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SOP 22

Standard Operating Procedure 

for 

Calibration of Traffic Speed Gun Tuning Forks and 

other Acoustic Frequency Emitting Devices

1 Introduction 

Purpose 

This Standard Operating Procedure (SOP) describes the procedure to be followed for 

the calibration of tuning forks which are used to certify traffic control speed guns, and 

for calibration of other acoustic frequency emitting devices. The procedure may also 

be used to calibrate tuning forks for applications such as musical tuning. This 

procedure utilizes either 1) a Global Positioning System Disciplined Oscillator 

(GPSDO) or 2) an electronic frequency counter that is directly compared to the NIST 

transmitted frequency standards to reference the Coordinated Universal Time (UTC) 

standard maintained by the NIST and the United States Naval Observatory (USNO). 

The accuracy of the calibration is limited by the mechanical instability of the device 

being tested. Detailed measurement ranges, standards, equipment, and uncertainties 

for this SOP are generally compiled in a separate document in the laboratory.

Applicable References

Speed-Measuring Device Performance Specifications: Across-the-Road 

Radar Module, DOT HS 812 266, Department of Transportation, 

National Highway Traffic Safety Administration (NHTSA). 

NIST SP 432: NIST Time and Frequency Services. 

The Use of GPS Disciplined Oscillators as Primary Frequency 

Standards for Calibration and Metrology Laboratories, M. Lombardi,

NCSLI Measure J. Meas. Sci., vol. 3, no. 3, pp. 56-65, September 2008.

Evaluating the Frequency and Time Uncertainty of GPS Disciplined 

Oscillators and Clocks, M. Lombardi, NCSLI Measure J. Meas. Sci., 

vol. 11, no. 3-4, pp. 30-44, December 2016. 

Time and Frequency Measurements Using the Global Positioning 

System, Michael A. Lombardi, Lisa M. Nelson, Andrew N. Novick, 

Victor S. Zhang, Cal Lab Magazine, July, August, September 2001. 

NIST Time and Frequency Broadcasts from Radio Stations WWVB, 

WWV, and WWVH, Matthew Deutch, Ernie Farrow, John Lowe, Glenn 

Nelson, Dean Okayama, Don Patterson, Douglas Sutton, and William 

Yates, 2001 NCSLI Workshop and Symposium. 
 

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Calibration of Police Radar Instruments, D. W. Allan (NBS), F. H. 

Brzoticky (CO Dept. of Agriculture), NBS Special Publication 442, 

Report of the National Conference on Weights and Measures, 1976. 

Prerequisites

Verify that the metrologist is experienced in making frequency 

measurements.

Verify that suitable check standards are present and used in an active 

measurement assurance program.

Verify the laboratory environment is within an acceptable temperature 

and humidity range. 

Table 1. Environmental limits for calibrations. 

Temperature Relative Humidity

18 ̊C to 25 ̊C 40 % to 60 %

2 Methodology 

Summary

A tuning fork, or other acoustic frequency emitting device, is calibrated by 

measuring its acoustic frequency with an electronic frequency counter that is 

calibrated, and has metrological traceability through the L1 1 575.42 MHz GPS 

signal broadcast by the United States Air Force from Colorado Springs, 

Colorado, referencing the U.S. Naval Observatory (USNO) Coordinated 

Universal Time (UTC) standard or through comparison with the NIST 

transmitted radio frequency signal (WWV, WWVH), or telephone frequency 

signal. No adjustments are made to tuning forks; they are either approved or 

rejected. Because U.S. law enforcement personnel traditionally use U.S. 

Customary units, units of miles per hour (mph) are referenced throughout this 

SOP.

Equipment / Apparatus 

An electronic frequency counter capable of 0.1 hertz (Hz) resolution 

throughout the range from direct current (DC) to 10 000 Hz. 

A transducer to convert sound energy to electrical (DC) energy. The 

output must be strong enough for counter input sensitivity requirements. 

