PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen,
Germany

Design of a new testing chamber to measure the absorption
coefficient down to 25 Hz
Peter D’ANTONIO 1; Melanie NOLAN 2; Efren FERNANDEZ-GRANDE 3; Cheol-ho JEONG4RPG Acoustic Systems, LLC, USA

12, 3, 4

Acoustic Technology, Department of Electrical Engineering, Technical University of Denmark, Denmark

ABSTRACTThis presentation will describe a new 285 m3 testing chamber that will allow the measurement of therandom incidence absorption coefficient and the normal incidence low frequency absorption
coefficient, according to ISO 10534-2. The rev room’s cuboid dimensions were determined from an
optimization procedure that minimizes the standard deviation of the modal response. Both concrete,dome-shaped boundary diffusors and hanging convex panels, arranged in a primitive root pattern, areused to provide diffusivity, which is verified using a 200 mm reference absorber according to therevised ISO 354. The isotropy of the incident sound will also be evaluated with a new SOund Field
Analysis Recorder (SOFAR) and quantified with an analysis of the wavenumber spectrum. 18 impulse
responses are collected from 3 sources and 6 distributed microphones. The MLS impulse response data
is processed with a proprietary Matlab program, which automatically removes the rms noise floor,
creates an energy decay from the optimal linearity limit, achieving maximum dynamic range, from allof the microphone-speaker pairs. A steel and concrete lined low frequency impedance tube measuring
0.6 m x 0.6 m x 5.8 m long and 7 tons is used to measure absorption from 25-250 Hz.
Keywords: ISO354, Absorption, Isotropy

1. INTRODUCTION

When RPG relocated its manufacturing to a new location, there was an opportunity to build a new
Acoustical Research Center (ARC), containing a reverberation room adhering to the latest ISO
Working Group recommendations. Since this is not a commercial facility, we had to economicallymodify a non-ideal space. This paper describes the planned reverberation room, which is in the processof being completed as of this writing. Hopefully more of the actual experimental details will bepresented at the ICA conference in Aachen. The random incidence absorption coefficient is an
essential parameter in acoustical design and yet more than 100 years after the reverberation room
method was suggested, we are still not able to measure it accurately. While the intra-lab precision ishigh in most laboratories, the accuracy is uncertain and the lack of agreement among labs is not
acceptable. Therefore, the ISO 354 (1) standard is under continual development and revision. Much
more recently, a scattering coefficient, measured in a reverberation chamber and subject to its
limitations, has been enshrined as ISO 17497-1 (2) to complement the absorption coefficient. The
scattering coefficient, s, is a ratio of energy scattered in a non-specular manner to the total reflectedenergy.

dr.peter.dantonio@gmail.com; pdantonio@rpgacoustic.com
melnola@elektro.dtu.dk
3
efg@elektro.dtu.dk
4
chj@elektro.dtu.dk
1
2

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This was developed to be used in geometrical room acoustic modeling programs (3). Since thereverberation room method of measuring the absorption coefficient assumes a perfectly diffuse soundfield, this requires isotropic sound incidence and random relative phases. Therefore, this new lab will
utilize the revised ISO approach for evaluating diffusivity with a reference absorber and also plan toexperimentally measure the degree of isotropy of the incident sound with a new SOund Field Analysis
Recorder (SOFAR), which determines an isotropy coefficient, based on an analysis of the wavenumber
spectrum in the spherical harmonics domain, using a method proposed by Nolan (4). The wavenumber
spectrum, which results from expanding an arbitrary sound field into a plane-wave basis, is used tocharacterize the spatial properties of the observed sound field. The wavenumber spectrum is then
expanded into a series of spherical harmonics, and the moments from this expansion are used tocharacterize the isotropy of the wave field. To extend the low frequency capability of the test chamber
to measure the normal incidence absorption coefficient down to 25 Hz, a 7 ton steel-faced concrete
impedance tube measuring 0.6 x 0.6 x 5.8 m was installed in the room.

