February 2012 

NASA/TM–2012-217332 

A Study in a New Test Facility on 

Indoor Annoyance Caused by Sonic Booms 

Jonathan Rathsam, Alexandra Loubeau, and Jacob Klos 

Langley Research Center, Hampton, Virginia 
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February 2012 

NASA/TM–2012-217332 

A Study in a New Test Facility on 

Indoor Annoyance Caused by Sonic Booms 

Jonathan Rathsam, Alexandra Loubeau, and Jacob Klos 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

Acknowledgments 

The authors thank Regina Johns for recruiting and scheduling test subjects, as well as 

administering hearing tests. 

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official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics 

and Space Administration. 
Abstract

A sonic-boom simulator at NASA Langley Research Center has been constructed

to research the indoor human response to low-amplitude sonic booms. The research

goal is the development of a psychoacoustic model for individual sonic booms to

be validated by future community studies. The study in this report assessed the

suitability of existing noise metrics for predicting indoor human annoyance. The test

signals included a wide range of synthesized and recorded sonic-boom waveforms.

Results indicated that no noise metric predicts indoor annoyance to sonic-boom

sounds better than Perceived Level, PL. During the study it became apparent that

structural vibrations induced by the test signals were contributing to annoyance, so

the relationship between sound and vibration at levels of equivalent annoyance has

been quantified.

1
Contents

1 Introduction 3

2 Facility and Sound Generation Mechanism 4

3 Test Signals 5

4 Test Method 8

5 Analysis of Results 9

5.1 Objective Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 9

5.1.1 Acoustic Measurements . . . . . . . . . . . . . . . . . . . . . 9

5.1.2 Vibration Measurements . . . . . . . . . . . . . . . . . . . . . 9

5.2 Subjective Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . 13

5.2.1 Comparison of Noise Metrics . . . . . . . . . . . . . . . . . . 13

5.2.2 Potential Imperfect Modeling of Loudness . . . . . . . . . . . 14

5.2.3 Multimodal Annoyance Response to Loudness and Vibration 15

6 Conclusions 19

A Loudness Levels of Signals 22

B Signal Processing Flow Chart 27

2
1 Introduction

Advances in aircraft design techniques suggest future aircraft with a sonic boom

quiet enough to be acceptable for overland flight. NASA has set a goal to create

a validated psychoacoustic model to assess the indoor annoyance caused by lowamplitude sonic booms. The model will inform the development of an outdoor,

noise-based regulation for low-amplitude sonic boom exposure. The study reported

here was conducted in an indoor sonic-boom simulator at NASA Langley Research

Center. Its primary intent was to evaluate the performance of existing noise metrics

in predicting indoor annoyance to a wide range of sonic-boom signals. During the

study it became apparent that structural vibrations induced by the test signals were

contributing to annoyance, so the relationship between sound and vibration at levels

of equivalent annoyance has been quantified.

The link between structural vibration and annoyance is well-documented in field

studies of community reactions to sonic booms. In one study, 93% of 1145 residents

surveyed reported “interference with ordinary living activities” due to “shaking of

the house”, and 38% reported annoyance due to “shaking of the house” [1]. A

more recent field study indicated that 75% - 95% of surveyed residents reported

noticing rattles or vibration associated with sonic booms [2]. A list of community

surveys on reactions to sonic booms can be found in [3]. Although vibration has

been linked with indoor annoyance in these field studies, it has not previously been

investigated in controlled laboratory studies. Below are summaries of the main

existing laboratory studies on indoor annoyance caused by sonic boom and blast

noise.

A study in a previous laboratory facility was conducted on indoor annoyance

caused by blast noise [4]. The blast noise was simulated by a large acoustic piston, produced by stretching a heavy rubber membrane across a large shake table

of dimensions 12 ft by 12 ft. In the same large room that housed the acoustic

piston, a house mock up was constructed for test subjects. The house mock up

was vibration-isolated from the shake table, so vibration was either nonexistent or

barely perceptible. A paired-comparison test method was used to quantify annoyance caused by blast noise with and without rattle noise. It was found that the

reference signal had to be increased by 6 - 13 dB to yield the same annoyance as the

test signal in the presence of rattle. The only metrics analyzed in the study were

A-weighted and C-weighted Sound Exposure Level.

In another study, sound-reproduction systems were installed in private residences

so annoyance caused by sonic-boom waveforms could be measured with high situational realism [5]. The test apparatus was not intended to control or measure

vibration and rattle, so these variables were not considered in the analysis. A category scaling test method was used, and the data was analyzed using regression and

correlation. Equivalent annoyance resulted when individual event level was adjusted

by 3 dB per halving or doubling of number of events. This so-called “energy addition

theory” was found applicable to sonic booms even when they occurred relatively infrequently during the day. Results indicated that Perceived Level Mark VII (PL) [6]

was a significantly better predictor of annoyance than other noise metrics. However,

no time-varying metrics were studied.

3
A previous study at NASA Langley Research Center was conducted using a

small, loudspeaker-driven booth for reproducing outdoor sonic-boom waveforms.

A filter was applied to outdoor waveforms to simulate the effects of transmission

through structural walls [7]. A magnitude-estimation technique was used, and the

data was analyzed via regression and correlation. Vibration and rattle were nonexistent in the test apparatus. The key finding in this study was that loudness and

annoyance ratings were equivalent for outdoor signals, while annoyance ratings were

higher than loudness ratings for indoor signals. Based on this result, subjects in the

current study were asked to rate annoyance instead of loudness. Another key result

was that Perceived Level (PL) was found to be the best predictor of annoyance for

indoor and outdoor booms.

A fourth study was conducted using a simulator with a demountable partition,

which allowed both exterior and interior sonic booms to be simulated [8]. The study

investigated the increment in noise metric value by which reference signals had to

be increased to maintain subjective equality with sonic booms at increased levels.

The ratio of required increase in reference signal level to increase in sonic boom

level is called the relative growth rate of annoyance. The key finding was that the

relative growth rate of annoyance depended on the reference sound. Relative growth

rates of annoyance were typically 2 : 1 between either broadband or mid-frequency

references and sonic booms, but the relative growth rate was 1 : 1 when the reference

was an octave-band noise burst centered at 63 Hz. This result suggests that the lowfrequency content of sonic booms, rather than the impulsiveness, controls annoyance.

In contrast to [4], results indicated that the reference sound had to be increased by

only 5 dB to yield the same annoyance as the test signal in the presence of rattle.