2.2.2.1 A clamping type contact microphone, e.g., Signal Flex SF-30 

Universal Tuner Pickup, or similar, is preferable for tuning 

forks. 
 

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2.2.2.2 A microphone, e.g., Shure SM57, Cardioid, Dynamic, or similar, 

is preferred for other acoustic frequency emitting devices.

A GPS time and frequency reference receiver with antenna. 

A short-wave receiver and antenna.

A calculator if converting frequency (Hz) to miles per hour (mph). 

A thermometer to measure ambient temperature.

Reference, Option A, Use of GPSDO

The tuning fork, or other acoustic frequency emitting device, must be in 

temperature equilibrium with the laboratory environment, typical 

equilibration time is not less than 2 hours. Read and record the ambient 

temperature.

Verify that the GPS frequency counter displays “ExtRef” on the display 

prior to use. This indicates the unit is utilizing the GPS reference 

receiver output as its reference. 

Confirm that the GPS reference receiver signal light is illuminated

indicating a locked signal. 

Adjust the frequency counter to a gate setting interval of 0.2 s to 0.5 s. 

Reference, Option B, Use of Short-wave Receiver and NIST-transmitted Radio 

Signal. 

The tuning fork, or other acoustic frequency emitting device, must be in 

temperature equilibrium with the laboratory environment, typical 

equilibration time is not less than 2 hours. Read and record the ambient 

temperature.
 

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Assemble the system as shown in Figure 1. 

Figure 1. System Configuration. 

Tune the short-wave receiver to the best usable standard frequency of 

2.5 MHz, 5 MHz, 10 MHz, 15 MHz, or 20 MHz. 

2.4.3.1 If the 10 MHz signal is not usable, a frequency divider / 

multiplier must be inserted at the frequency counter standard 

frequency output. Set the divider / multiplier to convert the 10 

MHz standard frequency output to the best usable WWV(H) 

frequency.

2.4.3.2 Because of heterodyning, the received WWV signal and the 

counter standard frequency output will cause the short-wave 

receiver field strength meter to oscillate. The oscillation rate is 

directly proportional to the frequency difference between the 

two signals.

If the meter oscillates three complete cycles or less in 1 second, 

the frequency counter is accurate enough for tuning fork 

certification.

If the meter oscillates more than three cycles in 1 second or does 

not oscillate at all, consult the maintenance manual for "time 

base oscillator adjustment procedures" or refer the counter to a 

manufacturer's authorized repair facility.
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Reference, Option C, Use of Tuning Fork Gauge and NIST-transmitted Radio 

Signal.

The tuning fork, or other acoustic frequency emitting device, must be in 

temperature equilibrium with the laboratory environment, typical 

equilibration time is not less than 2 hours. Read and record the ambient 

temperature.

Verify accuracy of the Tuning Fork Gauge via the NIST telephone 

signal broadcast via a telephone connection pick-up coil.

Table 2. Reference calibration sources.

Service Location Telephone 

Number

Radio Call 

Letters

Broadcast 

Frequencies

NIST Ft. Collins, CO (303) 499-7111 WWV 2.5 MHz 

5 MHz 

10 MHz 

15 MHz 

20 MHz

NIST Kauai, HI (808) 335-4363 WWVH 2.5 MHz 

5 MHz 

10 MHz 

15 MHz

U.S. Naval 

Observatory 

(USNO)

District of Columbia (202) 662-1401 

(202) 762-1069

----- -----

USNO Colorado Springs, CO (719) 567-6742 ----- -----

National

Research Council

(NRC)

Ottawa, Ontario, Canada (613) 745-1576 

(English)

(613) 745-9426 

(French)

CHU 3.33 MHz

7.850 MHz

14.67 MHz

If the gauge meets accuracy requirements, continue with measurements 

of the tuning forks. If the gauge does not meet accuracy requirements, 

it is removed from service and submitted for calibration and adjustment 

to the manufacturer. 

Procedure, Measure the Tuning Fork Frequency.

