

then the two meters show a correlated response and a^ should be used as the process parameter for random error, qr. Otherwise or = a. In the ex- pression for F, m is given in Table B-l.

93
B.2.3. Meter Systematic Errors

Meter:

Factors: (orientation, reflecting surface, obstructions, etc.)

TABLE B-3

Determination of Sound Level Meter Systematic Errors

Source of Signal

(equivalent to type of

sound to be measured) 3

Test No. Day /Time

Level 1 Level 2 Level k

Reading Reading Reading

Value Value Value

x

l x

2 \

(dB) (dB) (dB)

* * *

* * * * * *

n-1

n

Averages \

If a reproducible signal source is not available, differences from the

value given by a reference standard may be used.

Unless some physical model exists (i.e., functional form) the difference

between the maximum and minimum will be taken as the limit to the possible systematic error, E; from this factor, that is,

E = x - x . max mm

For each factor involved, the systematic error for each will be determined by this method, provided the effects of joint variation of two

factors are additive and independent.

A list of those factors known to have some effect, but which were not

investigated, should be maintained.

94
B.2.4. Uncertainty

The uncertainty of a single determination is given by3a,

U + b + —

S '

' r~ /m

+ E E. + 3o.

1 R

(B-l)

where m is given in Table B-l.

B.3. Maintenance of Process

B.3.1. Duplicate Measurements

A schedule for making duplicate determinations by a second meter will be

incorporated into the regular work load to give values as shown in Table

B-4. These should be spread far enough apart in time so that successive

results are statistically independent.

TABLE B-4

Determination of Process Control Parameters

Number Event/Date

Reading

from

Meter #1

X

(dB)

*

k

k

k

k

Reading

from

Meter #2

y

(dB)

*

k

k

k

k

Difference

d

(dB)

1

2

3

4

5

k

k

k

k

k

average;

standard deviation;

d 5 =

S

5 = Summary after each

group of 5 events

6

78

*

k

k

k

k

k

k

k

k

95
If I

5 - d\/(o^//5) > 3 the process is out of control in that one or both

of the meters give erroneous results. Recalibration may be necessary.

If s^/aj > /F(0.01,5,n) where F is the critical value of the F probability

distribution (with 5 and n degrees of freedom, where n is given in Table

B-2) exceeded with probability .01, then the process is out of control on variability. Table B-2 should therefore be repeated to establish a new

value for aj.

The values for d and a^ should be periodically updated by incorporating

this sequence of differences with those of Table B-2.

B.3.2. Check on Systematic Errors

Differences between Meter #1 and Meter #2 arising in the subsection on duplicate measurements will be plotted as a function of time, and also

as a function of average meter readings, of values for ambient conditions

(e.g., temperature) and any other variables known to affect noise measurements. A significant dependence of the result on these variables will be

studied with a view to adjusting the uncertainty statement appropriately.

A schedule of measurement designed to confirm the values of the meter's

systematic errors should be implemented.

B.4. Statement of Uncertainty

If the process may be regarded as being in a state of statistical control

then the uncertainty value given by Eq . (B-l) will be used.

96
APPENDIX C

SOME ELECTRICAL CHARACTERISTICS OF SOUND LEVEL. METERS

C.l. Detector Circuit

In order that one record the correct sound level as measured by a sound

level meter it is necessary to ascertain how accurately its detector

circuit can convert a wide variety of signals into a rms value. As far

as the detector circuit is concerned it is sufficient to consider only a class of well-characterized signals in which the ratio of the peak value

of the signal to its rms value varies. Such a ratio is called the crest

factor and is presented mathematically in Section C.3. The signal chosen

to investigate the detector circuits was a tone burst, which is also defined explicitly in Section C.3. The experimental technique, which is

discussed subsequently, determined not only the accuracy of the detector

circuit but also that of the A-weighting network.

The accuracy of the detector and the A-weighting network is determined as follows. The microphone is removed and the sound level meter is switched

to A-weighting and to "slow" meter response. A continuous signal at one

of the center frequencies of the octave bands from 125 to 4000 Hz is

passed through a precision attenuator calibrated in 0.01-dB increments.