2. TEST CHAMBER DESIGN
2.1

Existing space

Figure 1(left) Existing space; (right) Rendered rev room rotated counterclockwise 90 degrees with thefront wall in Fig. 1 (left) on the left
The existing space, shown in Figure 1 (left), was formerly used as a blast room for a chemicalcompany. The room had a concrete floor and three permanent cinderblock walls. The short wall had a“garage-style” corrugated metal door and one of the long walls had a window. The roof, which was
replaced, was fitted with panels that would open from the impact of an explosion. The volume was 503
m3 and the goal was to partition the room into a test chamber and a control room. The capability ofutilizing suggested dimensional ratios was not possible, due to the existing walls and the only
dimensional variables were shortening the long wall and adding a ceiling onto the existing ceiling
trusses. Due to weight issues, the new ceiling, consisting of two layers of 16 mm drywall, was attached
to 406 mm spaced 51 mm x 152 mm planks resting on the lips of the ceiling trusses. The corrugateddoor was removed and filled with cinderblock, as was the window. To determine the optimal locationof the new wall in the long dimension, a cuboid image method (5), called the Room Sizer, was utilized
to find dimensional ratios with the lowest standard deviation in the modal frequency range. The floor,
walls and ceiling surfaces were sealed and painted to minimize porosity. The rendered, renovated rev
room, with diffusing surfaces, impedance tube and reference absorber, is shown in Figure 1 (right).
2.2 Dimensional ratios
Since three wall boundaries were fixed and we were constrained to remaining close to the ceiling
trusses, an optimization program (5) was used to find an optimal length for the new wall, which
provided suitable dimensional ratios with the lowest standard deviation in the modal range. Figure 2
illustrates a graph of acceptable dimensional ratios, with 1:1.03:1.3 being the closest to what wasachievable. The length, width and height were 7.89 m, 6.27 and 6.07 m, respectively, with an
unadjusted volume of 300.3 m3 and surface area of 270.8 m2

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1
1
1
1
1
1
1

1
1.03
1.08
1.08
1.09
1.09
1.13

1.33
1.3
2.79
2.8
1.35
1.36
2.76

Figure 2. Optimal dimensional ratios
2.3

Diffusing clouds and domes
To achieve the necessary diffusivity in the chamber (15) 1219 mm x 1524 mm overhead,transparent vinyl, 6.4 mm curved convex clouds, (20) 610 mm x 305 mm concrete, hemispherical
domes and (21) 864 mm X 356 mm spherical cap domes were randomly distributed, as seen in Figure
1 (right). The additional surface area added to the room by the domes, clouds, speakers, and impedance
tube is 87 m2 , yielding a ratio of diffusor surface area to adjusted, increased room surface area (358 m2 )of 24%. The adjusted room volume, reduced by the volumes of the domes, (3) JBL SRX835P speakers
and the impedance tube, is 285 m3 . The clouds are curved along the 1524 mm direction, forming a
convex surface with a cord length of 1067 mm and a height of 460 mm, to diffuse low frequencies. To
further improve diffusion at low frequencies, the clouds are arranged in a two-dimensional (2D)
primitive root (PR) sequence. Not all one-dimensional (1D) PR sequences can be converted into a 2D
array via the Chinese Remainder Theorem (3). To convert a 1D to a 2D PR array, the two factors must
be coprime, meaning they have no common factors other than 1. A PR sequence based on a prime N,
has (N-1) sequence values. The closest primes to 15 are 13 and 17. An N=17 PR sequence has 16
elements for which there are no two coprimes. Therefore, N=13 was selected, with coprimes of 4 and3, forming a 4x3 array. To provide 15 clouds, we selected the most suitable 5 x 3 array from the larger
periodic array, starting with the 6th sequence value, to accommodate the cloud heights with other itemsin the room. The sequence values are shown in Table 1. The distances of the base of the convex
Table 1. N=13 primitive root 2D array
12

8

1

5

12

10

11

3

2

10

4

7

9

6

4

shapes from the ceiling are equal to the ratio of the sequence values divided by the maximum sequencevalue, multiplied by the maximum displacement of roughly 3 m. This primitive root arrangement of
the ceiling clouds provides diffusion below 100 Hz. In Figure 3 (bottom right), we illustrate the rev
room with all domes, clouds, impedance tube and reference absorber.
2.4 ISO 354 experimental diffusivity evaluation
In Figure 3, we illustrate four configurations of the rev room with varying amounts of domes andclouds, described in Table 2. At each stage, the equivalent surface area m2 is measured to illustrate theincreased absorption with increased diffuser surface area. The final equivalent absorption area is thencompared with the required equivalent absorption area in the standard. The measured equivalent
absorption area of the reference absorber shall be equal to or larger than the values in Table B2 (1) for
the octave bands of 250 Hz and above. The correction factor ratio, g, is determined in octave bands,
but applied to all third octave bands in the octave for samples under test.