The study reported in this document was the second study conducted in the

facility. The first study analyzed indoor annoyance caused by sonic booms, but only

three test signals were played at seven amplitudes each. Fewer test signals had to

be used because each subject listened at all three listener locations to maximize

the number of different subjects responding at each location. Although the study

produced other useful results, the authors concluded that three test signals were

insufficient for the purpose of comparing noise metrics. In the current study the

subjects did not rotate seats, so more waveforms could be played back to each

group of subjects. A NASA Technical Memorandum documenting the first study is

currently being prepared.

2 Facility and Sound Generation Mechanism

The current test facility was built specifically for testing indoor annoyance caused

by sonic booms. Sonic-boom waveforms can be played over two arrays adjacent to

two exterior walls of the small room shown in Fig. 1. Only one array was used for

this study. The room has dimensions 12 ft x 14 ft x 8.5 ft and conventional wood

and drywall construction. The arrays of loudspeakers create a desired pressure

loading on the exterior surfaces of the wall that drives the structure into vibration,

and the structural vibrations couple with the interior volume. As a result the sound

transmission from exterior to interior occurs much as it would in the field. The inside

4
of the facility is furnished as a living room and seats three test subjects for each test

session, as shown in Fig. 2. Subjective judgments are logged on netbook computers

and monitored in real time via wireless local area network. Sound-absorbing wedges

were placed inside the facility’s two closets to minimize room reverberation time. A

document detailing the facility is currently being prepared and will be available as

a NASA Technical Memorandum.

Figure 1: A loudspeaker array is shown as attached to the exterior of the facility.

The array used in the current study is not visible in this photo and contains 24 cells

instead of 28 cells as shown here.

Figure 2: Listener locations within the facility.

3 Test Signals

A total of 23 test signals were used. The calculated loudness levels of these signals

are listed in Tables A1 - A4 in App. A. A signal processing flow chart for the

preparation of test signals is given in App. B. Five of the signals were low-amplitude

5
LP Filter Order

2 3 5

Corner Frequency

[Hz]

9 1 7 -

15 2 8 12

27 3 9 13

35 - 10 14

45 4 11 15

75 5 - -

110 6 - -

Table 1: Matrix of band-pass-filtered synthesized signals. Signals used in the study

are designated with their signal number in Tables A1 - A4 in App. A. All signals

are filtered with a fourth-order high-pass Butterworth filter.

N-waves measured with microphones on ground boards far from buildings and other

vertical surfaces [9]. The duration of these N-waves was approximately 150 ms with

rise times between 1 ms and 7 ms. These signals are numbered 16 − 20 in Tables

A1 - A4. The remaining 18 test signals were synthesized sonic booms. Two of the

synthesized booms were 200-ms-duration N-waves, with rise times of 6 ms and 9

ms. The rise time is the time elapsed as the shock grows from 10% to 90% of its

maximum amplitude. The desired rise time of these two signals is incorporated into

the synthesized waveform at the front and rear shocks according to Eq. 1 [10]

p(t) = ∆p

2



1 + tanh 

t

T

 (1)

where p(t) is the instantaneous pressure, ∆p is shock amplitude, t is the time, and T

is the rise time. This synthetic procedure for introducing a rise time into a nearlyinstantaneous shock is known as “tanh-thickening.” The two signals with rise times

of 6 ms and 9 ms are numbered 22 and 23 in Tables A1 - A4 and belong to the family

of signals used in the first study conducted in the facility. A third synthesized signal,

number 21, is the ground signature predicted for a low-boom aircraft configuration.

The remaining 15 signals were constructed to systematically vary spectral content in order to identify differences among metrics, as described below. To motivate

the method of constructing these 15 signals, it is necessary to consider first the

range of noise metrics. The primary difference among the following metrics is their

weighting function, particularly at low frequencies: Perceived Level (PL) [11], Aand C-weighted Sound Exposure Level (ASEL and CSEL) [12], Stationary Loudness (MGSL) [13], Time-Varying Loudness (MGTVL) [14], Zwicker Loudness Level–

diffuse (LLZd) [15], and Perceived Noise Level (PNL) [16]. If signals are designed

with varied low-frequency content, it is possible to expose these differences and

reduce correlations among metrics.

Each synthetic signal began as two delta functions separated by 200 ms, as

shown in Fig. 3(a). Separate low-pass and high-pass Butterworth filters with the

same corner frequencies, f0, were successively applied to yield a waveform as in

Fig. 3(b). The resulting spectrum looked like a band-pass filter centered about

6
0 0.2 0.4 0.6

0

0.2

0.4

0.6

0.8

1

Time [s]

Amplitude

0 0.2 0.4 0.6

Time [s]

Amplitude

Frequency [Hz]

ESD [dB]

f

0

9 15 27 35 45 75 110

Frequency [Hz]

ESD [dB]

2

3

5

FFT

FILTERS

APPLIED

(REPEAT)

(a)

(d)

(b)

(c) 10 dB 10 dB

Figure 3: Method for constructing filtered-impulse test signals.

CSEL ASEL LLZd MGSL TVL PLmod PNL

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(Metric)

Correlation Coefficient

Loc 1

Loc 2

Loc 3

Figure 4: Correlations between PL and other noise metrics for listener locations 1 -

3.

7
frequency f0, as shown in Fig. 3(c). This procedure was repeated at various corner

frequencies, indicated with vertical lines in Fig. 3(d). All signals were filtered with a

fourth-order high-pass Butterworth filter, and a low-pass Butterworth filter of either

second, third, or fifth order. The procedure resulted in a full matrix of 21 signals

shown in Table 1. These signals were subsequently down-selected to the test sounds

numbered 1 − 15 in Table 1. The signals were down-selected to keep the test length

within the attention span of an average subject.

Each test signal was played at six amplitudes. The amplitudes were intended

to be evenly distributed above and below the equality point. A pilot test with 12

subjects was conducted to ensure that the range of amplitudes for each test signal

was roughly centered about the amplitude of subjective equality with the reference.

The range of amplitudes was chosen to make signals loud enough to be audible, but

not so loud that they caused audible creaks or rattles in the test facility. A separate

pilot test with 12 subjects showed that equality point remained consistent for two

different reference sounds.

After the study it became apparent that test signals were mistakenly played

with inverted polarity. The error does not affect calculated noise metrics because

all metrics are based on signal energy, or pressure-squared quantities. Also, the

authors listened to boom signals with intended and inverted polarity and concluded

that there were no audible differences in the test signals as heard inside the facility.

In the future, the polarity of the desired waveforms will be confirmed.

In summary, a suite of signals was designed with the requirement of maintaining

a sonic-boom-type character of a front shock and a rear shock in the time domain.

The correlation of several metrics with PL across all 23 test signals is shown in Fig.

4. A-weighted Sound Exposure Level (ASEL) has a high correlation with PL, but

for most other noise metrics the correlation is not strong. As a result, differences

are expected among metrics in their capacity to predict annoyance.