The attenuator is set such that the output of the continuous signal cor- responds to 80 dB full scale. The signal is now converted to a tone

burst having the number of "on" and "off" cycles described in Section

C.3. The attenuator is adjusted until the meter again reads 80 dB. The

difference in the attenuator readings for the continuous signal and for

the tone burst is denoted Am(dB) . The theoretical value of this attenuation, which is also computed in Section C.3., is denoted A t (dB). The

differences between these two values, A t - Am , gives a measure of the

accuracy of the sound level meter's detector and A-weighting network as a function of frequency and crest factor. Typical results for one sound

level meter from each of four manufacturers are given in Tables C-l to

C-4. As can be seen from these results there is considerable variation

in the error as a function of frequency for three of the four sound level

meters. Thus one should expect large errors in the sound level meter

readings when noises that are impulsive in character, such as in factories

using punch presses, dropforges, or any type of machinery that has an intermittent cycle, are being measured with sound level meters having large errors at high crest factors.

C.2. Meter Linearity

In addition to the possible errors caused by the sound level meter's detector circuit as a function of the crest factor of the signal there is

also the linearity of the meter scale itself and the linearity of the

range potentiometer to be considered. Both these errors can relatively

easily be experimentally determined and corrected for in all subsequent

readings taken with that particular meter. Typical values obtained for

97
TABLE C-l

Difference Between A -A for SLM-U

t m

as a Function of Frequency and Crest Factor5

A -A (dB)

t m

N/M 125 Hz 250 Hz 500 Hz

Full Scale

1000 Hz 2000 Hz 4000 Hz

8 - .3 - .32 - .33 - .37 - .50 - .70

4 - .64 - .64 - .65 - .67 - .77 - .97

2 -1.03 -1.11 - 1.02 - 1.03 - 1.10 - 1.30

1 -1.25 -1.2 - .86 - 1.20 - 1.30 - 1.47

1/2 - .95 - .89 - .78 - .90 - .96 - 1.10

1/4 - .11 - .07 - .02 - .06 - .07 - .20

1/8 + .69 + .65 + .55 X .59

1/16 - 4.09 - 4.30 - 4.23 -10.03

1/32 -23.28 -26.33 -30.97 -33.87

1/64

Full Scale - 10

-30.10

dB

8 - .37 - .4 - .32 - .47 - .56 - .80

4 - .82 - .84 - .80 - .91 - .90 - 1.25

2 -1.58 -1.61 - 1.59 - 1.61 - 1.68 - 1.95

1 -2.82 -2.8 - 2.21 - 2.87 - 2.86 - 3.10

1/2 -4.46 -4.54 - 4.15 - 4.51 - 4.50 - 4.67

1/4 -5.9 -6.01 - 5.97 -6.05 - 6.04 - 6.15

1/8 -6.01 -6.15 - 6.16 - 6.20 - 6.13 - 6.19

1/16 -4.91 -5.11 - 5.18 - 5.14 - 5.02 - 5.05

1/32 -4.62 - 4.17 - 4.01 - 3.84 - 3.80

1/64 -11.94 -11.30 -10.21 -18.73

1/128 -24.23 -25.54 -26.13 -24.31

*See Section C.3. for the definitions of N and M and Table C-5 for the

corresponding crest factors.

98
TABLE C-2

Difference Between A -A for SLM-V

t m

as a Function of Frequency and Crest Factor*

A -A (dB)