Grasp the tuning fork with the clamping type contact microphone near 

the serial numbered end of the fork. Avoid touching the tuning fork as 

much as possible to minimize warming the tuning fork thus changing its 

frequency. Strike the tuning fork with a semi-hard object, e.g., a wood 

block or a plastic mallet, etc. and immediately place the tuning fork 

2.5 cm to 10 cm away from the receiver (alternatively, strike the tuning 

fork with the material while it is placed near the receiver). Never use a 

metallic or stone object to strike the tuning fork. Observe the frequency 
 

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immediately and record the frequency and temperature at the time of the 

measurement. 

Repeat previous step with the tuning fork grasped 180 degrees from the 

first reading (flip the tuning fork over) and striking the alternate tine. 

Repeat previous step again with the tuning fork grasped 180 degrees 

from the second reading (flip the tuning fork over again) and strike the 

original tine.

Record the average of the three recorded readings as the oscillation 

frequency of the tuning fork. 

Take readings of an acoustic frequency emitting device.

Utilize a microphone for this process. 

Strike the acoustic frequency emitting device with a semi-hard 

instrument, e.g., a wood block or a plastic mallet, etc. while the system 

is placed 2.5 cm to 10 cm away from the receiver. Never use a metallic 

or stone object. Observe the frequency immediately and record the 

frequency and temperature. 

Repeat the process until a minimum of three stable observations are 

achieved. This may involve adjusting the proximity of the microphone 

to the device being tested.

Average the stable frequency observations and record this as the 

frequency for the item being calibrated. 

3 Calculations for Tuning Forks. 

Multiply the average recorded measurement result (tuning fork oscillation 

frequency) by the appropriate conversion factor shown in Table 4 or use 

Equation 2 as shown in section 3.2. The calculation of the tuning fork speed, in 

miles per hour, is determined from Eqn. 1. The speed of light is slower in air 

than the defined vacuum speed. 

0 2 d

c f f

ν = Eqn. (1) 
 

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Symbols Used in this Procedure 

Table 3. Symbols used in the procedure.

Symbol Description

v calculated speed for the tuning fork in miles per 

hour (mph)

fd measured tuning fork frequency

c speed of light in miles per hour; The speed of light 

is an internationally accepted constant defined to be 

exactly 299 792 458 m/s (approximately 

670 616 629.384 395 1 mph). The offset amount, 

considered insignificant here, is determined by air 

pressure, humidity, temperature, pollution amount 

and type, etc.

f0 designated radar band frequency

Table 4 has calculated values for conversion factors from Hz to mph for 

simplicity and is determined by the band and frequency but may be calculated 

using Eqn. 2. Unique factors for Kustom Signals, Inc. forks may be required. 

0

conversion factor

2

c

f = Eqn. (2) 

Table 4. Tuning fork conversion factors.

Band Frequency 

(GHz) Conversion Factor Conversion Factor (Kustom Signals1)

X-band 10.525 0.031 858 3 0.031 867 4 

K-band 24.150 0.013 884 4 0.013 884 4 

Ka1-band 33.800 0.009 920 4 NA

Ka-band 34.700 0.009 663 1 0.009 445 28 

Ka-band 35.500 0.009 445 3 

Example: A typical 50 mph K-band fork may have an oscillation frequency of 

3 652.4 Hz. Its speed is calculated as follows: 

3 652.4 Hz × (0.013 884 4 mph/Hz) = 50.7 mph 

 

1 Kustom Signals, Inc. information is provided as an example with appropriate conversion factors and is not intended as an endorsement or 

preference. 
 

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Record and report this product as the "speed" of the tuning fork to the nearest 

0.01 mph or 0.1 mph as requested. 

The tolerance of a tuning fork is determined by the manufacturer. 

A few manufacturers (i.e., Kustom Signals, Inc.) have designed their 

speed guns to truncate (round-down) to the first whole mile per hour. 

This is done to give the benefit of fractional speeds to the motorist. 

