Aron D. Hozman

Glenn Research Center, Plum Brook Station, Sandusky, Ohio

William O. Hughes

Glenn Research Center, Cleveland, Ohio

An Evaluation of the Additional Acoustic Power 

Needed to Overcome the Effects of a Test-Article’s 

Absorption During Reverberant Chamber Acoustic 

Testing of SpaceÀ ight Hardware

NASA/TM—2014-218432

December 2014
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Aron D. Hozman

Glenn Research Center, Plum Brook Station, Sandusky, Ohio

William O. Hughes

Glenn Research Center, Cleveland, Ohio

An Evaluation of the Additional Acoustic Power 

Needed to Overcome the Effects of a Test-Article’s 

Absorption During Reverberant Chamber Acoustic 

Testing of SpaceÀ ight Hardware

NASA/TM—2014-218432

December 2014

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Noise-Con 2014

sponsored by the Institute of Noise Control Engineering of the USA (INCE/USA)

Fort Lauderdale, Florida, September 8–10, 2014
Acknowledgments

The authors would like to thank Dr. Jerome Manning and Dr. Patricia Manning from Cambridge Collaborative Inc. for their 

technical contributions to this paper. Appreciation is also given to Mr. Jesse Oliver and his SpaceX Falcon 9 Payload Fairing team 

for their cooperation and assistance when implementing this methodology during their test program.

Available from

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Trade names and trademarks are used in this report for identi¿ cation 

only. Their usage does not constitute an of¿ cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2014-218432 1 

An Evaluation of the Additional Acoustic Power Needed to 

Overcome the Effects of a Test-Article’s Absorption During 

Reverberant Chamber Acoustic Testing of 

Spaceflight Hardware 

Aron D. Hozman 

National Aeronautics and Space Administration 

Glenn Research Center 

Plum Brook Station 

Sandusky, Ohio 44870 

William O. Hughes 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The exposure of a customer’s aerospace test-article to a simulated acoustic launch environment is 

typically performed in a reverberant acoustic test chamber. The acoustic pre-test runs that will ensure that 

the sound pressure levels of this environment can indeed be met by a test facility are normally performed 

without a test-article dynamic simulator of representative acoustic absorption and size. If an acoustic test 

facility’s available acoustic power capability becomes maximized with the test-article installed during the 

actual test then the customer’s environment requirement may become compromised. In order to 

understand the risk of not achieving the customer’s in-tolerance spectrum requirement with the test-article 

installed, an acoustic power margin evaluation as a function of frequency may be performed by the test 

facility. The method for this evaluation of acoustic power will be discussed in this paper. This method 

was recently applied at the NASA Glenn Research Center Plum Brook Station’s Reverberant Acoustic 

Test Facility for the SpaceX Falcon 9 Payload Fairing acoustic test program. 

Introduction 

Exposing aerospace test-articles (e.g., spacecraft and payload fairings) to simulated, launch-event, 

high intensity acoustics is accomplished by one of two methods.

Aerospace test-articles may be exposed to a direct acoustic field created by a shroud of dynamic 

speakers that are in close proximity to the test-article. This test method is commonly referred as the 

Direct Field Acoustic Test (DFAT) method.

Reverberant acoustic testing is the other method. With this more established method, a reverberant 

acoustic field is created within a large chamber and excites the aerospace test-article which is installed in 

the chamber. One advantage of using reverberant acoustic testing, over the DFAT, is when a customer’s 

acoustic spectrum requirements exceeds a 148 dB overall sound pressure level (OASPL). Such high 

pressure levels are beyond the current capability of DFAT. 

For reverberant acoustic testing, it is recommended (Ref. 1) that the volume of the test-article is no 

greater than 10 percent of the empty chamber’s volume in order to ensure that the presence of the testarticle does not interfere with the spatial uniformity of the reverberant field. Many of the (approximately 

25) active reverberation chambers throughout the world are capable of meeting the 10 percent test-article/ 

chamber ratio volume guideline for many aerospace test-articles. These test facilities all have their own 

unique shape, volume, wall surface absorption, and compliment of noise sources/coupled horns. 

 
NASA/TM—2014-218432 2 

Less unique is the sound medium in the chamber during test, being either that of gaseous nitrogen (GN2) 

with its corresponding low oxygen level (typically  10 percent oxygen), or low-humidity compressed air. 