t m

N/M 125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz

Full Scale

8 + .07 + .08 + .04 + .03 - .06 - .25

4 + .03 + .06 + .05 + .10 .00 - .22

2 - .16 - .17 + .02 + .11 + .05 - .18

1 - .68 - .76 - .84 - .91 - .51 - .40

1/2 -1.02 -1.19 - 1.74 - 1.34 - .80 - .65

1/4 -1.4 -1.71 - 2.71 - 2.08 - 1.42 - 1.37

1/8 -2.11 -2.89 - 4.54 - 3.25 - 2.65 - 2.71

1/16 -37.54 -36.60 -26.71 -18.03

1/32 -35.12

Full Scale - 10 dB

8 + .13 + .05 + .09 + .13 .00 - .25

4 + .08 + .11 + .15 + .09 + .05 - .19

- .01 - .04 + .15 + .19 + .10 - .10

1 - .44 - .5 - .51 - .57 - .26 - .25

1/2 - .68 - .8 - 1.24 - .91 - .40 - .34

1/4 - .95 -1.21 - 1.91 - 1.38 - .82 - .83

1/8 -1.45 -1.95 - 2.84 - 2.20 - 1.80 - 1.81

1/16 -2.16 -3.36 - 3.94 - 3.50 - 3.31 - 3.43

1/32 -5.02 - 5.37 - 5.28 - 5.17 - 5.32

1/64 -11.34 -10.15 -10.21 -10.93

1/128 -29.68 -21.14 -14.93 -16.96

*See Section C.3. for the definitions of N and M and Table C-5 for the

corresponding crest factors.

99
TABLE C-3

Difference Between

t~

A f m

or SL^ -W

as a Function o : Frequency and Crest Factor*

A

-

t

b (dB) m

N/M 125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz

Full Scale

8 + .03 .00 + .09 - .07 - .06 - .35

4 - .02 + .01 - .39 - .01 - .10 - .39

2 0.00 + .06 - .30 - .01 - .10 - .30

1 + .07 + .10 + .05 + .03 - .06 - .25

1/2 + .08 + .10 + .01 + .09 0.00 - .19

1/4 + .10 + .19 - .07 + .02 + .03 - .17

1/8 + .25 + .20 + .19 + .10 + .20 - .01

1/16 + .46 - .06 - .03 + .30 + .29 + .07

1/32 - .02 - .12 + .07 - .07 - .32

1/64 -1 .43 -1 .50 -1.71 -2.03

1/128 -6 .08 -5 .14 -5.83 -9.11

Full Scale -- 1C dB

8 - .07 + .04 - .01 + .03 - .06 - .35

4 - .07 + .06 + .05 + .09 0.00 - .39

2 - .03 + .06 + .06 + .09 0.00 - .40

1 - .03 + .03 + .29 + .13 - .06 - .35

1/2 + .02 + .06 + .26 + .19 0.00 - .34

1/4 + .03 + .09 + .19 + .12 + .03 - .32

1/8 + .11 + .05 + .16 + .20 + .10 - .26

1/16 + .23 + .01 + .16 + .20 + .09 - .23

1/32 - .05 + .23 + .27 + .13 - .22

1/64 + .26 + .28 + .19 - .13

1/128 + .32 + .36 + .22 - .01

*See Section C.3. for the definitions of N and M and Table C-5 for the

corresponding crest factors.

100
TABLE C-4

Difference Between A -A for SLM-Y

t m

as a Function of Frequency and Crest Factor*

. A -A (dB)