4 Test Method

The test method was paired-comparison with a reference sound. The reference

sound was the tanh-thickened N-wave of duration 200 ms and rise time of 6 ms,

i.e. signal 22 at amplitude 3 in App. A. This sound was also used as a test sound.

The method requires that subjects hear a pair of sounds and choose which sound is

more annoying. Each pair consisted of the reference sound at a constant amplitude

and a test sound at one of six amplitudes. Subjects heard each pair in both orders,

A-B and B-A. The 23 test sounds, each replayed at 6 amplitudes, paired with the

reference in both orders, yielded 276 pairs, which took approximately 1 hour and

15 minutes to judge. Each group of test subjects heard the pairs presented in a

different random order. The simulator seats three subjects, and ten groups were

tested for a total of 30 subjects. Subjects remained in the same seat throughout the

test.

Thirty subjects (10 male, 20 female) participated in the study. The subjects were

obtained from a subject pool of local residents and were paid for their participation

in the study. Ages of the test subjects ranged from 18 to 64 years with a median

8
age of 41 years. All subjects were audiometrically screened prior to the test to

demonstrate auditory acuity within 40 dB of audibility thresholds for tones from

500 Hz to 6 kHz.

5 Analysis of Results

5.1 Objective Data Analysis

5.1.1 Acoustic Measurements

To estimate the range of exposure, the test signals were measured at six locations

within the simulator: current listener locations 1 - 3, and proposed listener locations,

4 - 6. The coordinates of each microphone location are given in Table 2, and

shown in Fig. 5. Single half-inch microphones were placed approximately at seated

ear height. Head and torso effects were therefore not taken into account. Each

acquired sound represents the time-domain average of 10 repeats to reduce effects of

background noise and microphone thermal noise inherent in any single measurement.

A fading window was applied to each measured waveform prior to Fourier Analysis

to minimize spectral leakage. The window function was 2 seconds in length, as

shown in Fig. 6. It consisted of the first half of a 1-sec-duration Hanning window,

followed by one second of unity gain, followed by the second half of a 1-sec-duration

Hanning window. The window was aligned as needed to position the entire boom

signal within the unity portion of the window.

Analysis of subjective response data is least complicated when each signal causes

the same loudness level at all listener locations. However, the variation in loudness

levels among listener locations 1 - 3 for a single test sound was as much as 10 PL dB

due to varied distance from the wall with the active loudspeaker array, as shown in

Fig. 5, as well as due to room acoustics. For the current single-array configuration,

an analysis of sound levels measured at the six locations was performed to determine if listener locations could be found with more uniform exposure. A repeated

measures ANOVA test was conducted on the loudness level (PL) of all 138 signals

at all six locations. Mauchly’s Test of Sphericity [17] yielded a significant result,

indicating that the covariance in loudness level among the locations is not uniform.

However, the F-statistic in the ANOVA test was invariant whether or not it was

corrected for violations of sphericity. The results indicated a significant difference

in loudness level among all six locations, F(5, 685) = 783.12, p ≤ 0.0001. Post-hoc

Bonferroni comparisons across the listener locations indicated that the mean loudness level of signals at locations 1 and 5 is not significantly different at the 95%

confidence level. By contrast, the mean loudness level of signals at all other locations is different. Subsequent measurements have shown that loudness exposure is

more uniform in the room with both arrays active.

5.1.2 Vibration Measurements

Subjects were asked in post-test conversations if certain types of signals were consistently more annoying than others. Subjects responded that they were annoyed

if they “felt the room shake” or when it “sounded like someone had fallen in the

9
M1

M2

M3

M4

M5

M6 A3

A2

A1

ACTIVE ARRAY

Figure 5: Interior of simulator indicating location of measurement transducers. Location coordinates are listed in Table 2.

room next-door.” The authors interpreted these comments as references to vibration. Based on this feedback, the vibration caused by the 23 test signals at 6 levels

was measured on the ground at the foot position of each listener location. The accelerometer locations are listed in Table 2 and shown in Fig. 5. Each test sound was

repeated 10 times and averaged to reduce effects of background noise inherent in

any single measurement. The measured vibration data was filtered by a weighting

function, wk, shown in Fig. 7. The perception threshold for whole-body vibrations

is a wk-weighted peak amplitude of 1.5

cm

s

2 [18].

The vibration at the floor was measured with and without approximately 150-

lb weights in all seats to determine whether the weight of human subjects had an

observable effect on floor vibrations. The wk-weighted peak accelerations measured

with and without loading at all three listener locations were compared using a twofactor repeated-measures ANOVA analysis. The two-factors were listener location

and loading condition. The repeated-measures ANOVA technique was chosen because the same test signals were analyzed at each listener location. The analysis

simultaneously tested three hypotheses: 1) measured vibration did not vary with

10
Sensor x [m] y [m] z [m]

Mic 1 3.47 (11’ 5”) 1.89 (6’ 2”) 1.13 (3’ 8”)

Mic 2 2.33 (7’ 8” ) 2.71 (8’ 11”) 1.13 (3’ 8”)

Mic 3 1.21 (4’ 0”) 2.77 (9’ 1” ) 1.11 (3’ 8”)

Mic 4 2.37 (7’ 9”) 0.57 (1’ 10”) 1.10 (3’ 7”)

Mic 5 1.78 (5’ 10”) 0.57 (1’ 10”) 1.11 (3’ 8”)

Mic 6 1.19 (3’ 11”) 0.52 (1’ 8”) 1.10 (3’ 7”)

Accel 1 2.95 (9’ 8”) 1.63 (5’ 4”) 0 (0’ 0”)

Accel 2 2.13 (7’ 0”) 2.13 (7’ 0”) 0 (0’ 0”)

Accel 3 1.22 (4’ 0”) 2.13 (7’ 0”) 0 (0’ 0”)

Table 2: Location coordinates of measurement sensors. Microphones were placed

at ear height of seated subjects and accelerometers were attached to the hardwood

floor. The coordinate origin is shown in Fig. 5.

0 1 2 3 4 5 6

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time [s]

Amplitude

Window

Signal

Windowed Signal

Figure 6: Time-domain fader window applied to an interior microphone measurement.

listener location, 2) measured vibration did not vary with loading condition, and 3)

there was no interaction effect between loading condition and listener location. For

each hypothesis test, Mauchly’s Test of Sphericity [17] yields a significant result, indicating that the covariance in wk-weighted peak acceleration among the conditions

is not uniform. However, the resulting F-statistic is invariant whether or not it is

corrected for sphericity violations.