GN2 is the preferred gas due to its cleanliness, and its lower absorptive characteristics above 4 KHz. 

The Reverberant Acoustic Test Facility (RATF) at the NASA Glenn Research Center Plum Brook 

Station in Sandusky, Ohio is an example of a large-volume (101,000 ft3

), very powerful (163 dB OASPL) 

reverberant acoustic test chamber (Refs. 2 and 3) which uses GN2. Figure 1 is a photograph of the 

SpaceX Falcon 9 Payload Fairing in this NASA test chamber. The volume of the Falcon 9 test-article was 

10 percent of the NASA RATF’s empty chamber volume. 

Figure 1.—The SpaceX Falcon 9 Payload Fairing was successfully tested at the 

NASA Glenn Research Center Plum Brook Station’s Reverberant Acoustic Test 

Facility (RATF) during May to June 2013. 
NASA/TM—2014-218432 3 

This paper describes a method to mitigate the test risk of achieving a customer’s target sound pressure 

level (SPL) spectrum during reverberant acoustic testing due to the absorption inherent to the test-article. 

Each particular test-article will have its own absorption values which may be estimated as a function of 

frequency. Typically, both the target SPL spectrum and the test-article’s absorption are stated at the 

one-third octave band (OTOB) center frequencies. 

To address the effects of the test-article’s absorption on quantifying the maximum achievable SPL 

versus OTOB frequencies of a company’s reverberant acoustic test chamber, the following parameters are 

needed: 

1. The test chamber’s linear dimensions (width, depth, and height) and geometry. (If the chamber’s 

shape is not rectangular in each plane, then chamber drawings should be provided. It’s also 

advisable to have drawings that include the layout of the chamber’s horns and vents, in order to 

determine those surface areas). 

2. The Reverberation Time (RT60) values per OTOB for the empty chamber condition (i.e. no 

test-article inside the chamber). 

3. The Reverberation Time (RT60) values per OTOB for the chamber with the test-article installed. 

The RT60 values are determined from the measured decay rates in the chamber, and are equal to the 

time in seconds for 60 dB of decay to occur after the sound excitation source has been turned off. If the 

RT60 values (in items 2 and 3 above) are not available, they may be calculated from a recording of the 

time-history decays of sound inside the chamber. The Interrupted-Noise Method (Refs. 4 and 5) is one 

approach that is often used to record and measure RT values. Because of the noise source excitation levels 

and the microphones’ dynamic range limits due to their sensitivity, it is often necessary to extrapolate to 

an RT60 value from a lesser decay, such as a RT20 value. 

As an example with this Interrupted-Noise Method, a RT20 calculation may be performed with a 

minimum of 35 to 40 dB of dynamic range from the excitation level to the measurable background noise 

level. This dynamic range is made up of: the required 5 dB of early roll-off decay when the excitation 

noise source is turned off, a minimum 20 dB of actual linear decay, and an allowance of a 10 dB margin 

above the background noise floor. This RT20 value is then simply extrapolated to the RT60 value. (A direct 

measurement of RT60 would require a dynamic range of 75 dB from the excitation level to the background 

noise level, which is often not attainable in test.). Figure 2 illustrates the Interrupted-Noise Method for 

decay measurements. 

Figure 2.—ISO354 Interrupted Noise Method of determining 

reverberant room decay rates. 
NASA/TM—2014-218432 4 

Before the delivery of the customer’s test-article to the acoustic test facility, it is common practice to 

perform initial empty chamber testing to the customer’s specified acoustic target SPL spectrum. This 

empty chamber testing determines what compliment of horns and modulators are best suited to meet the 

spectral levels. This target level testing would be sufficient only if the test-article’s absorption is assumed 

to be insignificant. If the test-article’s absorption is expected to be significant then further attention is 

required to address the additional acoustic power needed within the chamber to overcome this acoustic 

power sink. 

Therefore a method is needed to estimate these absorption effects when the test-article’s absorption is 

significant (i.e., account for the additional acoustic power required). 

Method for Determination of Additional Acoustic Power 

The following steps are the approach taken to determine if the empty chamber test was performed 

with adequate sound power to ensure that the target SPL spectrum can be reached when testing with the 

test-article installed in the chamber. 