t m

N/M 125 Hz 250 Hz 500 Hz

Full Scale

1000 Hz 2000 Hz 4000 Hz

8 + .03 + .07 + .09 + .08 + .04 - .30

4 - .02 + .04 + .05 + .12 + .10 - .24

2 - .23 - .17 + .11 + .19 + .17 - .13

1 - .82 - .80 - .81 - .82 - .30 - .25

1/2 -1.08 -1.13 - 1.79 - 1.11 - . .34 - .29

1/4 -1.50 -1.71 - 2.86 - 1.42 - .61 - .62

1/8 -36.34 - 7.60 - 3.84 - 3.21

1/16 -54.14 -40.40 -37.11 -37.23

1/32 -53.37 -48.13 -36.57 -36.17

1/64 -48.18 -33.61 -33.03

1/128

Full Scale - 10 dB

-30.53 -30.16

8 - .02 0.00 - .01 - .07 - .26 - .40

4 - .08 - .04 + .05 - .01 - .30 - .39

2 - .43 - .34 - .14 - .11 - .30 - .40

1 -1.22 -1.15 - 1.11 - 1.22 - .86 - .65

1/2 -1.57 -1.54 - 2.34 - 1.71 - 1.10 - .89

1/4 -1.95 -1.96 - 3.31 - 2.18 - 1.57 - 1.37

1/8 -2.51 -2.7 - 4.04 -2.85 - 2.40 - 2.41

1/16 -3.29 -4.01 - 4.94 - 4.10 - 3.81 - 3.88

1/32 -9.62 -10.37 - 7.73 - 7.07 - 6.82

1/64 -33.54 -27.50 -20.01 -18.23

1/128 -33.38 -32.38 -22.63 -21.41

*See Section C.3. for the definitions of N and M and Table C-5 for the

corresponding crest factors.

101
one Type II sound level meter from each of four manufacturers are shown

in Figs. C-l and C-2. Figure C-l shows the linearity of the meter scale

referenced to 10 dB down from full scale. Figure C-2 shows the linearity

of the range potentiometers or the meter scales.

C.3. Crest Factor of a Tone Burst through an Ideal A-weighting Network

Consider a sinusoidal signal of frequency f Q that has a peak magnitude A . If this signal is altered such that it is "on" for an integer number of

cycles N, "off" for an integer number of cycles M, and passed through an ideal A-weighting network, then it is not too difficult to show that the

square of the rms value of this altered signal, V

2 can be expressed as

V

2 = i |c I 2 H(nf')

D ' n ' o n=l

(C-l)

where f ' = f /(N+M)

o o

2 _

!u 2 (N+M) 2

A

2

1 - N+M

-1-2

°(jl\2

4 I N+M J n = M+N

1

- n ± M+N

and

4 H(nf') = II H.(nf')

j=l

is the ideal A-weighting given by

H (f) = 1-0042 (f/2Q.6 )

:

1 + (f/20.O 2

H

2 (f) = 1.0067

1 + (f/12200)

H (f) =

1. 0H6 (f/107.7)

1 + (f/107.7) 2

102
co

LU

LU>

LUQ

O

CO

LU

enlu

enO

LU

_l

<

o

CO

ccLU

hLU

LU

h-

>-

hf—

»

<

LU

(9P) N0I1VIA3Q i C_J

CD

I—

<

LU

103
0.6

0.4

0.2

GO 0.0

"O

2

-0.2

O

1- -0.4

<

> -0.6

LJJ Q

-0.8

-1.0

-1.2

SLM-U

-1.4

SLM-W

40 50 60 70 80 90 100 110 120 130

RANGE POTENTIOMETER SETTING (dB)

OR

METER SCALE READING (dB)

Figure C-2, Linearity of the range potentiometer or meter scale of four

DIFFERENT SOUND LEVEL METERS.

104
H (f) = 1-5445 (f/737.9) 2

h 1 + (f/737.9) 2

The crest factor, CF, is given by

CF = 20 log

1Q (A

Q

/V

D

) dB. (C-2)

Using Eq . (C-l) , the crest factor given by Eq . (C-2) is evaluated for

various combinations of frequency and N/M and presented in Table C-5.

For a continuous signal N=l and M=0 , yielding |

C

n | = 0, n 4 1, and

| C. | = A /2. Consequently Vj) -> V^ , the rms voltage for a continuous

sinusoidal signal, where

A

o _

v

c = T ^^oT

Since the tone burst contains less energy than the continuous signal

^C > ^D* Therefore, the decrease in amplitude compared to the continuous

signal, denoted A

t

, is

A

t = 20 log (VC /VD ) dB,

The quantity denoted Am

in Section C.l is the measured value of this de- crease. Therefore, the difference A

t -Am indicates the deviation from the

true value.

It should be noted that the preceding analysis does not include the effects

of the period and the damping of the meter movement. These effects (if

any), however, are included in the Am obtained by the method described in

Section C.l.