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Table 2. Three step diffusivity evaluation with domes and clouds
Domes

Clouds2

Step Length Wall SA m
1
2
3

#
4
2
2
8

SA m2 Opposite Wall SA m2

0.61 # 0.86
0.29 3 0.4
0.29 3 0.4
0.29 2 0.4
8

#
1
1
1
3

SA m2 Width Wall SA m2

0.61 # 0.86
0.29 1 0.4
0.29 2 0.4
0.29 1 0.4
4

#
3
3
3
9

SA m2 TD# TD SA 1.2 x 1.5 m

0.61 # 0.86
0.29 3 0.4
0.29 4 0.4
0.29 2 0.4
9

#
15
15
11
41

5.12
5.34
3.74
14.2

TC SA m2 TSA m2 TD+C2

SA m
5 3.725 3.725 3.7215

18.6 23.72
18.6 23.94
18.6 22.34
55.8
70

56

For example, in Step 1 the following diffusers are added to the room: (4) 0.61 m domes with asurface area (SA) of 0.29 m2 (after subtracting the base which is included in the room’s surface area),(3) 0.86 m domes with a SA of 0.4 m2 on the long wall of the rev room; (1) 0.61 m and (1) 0.86 m dome
on a short area of the opposite wall; (3) 0.61 m and (3) 0.86 m domes on the width wall and (5) convex
1.2 m x 1.5 m clouds with a total cloud surface area (TC SA m2 ) of 18.6 m2. The total surface area (TSA
m2 ) for Step 1 is 23.72 m2 . The combined dome and cloud surface area is 70 m2, with 41 domes and 15
clouds, totaling 56.

Figure 3. Sequential diffusivity test
2.5 Experimental isotropy coefficient
In addition to the ISO diffusivity test an experimental measure of the isotropy of the incident soundon the sample has been proposed by Nolan (4). The following is a brief summary of the theory. The
proposed method consists of expressing an arbitrary sound field on an array of sensors as thesuperposition of a set of plane waves:

where 𝑝𝑝(𝒓𝒓) is the measured sound pressure, 𝒄𝒄 is a complex coefficient vector and 𝑾𝑾 is a matrix
containing the plane wave functions 𝑒𝑒−𝑗𝑗𝑗𝑗∙𝒓𝒓 . Pure-tone sound fields are considered in this method. The
sound pressure measured at each of the 𝑀𝑀 transducers is expressed as4030

where 𝑃𝑃(𝒌𝒌 𝑖𝑖) = 𝒄𝒄𝑖𝑖 = |𝑃𝑃(𝒌𝒌 𝑖𝑖)|𝑒𝑒𝑗𝑗𝑗𝑗 (𝑃𝑃 ( 𝒌𝒌𝒌𝒌)) corresponds to the wavenumber (or angular) spectrum with |𝑃𝑃(𝒌𝒌 𝑖𝑖)|and 𝜙𝜙(𝑃𝑃(𝒌𝒌 𝑖𝑖)) its magnitude and phase, respectively. A spherical coordinate system 𝒓𝒓𝑚𝑚 = (𝑟𝑟, 𝜃𝜃𝑚𝑚 , 𝜙𝜙𝑚𝑚 ) =(𝑟𝑟, Ω𝑚𝑚) is considered where the direction of the waves is given by 𝒌𝒌 𝑖𝑖 = (𝑘𝑘, Ω𝑖𝑖). Subsequently, themagnitude of the obtained complex angular spectrum is expanded into a series of spherical harmonics:

Since the spherical harmonics are orthonormal, the complex coefficients 𝐴𝐴𝑚𝑚𝑚𝑚 (𝑘𝑘) of the expansion
can be calculated from

A wave field is termed isotropic if the wavenumber vectors of the incident plane waves are
uniformly distributed over all angles of incidence (corresponding to a sinusoidal distribution of thepolar angles and a uniform distribution of the azimuth angles). In this case, the magnitude of theangular spectrum is constant over the entire solid angle. Consequently, all the energy of the angular
spectrum |𝑃𝑃(𝑘𝑘, Ω)| resides on the monopole moment 𝐴𝐴 00(𝑘𝑘) of its spherical harmonic expansion inequation (3). This will not be the case if the contributing waves cover just a partial section of the solid
angle, as the higher-order moments would characterize the wave field. The energy of the n th ordermoment is given by the denominator in equation (5), so that the relative energy of the monopole
contribution can now be expressed as:

This quantity is suggested as a potential isotropy indicator and will be denoted by 𝜄𝜄(𝑘𝑘). The measure
ranges between zero and one and equals unity in the case where the flow of acoustic energy is equal in
all directions. Conversely, it approaches zero if the incident waves propagate in a single direction.
2.6 Measurement of the isotropy coefficient
A conceptual approach to measuring the sound field necessary to determine the isotropy coefficientis shown in Figure 4. The device is called a SOund Field Analysis Recorder (SOFAR) and is placed inclose proximity to the reference absorber in the rev room. The device consists of a movable gantry
containing 32 microphones spaced 25 mm apart located within a frame which allows accurate
displacements of the gantry every 25 mm parallel to the reference absorber. 32 impulse responses arerecorded at each of 32 positions for a total of 1,024 impulse responses in the first measurement plane.
The frame supporting the gantry is moved up 25 mm and an additional 1,024 impulse responses aremeasured. This data collection is repeated in two additional upward planes separated by 25 mm for a

Figure 4. Three layer SOFAR concept illustration

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total of 4,096 impulse responses. The 32 electret microphones are connected to preamps connected to
A/D converters, which are input into a computer running the data collection process. The impulse
responses are processed to provide the pressure responses p(r) in equation (1).
An automated prototype of the SOFAR is in development. The device consists of 4 verticalelements to which a rectangular frame is attached. The left and right legs of the frame containrectangular plates to which the gantry containing the 32 mics is attached. The frame containing the mic
gantry is mechanically adjustable vertically. The leg on the right side contains a stepping motor andencoder to automatically advance the gantry by 25 mm, after each data collection for the 32 positions.
The frame is then mechanically lifted 25 mm higher for the next cycle of impulse response
measurements and repeated at two additional heights above the sample. Thus, generating the 4,096
impulse responses which are fitted to determine the wavenumber spectrum with |𝑃𝑃(𝒌𝒌 𝑖𝑖)| and 𝜙𝜙(𝑃𝑃(𝒌𝒌 𝑖𝑖)) its
magnitude and phase, respectively.

3. DATA COLLECTION AND PROCESSING

To calculate the reverberation time, according to the backward integration of the impulse response
squared suggested by Schroeder, we must:- evaluate the optimal upper limit of infinity provided by the data and ensure that it does not extend into
the noise floor- truncate the impulse response at the point it reaches the noise floor by energetically subtracting therms noise
ISO 354 suggests the backward integration should begin at -35 dB, 30 dB down from an initial value of
t=-5 dB. In cases where the dynamic range of the data is insufficient to fulfill this 30 dB drop, theevaluation range may be reduced, provide it is at least 20 dB. This is rather ambiguous and requires a lotof manual limit selection in each of the 1/3-octave bands and microphone-speaker pairs. There is also aneed to quantify the linearity of the energy decay. For rapid data processing, this suggests the need for an
automated program.
The Automatic Reverberation TIme Calculator (ARTIC) program automatically filters the squared
impulse responses into 1/3-octave bands over the frequency range of interest, in which the following
procedure is carried out for each 1/3-octave band of each microphone-speaker pair (Figure 5):- Determine the upper limit or maximum decay confidence of integration, t∞ = tq , to form the energy∞qdecay by segmenting the response into a set of rms values over short intervals,
typically
40 ms (legend
Segmented rms), according to (6).
- Determine the maximum dynamic range, in which the segmented rms response is 3 dB above the noise(legend Noise rms)
- Fit a line to the segmented squared impulse response (IR) down to the beginning of the noise floor toestablish tq (legend IR fit line)- Energetically subtract the rms value of the noise to determine a noise-free, uncontaminated segmented
response- Calculate T60 extrapolated from the slope of the backward integrated, energy decay segmented
response out to tq (legend Drop to optimal linearity).