Therefore, the tolerance of these tuning forks is: 

- 0.00 mph to + 0.99 mph 

CAUTION: These speed guns must be mated to their associated tuning 

forks. These tuning forks cannot be used interchangeably with other speed 

gun manufacturers. It is recommended that all tuning forks be mated to their 

respective manufacturer speed guns.

Other manufacturers have designed their speed guns to round to nearest 

whole mph. These tuning forks have a tolerance of: 

- 0.50 mph to + 0.49 mph 

4 Measurement Assurance

Duplicate the process with suitable check standards using the same transducer 

used to take the observations of the device under test, either the clamping type 

contact pickup, or the microphone and create a control chart. 

Evaluate the values against the expected limits of the control charts. Plot the 

values to monitor changes over time. A t-test may be used to check the observed 

value against the accepted value. 

Check standard observations are used to calculate the standard deviation of the 

measurement process, sp. 

5 Assignment of Uncertainty

The limits of expanded uncertainty (U) include estimates of the standard uncertainty of the 

standard (us), estimates of the standard deviation of the measurement process (sp), an estimate 

for the uncertainty for the resolution of the frequency counter (ucounter), and an estimate for the 

uncertainty of the device used to record the ambient air temperature (utemp). These estimates 

are combined using the root-sum-squared method and the expanded uncertainty reported with 

a coverage factor (k), based on degrees of freedom, to give an approximate 95 % level of 

confidence. 
 

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Mechanical instability of a tuning fork, which varies with manufacturer, age, 

physical condition, etc., is the greatest cause of error in a tuning fork 

measurement. This has been experimentally shown to be less than ± 0.01 %. 

This portion of the uncertainty is included in the standard deviation of the 

process (sp).

Temperature changes of a tuning fork will cause its frequency (and thus speed) 

to change in a sufficiently linear fashion with inverse correlation due to the 

changing modulus of elasticity with temperature. The change is approximately

-0.000132 mph per each rated mph per 1 °F.

Example: At 70 °F, a 50 mph fork is measured to be 50.71 mph. At 10 °F, the 

measurement will be approximately 51.11 mph: 

50.71 mph + ((-0.000 132) × 50 × (10 - 70)) = 51.106 mph 

Figure 2. Temperature Correction Example.

Errors related to the broadcast signals (reference standards) are generally 

negligible, however may be included in the uncertainty budget (us).

Table 5. Example Uncertainty Budget Table. 

Uncertainty Component 

Description Symbol Source Typical Distribution

Uncertainty for the reference 

standard us

NIST traceable frequency 

standard (telephone, receiver, 

GPS clock)

NIST website (SP 960-12)

Rectangular

Standard deviation of the 

process

sp

Laboratory assessments, pooled 

standard deviation Normal

Uncertainty for the mechanical 

instability of the tuning fork ui

Normally included in the 

standard deviation of the 

process 

Rectangular

Uncertainty of the for 

temperature effects ut

Estimates may be calculated 

with equations in section 5.2 Rectangular

50.5

50.6

50.7

50.8

50.9

51

51.1

51.2

51.3

0 20 40 60 80 100

mph

Temperature °F

Temperature Correction Example
 

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Typically, the expanded uncertainty of the measurement process does not 

exceed ± 0.02 % plus small variations caused by laboratory temperature 

changes. Normally this impact is less than 0.05 mph. 

6 Certificate

Report results as described in SOP No. 1, Preparation of Calibration Certificates. Report the 

tuning fork serial numbers, tuning fork speed and/or acoustic instrument oscillation frequency 

(if appropriate), environmental conditions during the calibrations, specifically temperature, 

and the calculated uncertainties.

7 Acknowledgements and Validation 

This SOP and various iterations were developed by the States of Colorado, New Jersey, 

Alaska, and Virginia with collaboration and input from NIST (and NBS) staff David Allan 

and Michael Lombardi. This version is a consolidation of the various approaches to reference 

standards that are successfully being used for the calibration of tuning forks for legal 

applications. 

Tuning fork PTs have been coordinated by Garret Brown from Alaska for laboratory 

Recognition and Accreditation and for validation of this procedure.