The result of the first hypothesis test indicates a significant difference in measured vibration at different listener locations, F(2, 274) = 96.380, p ≤ 0.0001. The

result of the second hypothesis test indicates a significant difference in measured

vibration with and without loading, F(1, 137) = 61.496, p ≤ 0.0001. The result

11
10−1 100

101102

−50

−40

−30

−20

−10

0

10

Frequency [Hz]

Magnitude [dB]

Figure 7: Weighting function wk for whole-body vibration [18].

from the third hypothesis test indicates an interaction effect between listener location and loading condition, F(2, 274) = 18.439, p ≤ 0.0001. Fig. 8 illustrates this

interaction effect and other trends in the measured data. The loading had almost

no effect on vibration at listener location 2, but the loading did cause a measurable

difference in vibration at locations 1 and 3. Accelerometer 2 was located at the

center of the room in the x-direction, so it probably lies on a nodal line for significant vibrational modes. The results indicate that vibration measurements should

be made with loading to approximate the weight of human subjects. The results

also indicate that vibration cannot be considered uniform across listener locations.

1 2 3

0

0.5

1

1.5

2

2.5

3

3.5

4

Listener Location

Mean 

wk−weighted peak acceleraton [cm/s

2

]

Unloaded

Loaded

Figure 8: Mean measured vibration at two levels of loading across three listener

locations.

12
5.2 Subjective Data Analysis

5.2.1 Comparison of Noise Metrics

The paired-comparison test method results in the proportion of subjects more annoyed by each test signal than by the reference signal, or simply the “percent more

annoyed”. Each test signal is played at six amplitudes. Generally the percent more

annoyed increases with signal amplitude. When percent more annoyed is plotted

against test-signal level, the data can be fitted by a logistic regression curve, which

has an S-shape, as shown in Fig 9. The point on the curve at which percent more

annoyed equals 50% is called the equality point, or EP. It represents the level of

subjective equality between the test signal and the reference signal.

EP 0

20

40

60

80

100

(Noise Metric)

% More Annoyed

Figure 9: The subjective responses were fitted by a logistic regression curve with an

S-shape. The equality point, EP, is the level at which 50% of the respondents are

more annoyed by the test signal.

A B C

0

20

40

60

80

100

(Noise Metric)

% More Annoyed

Figure 10: The notional metric groups the equality points B and C close together,

but not equality point A. The figure of merit, M, quantifies the spread in equality

points.

13
A perfect noise metric would yield the same EP for all signals judged equally

annoying. The predictive capability of the metric is, therefore, quantified by the

numeric spread of equality points for the 23 test sounds. The narrower the spread

in equality points, as illustrated in Fig. 10, the better the predictive capability of

each noise metric.

As mentioned earlier, the levels from a single test sound varied by up to 10

PL dB across listener locations due to room acoustics and distance from the array.

The variation in levels prevents direct comparison of equality points across listener

locations. Instead equality points are compared based on their deviation from the

reference equality point. The reference sound was used as a test sound, compared

with itself, and the resulting equality point was recorded. The reference equality

point at each location was then subtracted from the equality point of each test signal

at that location. This normalization by the reference equality point enabled direct

comparison of equality points across listener location.

The normalized differences were averaged across all listener locations to produce

a figure of merit M, as shown in Eq. 2. In the equation, EP is the equality point

for the reference signal or for a test signal 1 - 23. The lower the value of M, the

better the predictive capacity of the metric. The results for some common metrics

are shown in Fig. 11. The metric PLmod is explained in Sec. 5.2.2. The error

bars represent 95% confidence intervals about the figure of merit, M, and were

constructed using a bootstrap resampling technique [19]. However, the error bars

cannot be used to compare the metrics directly.

M =

X

3

location=1

X

23

signal=1









EPsignal − EPref









location

[dB] (2)

An ANOVA procedure was used to compare the figures of merit, M. A repeatedmeasures technique is not chosen in this case because the analysis is conducted

across different metrics. There is a significant difference across figures of merit, M,

F(7, 520) = 6.47, p ≤ 0.0001. Post-hoc Bonferroni comparisons indicate that the

difference in M is not significant among ASEL, PL, PLmod, and MGSL. In other

words, these metrics were the best predictors of equivalent annoyance for these

test signals. The value of M for all other metrics is significantly greater than for

ASEL. The similarity between ASEL and PL is expected due to the high correlation

between ASEL and PL as shown in Fig. 4.

5.2.2 Potential Imperfect Modeling of Loudness

The equality point is examined separately for each of the filtered-impulse test signals

indicated with a numeral in Table 1. If the PL metric were predicting annoyance

with no error, each equality point would occur at the same loudness level for all

signals. As shown in Fig. 12(a), for a fifth-order low-pass filter, the equality point

increases monotonically with center frequency at each listener location, indicating a

systematic error in the performance of PL. This trend suggests that the weighting

function may overemphasize low frequencies. The trend is also present to a lesser

extent for the third-order and second-order low-pass filtered sounds. Signals pro14
duced with lower-order filters contain more high-frequency energy, as shown in 3(d),

which tends to obscure the differences.

The authors developed two hypotheses to explain the observation that equality

point increases with center frequency. The first hypothesis is that the PL metric

is improperly modeling low-frequency annoyance. The PL metric is based on the

Sone curves which are designed to model the sensitivity of the human ear. Stevens,

who developed PL, extended the Sone curves in a calculation procedure called Mark

VII so all curves approach a value of 160 dB at 1 Hz [11], shown in Fig. 13(a). It

seems unlikely that this is a true representation of the human hearing system. As an

experiment, the limiting level for the Sone curves was reduced from 160 dB to 115

dB at 1 Hz, as shown in Fig. 13(b). There was no experimental evidence to suggest

a value of 115 dB. Calculating the PL using the modified Sone curves is referred to as

modified PL, or PLmod, throughout this document. The loudness levels calculated

by Modified PL are shown in Fig. 12(b). Interestingly, the monotonic relationship

between equality point and filter center frequency observed in Fig. 12(a) does not

exist for Modified PL. The authors recognize that any improvement in loudness

modeling achieved by modifying the Sone curves was not captured by the figure

of merit, M, which was used to compare the metrics. While these results suggest

imperfect modeling of low-frequency loudness by PL Mark VII, results from a more

focused test design would be needed to confirm this claim.

ASEL PL PLmod MGSL LLZd MGTVL CSEL PNL 2

3

4

5

6

7

8

Loudness Metric

Figure of Merit, M [dB]

Figure 11: Figure of merit, M, for each noise metric. The error bars indicate a 95%

confidence interval about the mean based on a bootstrap resampling technique [19]

using 10,000 resampled points.

5.2.3 Multimodal Annoyance Response to Loudness and Vibration

A second hypothesis to explain the relationship between equality point and filter

center frequency arises when annoyance is considered as a multimodal response.