Step A—Overview of Fundamental Acoustic Equations: Review the fundamental acoustic equations 

(Ref. 6) related to a reverberant acoustic chamber test. 

The SPL in the reverberant chamber is calculated by a power balance between the chamber’s input 

power and the power dissipated due to absorption and other energy loss mechanisms within the chamber. 

The spatial averaged mean-square sound pressure, p2

!, in the chamber is given by the Room Equation 

(Eq. (1)): 

c

c R

c

p W U 2 4 (1) 

where Wc is the acoustic power input to the chamber in watts, Rc is the room constant in m2, U is the 

density of the gas within the chamber in kg/m3

, and c is the speed of sound of the gas in m/s. 

The room constant, Rc, defined in Equation (2), is determined from the absorption of the chamber 

surfaces and from the gas absorption, and has units of metric Sabines (m2

), 

R S mV

i

c i i ¦ D  4 (2) 

where Si is the area of each i

th surface of the room, Di is the diffuse field surface absorption coefficient of 

each i

th surface, V is the volume of the room in m3

, and the “m” is the energy absorption coefficient of the 

gas with units of inverse meters (m–1). For an empty chamber the summation of the individual surface 

area absorptions in metric Sabines accounts for all walls, floor, and ceiling surfaces, plus the chamber’s 

horns and vents openings. 

The (metric) Sabine Equation (Eq. (3)) relates the room constant to the room’s reverberation time, RT60. 

60

60

1.086c RT

V Rc (3) 

The RT60 values equals the time in seconds in each OTOB for 60 dB of decay to occur after the sound 

source has been turned off. 

The Room Equation (Eq. (1)) combined with Sabine’s equation (Eq. (3)), results in an expression of 

the mean-square acoustic pressure as a function of the reverberation time, as provided in Equation (4), 

60

2

2

60

4.343 RT

V

c

p Wc

U (4) 
NASA/TM—2014-218432 5 

where, Wc is the acoustic power input to the chamber in watts, RT60 is the reverberation time of the 

chamber in seconds, V is the chamber volume in m3

, U is the density of the gas within the chamber in 

kg/m3

, and c is the speed of sound of the gas in m/s. 

The compact relationship between the SPL and the acoustic Power Level (PWL) in the chamber can 

be expressed in decibels (dB) by Equation (5). This equation is valid for metric units and when GN2 is 

the gaseous sound medium in the chamber, 

 SPL = PWL + 10 log (RT60) – 10 log (V) + 14.17 dB (5) 

where, SPL is the measured Sound Pressure Level in the chamber in dB relative to 20 micro-Pascals, 

PWL is the measured acoustic Power Level in the chamber, in dB relative to 1 pico-watt, RT60 is the 

reverberation time for sound to decay 60 dB, in seconds, and V is the volume of the test chamber in m3

. 

The introduction of the test-article affects the above equations by decreasing the chamber’s volume 

(V), and increasing the total surface absorption due to the SiDi contribution of the test-article. 

The reverberation time is obtained from the measured decay rate, d in dB/sec (Eq. (6)). 

d

RT 60

60 (6) 

The decay rate of the chamber with the test-article will be larger relative to the decay rate for the empty 

chamber test. The RT60 of the chamber with the test-article will thus be shorter than the RT60 for the empty 

chamber test. This change in RT60 indicates that additional acoustic power will be necessary to meet the 

same target spectrum with the test-article in the chamber. 

Step B—Obtain the Reverberation Times of the Empty Chamber: Perform tests to determine the 

Reverberation Time of the empty chamber condition (RT60 EC) for each OTOB frequency, and the 

subsequent calculation of the acoustic absorption (in units of metric Sabines). 

These RT60 decay measurements may be obtained by utilizing the test facility’s existing noise sources 

(modulators/horns) via the Interrupted Noise Method (Refs. 4 and 5) as previously discussed. 

Alternatively, the Interrupted Noise Method can be applied to obtain the decay measurements by utilizing 

conventional dynamic speakers as the noise source. The dynamic speaker excitation source would be less 

costly from both a facility operations and labor resources perspective, and it would also be easier and 

quicker to implement. Note, using dynamic speakers as the sound source instead of the chamber’s noise 

generators may affect the relative decay rates for frequencies above 1 KHz (where the gas dominates the 

total absorption), especially if GN2 is used as the sound medium for the actual test-article acoustic test. 