Figure 5. Noise compensated squared impulse response and energy decay
at 4 kHz with several indicated dB drops down to the drop of optimallinearity
One can see from Figure 5 (right column) that the Uncompensated decay can introduce both
non-linearity and an artificial inflation of reverberation time. Also marked are the Segmented decay, the -54032

dB Reference position, the EDT drop of – 15 dB, the 15 dB and 30 dB drop from the Reference position andimportantly the Drop to optimal linearity. The program automatically locates tq as the point at which therms of the squared impulse response is 3 dB above the noise floor. To find the intersection point of
uncontaminated data and noise, the rms is calculated over short intervals (typically 40 ms), illustrated in
Figure 5 (left column) as Segmented rms, at 4 kHz. An IR line fit to the decaying portion of the rms
segments intersects the smallest value of segmented Noise rms. Data to the right of this point are known to
be noise and a reliable noise rms value is obtained. The segmented data is then truncated by energeticallysubtracting the Noise rms, according to, as outlined above.
The reverberation time extrapolated from the optimal linear dynamic range is determined for each
1/3-octave band and averaged with the values in all of the microphone-speaker pairs to form a plot ofreverberation time vs frequency.

4. LOW FREQUENCY IMPEDANCE TUBE

To extend the capability to measure the absorption below 100 Hz, we developed a 0.6 m x 0.6 m x
5.6 m, 7 ton impedance tube fabricated from steel covered concrete. The tube is shown in Figure 6.

Figure 6. Low frequency impedance tube
Figure 6 (left) shows the sample lid in the open position. Figure 6 (middle) shows the lid closed andFigure 6 (right) shows a membrane absorber with the movable measurement mic in one of threepositions. Combining data from three microphone pair positions (1,2; 1,3; and 2,3) allows
determination of the normal incidence absorption coefficient and complex surface impedance from 25
Hz to 250 Hz. The pressure measurements at each pair of position, e.g. p(x1) and p(x2), yields thetransfer function, S equation (6), the reflection factor, R equation (7), and the normal absorption
coefficient, a, equation (8).

p( x1 ) e - ikx1 + Reikx1
S==p( x2 ) e - ikx2 + Reikx2(6)e − ikx1 − Se − ikx2
R=
Se ikx2 − e ikx1(7)

α =1− R

2

(8)

5. CONCLUSION

As of this writing, we are in the process of completing the final commissioning of the rev room andthus this paper is limited to the design parameters and goals. It is the hope to present experimental
measurements at the conference. The rev room contains both spherical cap domes and suspended
convex clouds spaced from the ceiling in a primitive root sequence to provide low frequency diffusion
below 100 Hz. Measurements will be made according to (1) to obtain the scaling factor, g, to reducethe inter-lab variance. An automated, Matlab, data processing procedure is described, which removes
the rms noise floor and creates an energy decay to the optimal linearity limit, achieving maximal
dynamic range, from all the microphone-speaker pairs. A described SOFAR device, which is inprototype design, will be used to experimentally determine the randomness of the incident sound on

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the reference sample, using a described isotropy coefficient. A low frequency normal incidence,
impedance tube is described to extend the frequency range of the rev room down to 25 Hz.

ACKNOLEDGEMENTS

D’Antonio would like to thank RPG and its employees for providing the space for the Acoustical
Research Center and for the difficult task of converting a previously unsuitable space into afunctioning reverberation room. D’Antonio would also like to thank Lea Ann Pelleschi for all of the
CAD drawings and animations.

REFERENCES

1. Vercammen M. On the revision of ISO 354, measurement of the sound absorption in the reverberation
room. ISO/WD 354:2018.
2. Acoustics - Sound-scattering properties of surfaces. Part 1: Measurement of the random-incidence
scattering coefficient in a reverberation room. ISO 17497-1:2004(E).
3. Cox TJ, D’Antonio P. Acoustic Absorbers and Diffusers: Theory, Design and Application. 3rd ed. Boca
Raton, USA: Taylor & Francis; 2017. p. 131 & 359.
4. Nolan, M, Fernandez-Grande, E, Brunskog, J, Cheol-Ho, J. A wavenumber approach to quantifying theisotropy of the sound field in reverberant spaces. J Acoust Soc Am. 2018; 143(4):2514-2526.
5. Cox TJ, D’Antonio P, Avis MR, Room sizing and optimization at low frequencies. J Audio Eng Soc.
2004; 52(6). p. 358-362.
6. Acoustics - Measurement of room acoustic parameters. Performance spaces. BS EN ISO 3382-1:2009.

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