That is, annoyance is affected not only by sound, but also vibration, as demonstrated previously for railway noise [20] as well as helicopter over-flight noise [21].

If annoyance is influenced by both sound and vibration, then test signals producing

15
15 27 35 45

30

35

40

45

50

55

60

65

70

Pass−band Center Frequency [Hz]

Equality Point for PL [dB]

loc 1

loc 2

loc 3

(a) PL

15 27 35 45

30

35

40

45

50

55

60

65

70

Pass−band Center Frequency [Hz]

Equality Point for PLmod [dB]

Loc 1

Loc 2

Loc 3

(b) Modified PL

Figure 12: The equality point in PL for signals with fifth-order low-pass filtering.

Panel (a) shows PL, and Panel (b) shows modified PL. The error bars indicate a

95% confidence interval about the mean based on the logistic regression curve fit.

Horizontal lines represent the equality point of the reference signal at each location.

16
101

102103104

40

60

80

100

120

140

160

Frequency [Hz]

Band Pressure Level [dB]

1

2

5

10

20

50

100

(a) Existing Sone Curves

101102103104

40

60

80

100

120

140

160

Frequency [Hz]

Band Pressure Level [dB]

1

2

5

10

20

50

100

(b) Modified Sone Curves

Figure 13: Existing [11] and modified Sone curves. Sone index is indicated on each

curve.

17
0 2 4 6 8

40

45

50

55

60

65

Peak wk−weighted acceleration [cm/s2]

Loudness Level [dB PL]

Ref, Loc 1

Ref, Loc 2

Ref, Loc 3

Figure 14: The plot of equality points, expressed in PL dB, versus vibration including best-fit lines, plotted separately by listener location. All points represent

equivalent annoyance.

vibration could be judged equivalent at lower sound levels than signals not causing

perceptible vibration. This trend is observed in the experimental data plotted in

Fig. 14.

The plot of equality points, expressed in PL dB, against wk-weighted peak vibration, is shown in Fig. 14. All data points for each listener location represent levels

of equivalent annoyance caused by the test signals. Each color represents a different

listener location. The triangular data points represent the reference signal at each

listener location. The loudness level at the equality point, on the y-axis, is determined from the logistic regression procedure described in Sec. 5.2.1. No signal was

played exactly at the equality level so vibration values are determined using interpolation. Linear interpolation of the peak acceleration is appropriate because peak

acceleration increases nearly linearly with sound level in this range. The perception

threshold of 1.5

cm

s

2 [18] for full-body vibration is indicated with a dotted vertical

line. At vibration levels below threshold, the PL values for subjectively equivalent

sounds vary less than 5 dB in general from the reference loudness level, indicated

by triangular data points. Sounds above the vibration threshold are subjectively

equivalent at lower PL values, as much as 10 - 14 dB below the reference level.

All data points above the vibration perception threshold represent combinations

of vibration and loudness level that may produce a multimodal annoyance response.

Therefore, a best-fit line through these points estimates the trade-off between vibration and loudness level as causes of annoyance. The unshaded blue point is an

outlier on the loudness level scale. It was not used in computing the best-fit line.

18
Location Slope Std. Error 95% Confidence Interval

1 -3.36 .065 [-3.23, -3.49]

2 -3.92 .045 [-4.01, -3.83]

3 -1.84 .022 [-1.89, -1.80]

Table 3: Slopes of the regression lines in Fig. 14, indicating the magnitude of the

trade-off between vibration and sound level. The confidence interval is calculated

as the slope ± 1.96 × standard error. The units are dB

cm

s

2

.

A calculation procedure was used that accounts for error in both the vibration and

loudness level estimates [22]. The estimated slope of each line is given in Table 3.

As indicated, the uncertainty in the measured results yields a trade-off across all

three listener locations with 95% confidence of −1.80 to −4.01 dB

cm

s

2

. The fact that

all three correlations are negative suggests that test signals producing vibration are

indeed judged equivalent at lower levels than signals not causing vibration.

6 Conclusions

A study has been conducted to evaluate the performance of noise metrics in predicting indoor annoyance to a suite of recorded sonic booms and synthesized sonicboom-type waveforms. Most synthesized signals were designed to have the impulsive

character of a sonic boom but contain energy only within a desired spectral region.

This mixture of recorded and synthesized test signals provided enough spectral variation to distinguish the performance of several common noise metrics. The results

indicate that no metric predicts equivalent annoyance more reliably at the 95% confidence level than Perceived Level (PL). This result agrees with previous results in

the literature [5, 7], although the cited studies analyzed neither Stationary Loudness nor Time-Varying Loudness. For the sounds tested in this study, A-weighted

Sound Exposure Level, Stationary Loudness, and Time-Varying Loudness all predict

equivalent annoyance as well as, but not better than, PL.

Because all test signals were compared with a reference at a single level, the

results do not indicate how well the metrics describe the growth rate of annoyance. Absence of a growth-rate assessment may be viewed as a disadvantage of

testing many signals against a single reference sound. The advantage of the technique was an in-depth investigation of a single point on the loudness function. The

error in predicting subjective annoyance using PL was not random but related to

the signal’s low-frequency pass-band. Signals with lower-frequency content were

found equivalently annoying at lower loudness levels. Analysis indicated two possible causes of this phenomenon. The first possible cause is improper modeling of

loudness at low frequencies. When the slope of the Sone curves at low frequencies

was dramatically reduced, the monotonic relationship between equality point and

filter center frequency ceased to exist. The second possible cause was the presence

of vibration, which added an additional mode to the annoyance response of test

19
subjects. For these test sounds a trade-off was found of -1.80 to -4.01 dB

cm

s

2

at the

95% confidence level for equivalent annoyance. In other words, above the vibration

perception threshold, 1 PL dB was equivalent to between 1.80 cm

s

2 and 4.01 cm

s

2 of

wk-weighted peak vibration. Focused follow-on tests are needed to clarify the influence of vibration on annoyance versus possible improper modeling of low-frequency

loudness.

It was observed that the exposure was not consistent across listener locations

in the indoor simulator when the test signals were played over a single loudspeaker

array. Differences in loudness level were due to room acoustics as well as varied

receiver distance from the wall with the active array. Since the completion of this

study a second loudspeaker array adjacent to a second exterior wall has been activated for use in future tests. Subsequent measurements have shown that loudness

exposure is more uniform in the room with both arrays active. Seating locations for

future tests will be changed as necessary to achieve the most uniform exposure. If

exposure is uniform across listener locations then subjective responses can be compared directly among test locations without the need to normalize by the reference

signal level.

References

1. C. W. Nixon and P. N. Borsky, “Effects of sonic boom on people: St. Louis,

Missouri, 1961–1962,” The Journal of the Acoustical Society of America, vol. 39,

no. 5B, pp. S51–S58, 1966.