Step C—Estimate the Test-Article Absorption: As mentioned earlier, it is necessary to include the 

effects of the test-article’s acoustic absorption when performing the empty chamber tests to ensure that 

adequate acoustic power will be available when time comes to perform the test with the test-article inside 

the chamber. 

Based on experience, evaluate the customer’s test-article configuration (i.e., its shape, size, 

construction, materials, cavities, surface area) and its expected acoustic absorption to estimate a delta dB 

to be added to each OTOB of the customer’s target spectrum. So for example, to account for the testarticle absorption a +4 dB could be added to the customer’s acoustic test SPL at each OTOB when 

performing the empty chamber test. Note, it is not necessary that the estimated delta dB be uniform as 

applied to all OTOBs. 

Step D—Perform Empty Chamber Test using Bolstered Test Levels: Perform the empty chamber test 

with bolstered acoustic test spectrum which includes the delta dB estimate from the previous step. 

Confidence to proceed with the actual test-article’s full-level test is achieved only if the bolstered SPLs 

can be reached successfully in this empty chamber test. 
NASA/TM—2014-218432 6 

If the bolstered SPLs were not achieved for any OTOB, then other modulator/horn combinations, 

drive-signal filter bandwidth settings, and modulator pressure flows may be adjusted to reach the 

bolstered SPLs. If none of these adjustments work, then it is necessary to discuss the situation, maximum 

achievable SPLs, and assumptions (of Step C) with the customer. As one can see, this test should be 

performed months before the arrival of the test-article at the test facility in order to mitigate risk and allow 

time to achieve the bolstered SPLs. 

Step E—Perform Empty Chamber Test using Bolstered Test Levels, Again: Assuming the previous 

step was successful, it is prudent to repeat this bolstered SPL empty chamber test shortly before the testarticle is placed inside the acoustic chamber. This re-test provides confidence that the chamber’s acoustic 

characteristics have not changed over time; in addition, this provides a timely check-out of all the 

necessary acoustic control and noise generation equipment and systems. 

Step F—Obtain the Reverberation Times of Chamber with Test-Article Installed: Assuming 

success for Step E above, perform a low level (i.e., –12 dB from the customer’s full level target spectrum) 

with the test-article installed in the chamber. At the end of this –12 dB exposure, continue to record the 

microphones’ decay rates to derive the RT60, in each OTOB, for the chamber with the test-article 

(RT60 C w/TA). 

Note that Step F can alternatively be performed using conventional dynamic speakers in lieu of the 

chamber’s noise modulators and horns. Using the dynamic speakers for this step should result in a savings 

of effort, schedule and cost. 

Step G—Calculate actual delta dB: Knowing the reverberation times from Steps B and F, one can now 

calculate the actual delta SPL values needed to overcome the test-article’s absorption. Rearranging 

Equation (5) to solve for PWL for the two tests conditions of: (1) empty chamber (EC), and (2) chamber 

with test-article (C w/TA), results in Equations (7) and (8). 

 PWLEC = SPLEC – 10 log (RT60 EC) + 10 log (VEC) – 14.17 dB (7) 

 PWLC w/TA = SPLC w/TA – 10 log (RT60 C w/TA) + 10 log (VC w/TA) – 14.17 dB (8) 

Combining Equations (7) and (8) by setting PWLEC = PWLC w/TA (i.e., the modulators produce the same 

amount of power for both cases), one can solve for the change in SPL, from hereafter known as “delta 

dB.” The calculated delta dB is provided in Equation (9). 

 SPLEC – SPLC w/TA = – 10 log (RT60 C w/TA) + 10 log (VC w/TA) + 10 log (RT60 EC) – 10 log (VEC) (9) 

Defining the volume of the chamber with the test-article as: 

 VC w/TA = (VEC – VTA), where VTA = actual volume of test-article (10) 

and substituting Equation (10) into Equation (9) results in, 

 SPLEC – SPLC w/TA = 10 log (RT60 EC) – 10 log (RT60 C w/TA) + 10 log (VEC – VTA) – 10 log (VEC) (11) 

Equation (11) may be reduced to Equation (12) as follows, 

 SPLEC – SPLC w/TA = 10 log (RT60 EC / RT60 C w/TA) + 10 log ((VEC – VTA) / (VEC)) (12) 