105
TABLE C-5

Theoretical Crest Factor for a Tone Burst of Various Frequencies

when Passed through an Ideal A-Weighting Network*

Crest Factor (dB)

N/M 125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz Linear

8 3.53 3.60 3.59 3.53 3.44 3.15 3.52

4 3.98 4.06 4.05 3.99 3.90 3.61 3.98

2 4.77 4.86 4.86 4.79 4.70 4.40 4.77

1 6.02 6.10 6.09 6.03 5.94 5.65 6.02

1/2 7.78 7.86 7.86 7.79 7.70 7.81 7.78

1/4 10.00 10.09 10.09 10.02 9.93 9.63 10.00

1/8 12.55 12.65 12.66 12.60 12.50 12.19 12.55

1/16 15.31 15.44 15.46 15.40 15.29 14.97 15.31

1/32 18.18 18.38 18.43 18.37 18.23 17.88 18.20

1/64 21.11 21.43 21.56 21.50 21.29 20.87 21.14

1/128 24.06 24.65 24.92 24.86 24.47 23.89 24.12

cycles of the tone burst of frequency f and M is

the number of "off" cycles. The period of the signal is (N+M)/f .

106
1NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLIC A'l'ION OK REPORT NO. NBS TN-931

2. Gov't Ac

N<>.

3. Recipient's Accession Nc

4. title and sum 111.1 Environmental Effects on Microphones and Type II Sound

Level Meters

5. Publication Date October 1976

6. Performing Organization Code 200.03

7. AUTHOR(S)

Edward B. Magrab, Editor

8. Performing Organ. Report Nc

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2003110

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ?.IP)

Same as 9.

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code.

15. SUPPLEMENTARY NOTES

None.

16. ABSTRACT (A 200-word or less [actual summary ol most significant information. If document includes a significant bibliography or literature survey, mention it here.) For four different manufacturer's Type II sound level meters numerous experimentally

determined data concerning the- effects of frequency, temperature, angle of incidence of

the sound, and types of ground cover and reflecting surfaces on sound level meter

readings are presented. Data are also given for the effects of ambient barometric

pressure on several manufacturers' acoustic calibrators, the effect of frequency and

crest factor on the sound level meters' detector circuit, the linearity of the sound

level meters' range potentiometer and meter scale, and the precision of the A-weighted

response in a randomly incident (diffuse) sound field. Additional data are given

concerning the effects of temperature and humidity on the sensitivity of electret,

condenser, and ceramic microphones. Finally, important statistical concepts and

recommended data monitoring procedures are presented to insure that the precision of

repeated sound level measurements is known.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Acoustic calibrators; A-weighting; barometric pressure; crest factor; ground cover; humidity; instrumentation; microphones; sound level meters; statistical control

processes; temperature.

18. AVAILABILITY \£ Unlimited

I

' For Official Distribution. Do Not Release to NTIS

\jX' Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. C13 . 49:931

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Springfield, Virginia 22151

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21. NO. OF PAGES

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NBS TECHNICAL PUBLICATIONS

PERIODICALS JOURNAL OF RESEARCH reports National Bureau

of Standards research and development in physics,

mathematics, and chemistry. It is published in two

sections, available separately:

• Physics and Chemistry (Section A)

Papers of interest primarily to scientists working in these fields. This section covers a broad range of physical and chemical research, with major emphasis on

standards of physical measurement, fundamental constants, and properties of matter. Issued six times a year. Annual subscription: Domestic, $17.00; Foreign, $21.25. • Mathematical Sciences (Section B)

Studies and compilations designed mainly for the mathematician and theoretical physicist. Topics in mathematical statistics, theory of experiment design, numerical

analysis, theoretical physics and chemistry, logical de- sign and programming of computers and computer sys- tems. Short numerical tables. Issued quarterly. Annual

subscription: Domestic, $9.00; Foreign, $11.25.

DIMENSIONS/NBS (formerly Technical News Bulletin) —This monthly magazine is published to inform

scientists, engineers, businessmen, industry, teachers,

students, and consumers of the latest advances in science and technology, with primary emphasis on the work at NBS. The magazine highlights and reviews

such issues as energy research, fire protection, building

technology, metric conversion, pollution abatement,

health and safety, and consumer product performance.