2. J. M. Fields, “Reactions of residents to long-term sonic boom noise environments,” Tech. Rep. NASA-CR-201704, NASA Langley Research Center, June

1997.

3. F. Coulouvrat, “Review of sonic boom impacts,” Tech. Rep. HISAC-T-1-10-19,

HISAC: Environmentally Friendly High Speed Aircraft, May 2006.

4. P. D. Schomer and A. Averbuch, “Indoor human response to blast sounds that

generate rattles,” The Journal of the Acoustical Society of America, vol. 86,

no. 2, pp. 665–673, 1989.

5. D. A. McCurdy, S. A. Brown, and R. D. Hilliard, “Subjective response of people

to simulated sonic booms in their homes,” The Journal of the Acoustical Society

of America, vol. 116, no. 3, pp. 1573–1584, 2004.

6. K. P. Shepherd and B. M. Sullivan, “A loudness calculation procedure applied

to shaped sonic booms,” Tech. Rep. NASA-TP-3134, NASA Langley Research

Center, November 1993.

7. J. D. Leatherwood and B. M. Sullivan, “Recent laboratory studies of loudness

and annoyance to sonic booms,” Tech. Rep. NASA-TM-107756, NASA Langley

Research Center, May 1993.

20
8. S. Fidell, L. Silvati, and K. Pearsons, “Relative rates of growth of annoyance of

impulsive and non-impulsive noises,” The Journal of the Acoustical Society of

America, vol. 111, no. 1, pp. 576–585, 2002.

9. J. Edward A. Haering, I. Larry J. Cliatt, T. J. Bunce, T. B. Gabrielson, V. W.

Sparrow, and L. L. Locey, “Initial results from the variable intensity sonic boom

propagation database,” in 14th AIAA/CEAS Aeroacoustics Conference (29th

AIAA Aeroacoustics Conference), pp. 1–58, May 2008.

10. J. A. Page, K. J. Plotkin, and C. Wilmer, “PCBoom version 6.6: Technical

reference and user manual,” Tech. Rep. WR 10-10, Wyle Report, March 2010.

11. S. S. Stevens, “Perceived level of noise by Mark VII and decibels (e),” The

Journal of the Acoustical Society of America, vol. 51, no. 2B, pp. 575–601,

1972.

12. ANSI, American National Standard Specifications for Integrating-Averaging

Sound Level Meters, 1997. ANSI S1.43-1997.

13. B. C. J. Moore, B. R. Glasberg, and T. Baer, “A model for the prediction of

thresholds, loudness, and partial loudness,” J. Audio Eng.Soc, no. 4, pp. 224–

240, 1997.

14. B. R. Glasberg and B. C. J. Moore, “A model of loudness applicable to timevarying sounds,” J. Audio Eng. Soc, vol. 50, no. 5, pp. 331–342, 2002.

15. ISO, Acoustics - Method for calculating loudness level, 1975. ISO 532-1975.

16. K. D. Kryter, “Scaling human reactions to the sound from aircraft,” The Journal

of the Acoustical Society of America, vol. 31, no. 11, pp. 1415–1429, 1959.

17. J. W. Mauchly, “Significance test for sphericity of a normal n-variate distribution,” The Annals of Mathematical Statistics, vol. 11, no. 2, pp. 204–209,

1940.

18. ISO, Mechanical vibration and shock - Evaluation of human exposure to wholebody vibration–Part 1:General requirements, 1997. ISO 2631-1:1997(E).

19. B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap. New York:

Chapman & Hall, 1993.

20. H. V. C. Howarth and M. J. Griffin, “The annoyance caused by simultaneous

noise and vibration from railways,” The Journal of the Acoustical Society of

America, vol. 89, no. 5, pp. 2317–2323, 1991.

21. P. D. Schomer and R. D. Neathammer, “The role of helicopter noise-induced

vibration and rattle in human response,” The Journal of the Acoustical Society

of America, vol. 81, no. 4, pp. 966–976, 1987.

22. D. York, N. M. Evensen, M. L. Martinez, and J. D. B. Delgado, “Unified equations for the slope, intercept, and standard errors of the best straight line,”

American Journal of Physics, vol. 72, no. 3, pp. 367–375, 2004.

21
Appendix A

Loudness Levels of Signals

Tables A1, A2, and A3 contain the Perceived Level [dB] and subjective judgments for all signals at listener locations 1, 2, and 3, respectively. Table A4 contains

the average loudness level of each signal at the facility exterior. Acquired exterior

signals were averaged across 18 microphone locations, and a fading window was applied prior to calculating loudness level, as described in Sec. 5.1.1. The descriptions

of signals 1 − 15 are given in Table 1. Signals 16 − 20 were field measurements.

Signal 21 is the predicted ground signature from a supersonic vehicle configuration,

and signals 22 and 23 are tanh-thickened N-waves with rise times of 6 and 9 ms,

respectively.

22
Amplitude Index

1 2 3 4 5 6

Test Signal

1 55.3—7 57.2—8 59.2—11 61.1—12 63.2—15 64.9—18

2 51.4—4 53.5—4 55.5—7 57.6—10 59.6—11 61.4—11

3 50.5—7 52.5—5 55.5—9 57.5—12 59.3—10 61.2—11

4 52.6—5 55.5—6 57.3—7 59.2—7 61.1—13 63.0—11

5 51.2—5 53.1—5 56.1—7 58.0—5 59.9—12 61.8—12

6 52.4—6 54.4—5 56.4—9 58.4—8 60.3—12 62.3—12

7 51.2—3 51.6—10 53.3—10 55.5—10 57.2—18 58.4—16

8 54.7—7 56.5—12 58.4—15 60.6—17 62.4—18 64.5—20

9 51.4—1 53.4—3 56.3—6 58.1—12 60.2—13 62.3—15

10 55.6—7 57.6—6 59.6—9 61.7—12 63.9—17 66.0—14

11 55.1—5 57.1—4 59.1—8 61.2—9 63.3—15 65.5—14

12 48.2—7 50.2—9 76.8—14 78.7—18 80.5—16 82.2—18

13 52.1—5 53.8—9 57.0—14 59.3—15 61.7—18 64.1—19

14 55.0—6 57.2—10 59.4—16 64.5—13 63.7—17 66.0—19

15 55.0—2 57.2—3 59.4—6 61.7—9 64.0—13 66.3—16

16 53.6—4 56.3—5 58.2—7 60.0—14 61.9—15 63.8—15

17 51.8—7 54.5—2 56.5—5 58.4—7 60.4—12 62.2—15

18 49.6—4 51.7—3 54.7—6 56.7—12 58.8—15 60.9—12

19 48.1—6 50.2—3 53.4—7 55.5—10 57.7—10 59.7—14

20 49.4—5 51.5—5 54.6—5 56.6—7 58.7—11 60.8—13

21 50.3—4 52.3—5 55.1—8 56.9—11 58.7—12 60.5—17

22 56.3—8 58.3—6 60.3—9 63.4—15 65.5—18 67.6—19

23 53.3—6 55.2—4 57.2—10 60.0—13 61.9—13 63.8—17

Table A1: Listener Location 1. Each of the 23 test signals was played at 6 amplitudes. In each cell, the first number is the Perceived Level [dB] of the signal. The

second number is the number of responses out of 20 indicating the test signal was

more annoying than the reference signal. Test signal 22 at amplitude 3 was also

used as the reference sound.