With the definition of “delta dB” = SPLEC – SPLC w/TA, this may now be reduced to Equation (13), 

 delta dB = 10 log [(RT60 EC / RT60 C w/TA) x (1 – (VTA / VEC))] (13) 

 
NASA/TM—2014-218432 7 

For the special case when the volume of the test-article (VTA) is less than 10 percent of the volume of 

the empty chamber (VEC), then Equation (13) simplifies to the approximation given in Equation (14). 

 delta dB | 10 log [RT60 EC / RT60 C w/TA] (14) 

By using the derived Equation (13), the actual delta dB is computed. If this actual delta dB does not 

exceed the estimated delta dB (from Step C) that was applied in the empty chamber testing (Steps D/E), 

then the risk of having potential deficient acoustic power due to the test-article absorption has been 

successfully mitigated. In this scenario, proceed with the customer’s test plan to eventually expose the 

test-article to the full-level target spectrum. 

However, if this actual delta dB (from Step G, Eq. (13)) exceeds the estimated delta dB (from Step C) 

that was applied in the empty chamber testing (Steps D/E) in an OTOB, then options need to be discussed 

with the customer for this scenario. Note, having an exceedance is not a statement of the facility’s 

limitation to reach these higher SPLs, but rather that its capability to do so has not yet been demonstrated. 

As such, one option would be to subtract this exceedance from the customer’s target spectrum (i.e., 

lowering the target SPL for the affected OTOBs). This would result in testing closer to the lower test 

tolerance value of the customer’s test target spectrum. Another option, although programmatically 

undesirable, would be to remove the test-article from the chamber, and repeat the empty chamber 

measurements (Step B) with the now known delta dB. 

Examples of these two scenarios are illustrated in Figure 3. In Figure 3, a +4 dB of delta dB was 

predicted/used for both of the test-article’s absorption during their empty chamber tests. A notional 

representation of the two test-articles’ calculated delta dB (from their low-level test measurements) are 

also shown in Figure 3. The calculated delta dB for Test-Article A is below the applied predicted delta 

SPL dB and therefore the full level testing can proceed with confidence, with minimal risk relative to the 

test chamber’s available acoustic power. However, the situation is different for Test-Article B where the 

calculated delta dB exceeds the applied predicted delta dB in two of the OTOBs (at the 160 Hz and 

200 Hz OTOBs). In this case, options would be discussed with the customer on how to proceed; primary 

to these discussions would be the amount of the exceedance (e.g., 0.5 dB would be more tolerable than 

say 2 dB). 

Figure 3.—Illustration of delta SPL dB for two notional test-articles. 
NASA/TM—2014-218432 8 

Summary 

It is important to realize that some test-articles may have significant sound absorption that may 

challenge the acoustic power capabilities of a test facility. Therefore, to mitigate this risk of not being 

able to meet the customer’s target spectrum, it is prudent to demonstrate early-on an increased acoustic 

power capability which compensates for this test-article absorption. This paper describes a concise 

method to reduce this risk when testing aerospace test-articles which have significant absorption. This 

method was successfully applied during the SpaceX Falcon 9 Payload Fairing acoustic test program at the 

NASA Glenn Research Center Plum Brook Station’s RATF. 

References 

1. High Intensity Acoustics Testing, Institute of Environmental Sciences and Technology, 

IEST-RP-DTE040.1, January 2003. 

2. R.N. Sorge, “Space Power Facility—Capabilities for Space Environmental Testing Within a Single 

Facility,” NASA/TM—2013-217816, November 2012. 

3. W.O. Hughes, M.E. McNelis, A.D. Hozman, and A.M. McNelis, “The Development of the Acoustic 

Design of NASA Glenn Research Center’s New Reverberant Acoustic Test Facility,” NASA/TM—

2011-217000, July 2011. 

4. Acoustics—Measurement of sound absorption in a reverberation room, 2nd edition, ISO 354:2003(E), 

May 15, 2003. 

5. Acoustics—Measurement of the reverberation time of rooms with reference to other acoustical 

parameters, ISO 3382:1997(E), 1997. 

6. J.E. Manning, “Risk Factors Associated with the Prediction of Large Reverberant Chamber Acoustic 

Levels Part 1: Chamber Absorption Values,” Cambridge Collaborative Inc. Report CC-13964-4, 

Rev 5.1, May 14, 2010.