In addition, it reports the results of Bureau programs

in measurement standards and techniques, properties of matter and materials, engineering standards and services, instrumentation, and automatic data processing.

Annual subscription: Domestic, $9.45; Foreign, $11.85.

NONPERIODICALS

Monographs—Major contributions to the technical liter- ature on various subjects related to the Bureau's scientific and technical activities. Handbooks—Recommended codes of engineering and

industrial practice (including safety codes) developed

in cooperation with interested industries, professional

organizations, and regulatory bodies. Special Publications—Include proceedings of conferences

sponsored by NBS, NBS annual reports, and other

special publications appropriate to this grouping such

as wall charts, pocket cards, and bibliographies.

Applied Mathematics Series—Mathematical tables, manuals, and studies of special interest to physicists, engineers, chemists, biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides

quantitative data on the physical and chemical properties of materials, compiled from the world's literature and critically evaluated. Developed under a world-wide

program coordinated by NBS. Program under authority

of National Standard Data Act (Public Law 90-396).

NOTE: At present the principal publication outlet for these data is the Journal of Physical and Chemical

Reference Data (JPCRD) published quarterly for NBS

by the American Chemical Society (ACS) and the American Institute of Physics (AIP). Subscriptions, reprints,

and supplements available from ACS, 1155 Sixteenth

St. N.W., Wash. D. C. 20056. Building Science Series—Disseminates technical infor- mation developed at the Bureau on building materials,

components, systems, and whole structures. The series presents research results, test methods, and performance criteria related to the structural and environmental

functions and the durability and safety characteristics

of building elements and systems.

Technical Notes—Studies or reports which are complete

in themselves but restrictive in their treatment of a

subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under proce- dures published by the Department of Commerce in Part

10, Title 15, of the Code of Federal Regulations. The

purpose of the standards is to establish nationally rec- ognized requirements for products, and to provide all concerned interests with a basis for common understanding of the characteristics of the products. NBS

administers this program as a supplement to the activities of the private sector standardizing organizations.

Consumer Information Series—Practical information,

based on NBS research and experience, covering areas

of interest to the consumer. Easily understandable language and illustrations provide useful background knowledge for shopping in today's technological marketplace.

Order above NBS publications from: Superintendent

of Documents, Government Printing Office, Washington,

D.C. 201,02. Order following NBS publications—NBSIR's and FIPS

from the National Technical Information Services,

Springfield, Va. 22161. Federal Information Processing Standards Publications

(FIPS PUBS)—Publications in this series collectively constitute the Federal Information Processing Standards Register. Register serves as the official source of information in the Federal Government regarding stand- ards issued by NBS pursuant to the Federal Property

and Administrative Services Act of 1949 as amended,

Public Law 89-306 (79 Stat. 1127), and as implemented

by Executive Order 11717 (38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR (Code of Federal

Regulations).

NBS Interagency Reports (NBSIR)—A special series of interim or final reports on work performed by NBS for outside sponsors (both government and non-government). In general, initial distribution is handled by the sponsor; public distribution is by the National Technical Information Services (Springfield, Va. 22161) in paper copy or microfiche form.

BIBLIOGRAPHIC SUBSCRIPTION SERVICES

The following current-awareness and literature-survey

bibliographies are issued periodically by the Bureau:

Cryogenic Data Center Current Awareness Service. A

literature survey issued biweekly. Annual subscription: Domestic, $20.00; Foreign, $25.00.

Liquified Natural Gas. A literature survey issued quarterly. Annual subscription: $20.00.

Superconducting Devices and Materials. A literature survey issued quarterly. Annual subscription: $20.00.

Send subscription orders and remittances for the pre- ceding bibliographic services to National Bureau of Standards, Cryogenic Data Center (275.02) Boulder,

Colorado 80302.
U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Washington. DC. 20234

OFFICIAL BUSINESS

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oUJTIO/y O YEARS

/6-l9l fo 1901-1976