23
Amplitude Index

1 2 3 4 5 6

Test Signal

1 50.8—8 52.9—11 55.0—13 56.8—15 59.0—19 60.6—18

2 46.6—2 48.9—4 51.1—9 53.4—12 55.4—10 57.3—18

3 45.8—4 48.1—3 51.4—7 53.6—6 55.5—11 57.5—11

4 48.6—6 51.9—5 53.8—11 55.7—10 57.7—14 59.6—13

5 47.1—7 49.1—6 52.3—9 54.2—6 56.1—13 57.8—12

6 48.4—5 50.4—4 52.4—10 54.3—9 56.2—13 58.0—13

7 43.5—5 44.3—3 46.2—7 49.0—12 51.1—16 52.4—18

8 47.9—7 50.0—14 51.9—15 54.1—17 55.7—19 57.9—19

9 46.6—2 48.7—3 51.6—8 53.5—9 55.5—10 57.4—14

10 51.7—3 53.7—6 55.6—4 57.6—12 59.7—18 61.8—18

11 52.1—6 54.0—3 56.0—7 58.0—9 60.0—14 62.0—18

12 40.9—8 43.0—9 45.7—16 47.4—17 49.5—16 51.0—20

13 45.6—7 47.2—9 50.1—15 52.3—18 54.5—15 56.8—20

14 50.1—10 52.0—9 54.2—9 56.2—14 58.3—18 60.5—17

15 51.3—5 53.2—7 55.4—4 57.5—9 59.7—10 61.9—17

16 49.9—4 52.6—3 54.5—7 56.4—9 58.2—12 60.2—16

17 49.2—4 51.8—8 53.7—7 55.6—9 57.6—15 59.4—19

18 45.1—5 47.4—2 50.8—8 53.0—9 55.1—12 57.1—14

19 43.7—6 46.1—7 49.6—7 51.9—5 54.2—10 56.2—12

20 45.0—4 47.3—5 50.7—3 52.9—8 55.0—5 57.0—15

21 46.7—5 48.6—6 51.3—8 53.2—13 55.0—14 56.7—17

22 52.7—5 54.6—4 56.5—9 59.5—13 61.5—18 63.6—19

23 48.8—5 50.9—4 52.9—7 55.8—17 57.6—14 59.5—20

Table A2: Listener Location 2. Each of the 23 test signals was played at 6 amplitudes. In each cell, the first number is the Perceived Level [dB] of the signal. The

second number is the number of responses out of 20 indicating the test signal was

more annoying than the reference signal. Test signal 22 at amplitude 3 was also

used as the reference sound.

24
Amplitude Index

1 2 3 4 5 6

Test Signal

1 48.2—6 50.4—4 52.6—10 54.7—12 57.0—16 58.7—20

2 43.9—1 46.1—2 48.4—3 50.8—6 53.0—11 55.1—16

3 42.9—1 45.1—2 48.4—5 50.6—4 52.6—8 54.6—10

4 45.6—2 48.9—2 50.8—4 52.7—6 54.6—9 56.5—14

5 44.5—1 46.6—3 49.7—1 51.7—6 53.5—6 55.4—10

6 46.1—0 48.1—3 50.2—2 52.1—10 53.9—7 55.7—9

7 45.2—3 46.2—9 48.0—15 50.4—17 52.2—19 53.6—19

8 49.9—9 51.3—13 53.0—19 55.2—19 57.0—20 59.2—19

9 42.3—2 44.7—0 48.3—2 50.6—6 52.9—13 55.0—17

10 47.8—3 49.9—2 51.9—7 54.0—12 56.0—13 58.0—17

11 48.5—2 50.4—1 52.4—4 54.4—8 56.3—13 58.3—17

12 46.1—7 47.7—12 49.9—16 51.7—20 53.5—20 55.2—20

13 45.9—6 47.6—7 50.7—14 52.9—14 55.2—19 57.5—20

14 47.5—6 49.5—8 51.7—10 53.7—16 55.8—18 58.1—19

15 46.0—3 48.0—3 50.1—2 52.0—3 54.1—8 56.2—16

16 46.7—1 49.7—2 51.7—4 53.5—6 55.4—12 57.4—17

17 45.9—1 48.8—3 50.8—2 52.8—8 54.8—11 56.6—12

18 42.3—2 44.6—2 48.0—6 50.3—2 52.4—8 54.4—10

19 40.8—1 43.2—1 46.7—1 49.1—3 51.5—2 53.6—9

20 42.3—1 44.7—2 48.1—4 50.3—3 52.5—6 54.5—9

21 43.5—0 45.6—1 48.7—6 50.8—12 52.7—12 54.7—18

22 49.9—0 51.9—6 53.9—9 57.1—18 59.1—18 61.3—18

23 46.4—3 48.5—1 50.6—3 53.6—11 55.5—18 57.4—18

Table A3: Listener Location 3. Each of the 23 test signals was played at 6 amplitudes. In each cell, the first number is the Perceived Level [dB] of the signal. The

second number is the number of responses out of 20 indicating the test signal was

more annoying than the reference signal. Test signal 22 at amplitude 3 was also

used as the reference sound.

25
Amplitude Index

1 2 3 4 5 6

Test Signal

1 77.2 79.2 81.2 83.1 85.2 87.1

2 73.2 75.2 77.1 79.2 81.2 83.2

3 72.3 74.2 77.2 79.1 81.0 83.0

4 74.2 77.2 79.1 81.0 83.0 85.0

5 72.2 74.1 77.1 79.1 81.1 83.0

6 73.1 75.1 77.0 79.0 80.9 82.9

7 72.9 74.8 76.8 78.6 80.5 82.6

8 75.8 78.0 79.9 82.1 84.1 86.3

9 72.3 74.3 77.3 79.4 81.4 83.4

10 77.2 79.3 81.2 83.2 85.2 87.2

11 77.2 79.2 81.2 83.1 85.1 87.1

12 72.9 74.7 76.8 78.7 80.5 82.2

13 72.4 74.3 77.2 79.2 81.1 83.1

14 77.5 79.5 81.6 83.6 85.6 87.6

15 77.2 79.2 81.2 83.2 85.1 87.1

16 74.3 77.2 79.3 81.3 83.2 85.2

17 74.3 77.2 79.2 81.2 83.2 85.1

18 72.3 74.2 77.1 79.2 81.1 83.2

19 72.2 74.1 77.0 79.1 81.1 83.0

20 72.2 74.1 77.1 79.1 81.0 83.0

21 72.4 74.3 77.3 79.2 81.0 82.9

22 78.1 80.1 82.1 85.1 87.0 88.9

23 75.1 77.1 79.1 82.1 84.1 86.1

Table A4: Perceived Level [dB] of test signals averaged across 18 microphones at

facility exterior. Test signal 22 at amplitude 3 was also used as the reference sound.

26
start

(A)

inflection

points, fs

(B)

BoomGen

(C)

t

rise −

t10−90

?

<

tol1

(D) adjust

pmax

(E)

normalize

max

value to 1

(F) NOM (G)

multiplier

(H) P L −

P Ldesired

?

<

tol2

(I) adjust

multiplier

(J) 6-Hz

HPF

(K) 2+

signals?

(L)

combine

signals

(M) time

delay,

second

waveform,

second

multiplier

(N) EQ

filter

(O)

normalize

to prevent

quantization

noise

finish

no

yes

waveform

no

yes

waveform + multiplier

yes

no combined waveform + greatest multiplier

equalized waveform

normalized equalized waveform + final multiplier

Appendix B

Signal Processing Flow Chart
• Create a tanh-thickened sonic boom waveform (A-E): The inflection

points of the desired boom signature, as ordered pairs of time and overpressure,

as well as the sampling frequency fs (A), are entered into the Matlab code

BoomGen (B). BoomGen produces a sampled sonic boom waveform of desired

peak overpressure with tanh thickening. The rise time of a tanh-thickened

waveform cannot be specified directly, but a desired rise time can be achieved

by iteratively adjusting pmax. The difference between the rise time of the

resulting waveform, t10−90, and a desired rise time, t

rise, is compared with

a user-specified tolerance, tol1 (C). If the resulting rise time is within the

tolerance of the desired rise time, the waveform is normalized to a maximum

value of unity (E). Otherwise, the maximum overpressure is adjusted (D), and

the waveform is regenerated in BoomGen (B).

• Scale the waveform to a desired loudness level (F-I): If no tanhthickened waveform is desired, then the processing begins with this stage. The

waveform is entered into the Matlab code NOM (F), which filters the waveform

into third-octave band sound pressure levels and calculates noise metrics. A

multiplier (G) is applied to the waveform, which converts the waveform unit to

pressure in pascals at the exterior array microphones. The Perceived Loudness

(PL) of the waveform is calculated, and the result is compared with the desired PL value. If the difference between the desired and predicted PL values

is less than a user-specified tolerance, tol2 (H), the waveform and the multiplier are passed on. Otherwise, the multiplier is adjusted iteratively (I) until

the predicted PL matches the desired PL within the tolerance, tol2.

• High-pass filter (J): The waveform is filtered by a 6-Hz high-pass filter (J)

to remove spectral content that cannot be reproduced in the facility.

• Combine multiple signals (K-M): Applying the equalization filter (N)

adds several seconds to the length of each signal. If multiple signals need to

be played in quick succession, the signals are combined into a single waveform

prior to equalization (L). In the combined waveform, the component signals

are separated by a short, user-specified time delay. Each waveform originally

had its own multiplier. The greatest multiplier is retained, and the waveform

originally associated with the lesser multiplier is scaled in amplitude by the

ratio of the lesser multiplier to the greater multiplier. The result of this manipulation is that each component waveform is scaled to its desired amplitude

although the entire waveform has only one multiplier.

• Apply equalization filter (N): The equalization filter (N) is applied to account for unavoidable filtering of the desired signal by the sound reproduction

chain.

• Normalize to maximize dynamic range (O): Although this step (O)

was not used in the current study, it will be used in future studies. The

equalization filter reduces the dynamic range of the waveform considerably.

For some waveforms the reduced dynamic range produces audible quantization

noise. The quantization noise does not typically transmit into the facility, but

28
it can be audible at the facility exterior. To solve this problem, the waveform

is renormalized (O) to a maximum value of 0.99, as shown in Eq. B1. A

value of 0.99 is chosen to ensure no clipping. The multiplier is also adjusted,

as shown in Eq. B2, so the resulting overpressure remains unchanged. As a

double check of the scaling, when the normalized waveform is multiplied by the

final multiplier, the result is the same as multiplying the equalized waveform

by the prior multiplier.

normalized waveform = 0.99 ∗ waveform

max (|waveform|)

(B1)

final multiplier = multiplier ∗ max (|waveform|)

0.99

(B2)

• Output: The processing technique produces an equalized waveform with an

associated multiplier. The multiplier corresponds approximately to the waveform’s peak overpressure in pascals at the facility exterior.

29
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

A Study in a New Test Facility on Indoor Annoyance Caused by Sonic 

Booms 

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Rathsam, Jonathan; Loubeau, Alexandra; Klos, Jacob

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

L-20108

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 71

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

A sonic-boom simulator at NASA Langley Research Center has been constructed to research the indoor human response to 

low-amplitude sonic booms. The research goal is the development of a psychoacoustic model for individual sonic booms to be 

validated by future community studies. The study in this report assessed the suitability of existing noise metrics for predicting 

indoor human annoyance. The test signals included a wide range of synthesized and recorded sonic-boom waveforms. Results 

indicated that no noise metric predicts indoor annoyance to sonic-boom sounds better than Perceived Level, PL. During the 

study it became apparent that structural vibrations induced by the test signals were contributing to annoyance, so the 

relationship between sound and vibration at levels of equivalent annoyance has been quantified. 

15. SUBJECT TERMS

Indoor annoyance; Simulator; Sonic boom; Subjective response

18. NUMBER

 OF 

 PAGES

34

19b. TELEPHONE NUMBER (Include area code)

(443) 757-5802

a. REPORT

U

c. THIS PAGE

U

b. ABSTRACT

U

17. LIMITATION OF 

 ABSTRACT

UU

Prescribed by ANSI Std. Z39.18

Standard Form 298 (Rev. 8-98)

3. DATES COVERED (From - To)

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

984754.02.07.07.18.03 

11. SPONSOR/MONITOR'S REPORT

 NUMBER(S)

NASA/TM-2012-217332

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PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

01- 02 - 2012