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

On the use of geometrical acoustic models of a reverberant chamber
to improve the reliability of sound absorption measurements
Francesco MARTELLOTTA*; Ubaldo AYR; Chiara RUBINODICAR – Politecnico di Bari, via Orabona 4, Bari, Italy

ABSTRACT
Measuring sound absorption in reverberant chambers, even when complying with ISO 354 standard, may
often return results affected by significant uncertainty, while repeatability is also a well known issue whendifferent laboratories are involved. When considering results from a single laboratory, obtained from a
specific chamber, several elements contribute to the quality of the measurement, some of them are moreevident (like the diffusers), while others are more difficult to account (like the sample position, mounting, andsealings). With reference to the diffusers, one effect typically attributed to insufficient diffusion is the factthat calculated absorption coefficients are higher than unity. The present paper investigates how these effects
may be better understood by means of geometrical acoustic modelling, analyzing the variations inreverberation time (and hence in absorption coefficients), resulting from different positioning of diffusers, aswell as locations of sample, sources and receivers in real rooms and comparing them with simulated values.
Keywords: Sound absorption; reverberant chamber; ISO 354

1. INTRODUCTION
Sound absorption coefficients of materials and surfaces are normally measured using small samples
mounted in a standing wave tube according to ISO 10354-2 standard (1). The method is known to beaccurate, but it is limited to normal incidence, and it clearly fails in reproducing real world mounting
conditions of larger samples. Under such conditions a measurement in a reverberant chamber,(according to ISO 354 standard (2)), is typically preferred because it also returns the diffuse field
behavior of the material and allows measuring sound absorption of objects and materials which require
more complex supporting structures (like ceilings, etc.). However, even this method is not immune
from criticism. In fact, it is known to return results that are not as accurate and repeatable as desired (3).
In fact, the method relies on the measurement of reverberation times with and without the sample to betested, and on the subsequent calculation of the sound absorption based on the classical Sabine's
formula. As it is an indirect measure, the accuracy of the method largely depends on the correctness ofthe formula used to relate absorption and reverberation time, which normally means that the roommust be ergodic, mixing and weakly absorbing to ensure the sound field to be sufficiently diffuse(4,5).
For the same reason sample dimension should not be too large to avoid further increasing unevensound propagation. When one, or more, of the above requirements are not met, use of classicaldiffuse-field formulas may result in large discrepancies between measured and predicted reverberation
time, consequently inducing significant inaccuracy in sound absorption determination.
In order to prevent such measurement problems, qualification tests are usually required bystandards. ISO standard 354:2003 (2) poses no limitations to reverberation time variances, but aminimum number of diffusers must be installed so that the measured absorption coefficient reaches amaximum and then remains stable. The recommended area of diffusers is between 15% and 25% of thetotal surface area, and the panels should have different sizes from 0.8 m2 to 3 m2 . Conversely, ASTM
C423-17 (6) requires the relative variation of decay rates with microphone position (to be moved in atleast five positions) to be smaller than a maximum limit, when the room is empty. The relative
variation is expressed as the ratio of the standard deviation between decay rate measurements and theirmean value. However, both the qualification procedures fail in some way, considering that a number ofround-robin tests (7,8) pointed out significant repeatability issues.
*

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francesco.martellotta@poliba.it

However, although not recognized by any standard, the effects of room geometry, its diffuseness,and sample placement may be investigated by means of computerized geometrical acoustic (GA)simulation tools. This idea was first introduced by Benedetto and Spagnolo (9) who suggested that,even in a standard reverberant chamber, sound absorption coefficients of materials could be moreaccurately determined by properly modelling the test room, and obtaining the absorption coefficientsof the material by matching the measured and simulated reverberation time. This procedure, like all
GA methods, is effective in medium-high frequency range and has been successfully tested in several
occasions (10,11), receiving an even more refined treatment based on an iterative least-mean squares
optimization (12). The latter approach, if properly applied first to the empty room, and then to theroom with the added sample, is expected to provide more accurate absorption coefficients for use insimulation models. In the present paper, taking advantage of a series of measurements carried out inthe reverberant chamber of the Laboratory of Building Physics of the Politecnico di Bari, several
configurations were investigated, changing diffusers positions and adding sound absorbing patches.
The effects of such changes on measured sound absorption coefficients were first discussed. Then, thesame configurations were analyzed in the GA simulation tool.

2. METHODS
2.1 Laboratory measurements
The reverberant room is a 200 m3 space, with a surface area of 208 m2, having six non-parallel walls
and a splayed ceiling to aid diffusion. The floor is finished in marble, while walls and ceiling are
plastered with a very smooth finishing coated with enamel varnish. Six curved diffusers made of
Plexiglas having different shapes and a total two-sided area of 20 m2 are randomly suspended from theceiling. The area of diffusers corresponded to 10% of the total surface area, thus slightly below theminimum recommended value (2) of 15%. Two loudspeaker positions and six microphone positions
were used to obtain average reverberation time values. Sabine’s formula was used to calculate
absorption coefficients. Air temperature and relative humidity were continuously recorded in order tocompensate for air absorption variations throughout each test. Corrections were made according toISO 9613-1 (13). A 10.8 m2 polyester fiber mat, 2 cm thick was used as test sample.
The measurement equipment included two omni-directional sound sources (Look-Line D301 andB&K 4295), two random incidence microphones (GRAS 40-AR), and a 24 bit/48 kHz sound card
(Echo Layla 24). Reverberation time was calculated from impulse responses obtained by exciting theroom with a 19 s logarithmic sine sweep.
The chamber configuration was changed as follows.
a) Config. A: Reference configuration; with diffusers suspended to the ceiling, one source
position on the corner and one at 1.5 m distance from reflecting surfaces (Figure 1a);b) Config. B: Damped; same as before, with three polyester fiber panels (10 cm thick, 0.6 m by 1.2m) located vertically at three corners so to create a varying depth air gap (bass trap mounting);c) Config. C: Damped with modified diffusers; same as reference with only two polyester fiber
panels located at opposite corners (Figure 1b), one of the ceiling diffusers (1.61 m2 area) was
mounted vertically on the floor, and one extra wooden diffuser (0.6 m by 0.5 m) was located ina corner. Both source positions were located on the floor close to corners.

a)b)

Figure 1 – Plan and cross section of the reverberant chamber under a) config. A, b) config. C

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2.2 Geometrical acoustic model
The geometrical acoustic model of the reverberant chamber was made using the commercial
software CATT Acoustic, with the TUCT v. 1.0 engine (14). This tool provides different algorithms tocompute impulse responses, mostly differing in terms of treatment of diffuse reflections. Algorithm 1
always treats first-order reflections deterministically, meaning that each ray is split into a part that isreflected according to the laws of GA and one that is scattered. Conversely, higher order reflections are
not split, but are treated randomly depending on the scattering coefficient of the surface (e.g. if thelatter is 0.1, 9 reflection out of 10 will be reflected specularly, while the others will be reflected
randomly). A more refined method, named Algorithm 2, uses a first degree of actual ray split-up for allreflection orders where all specular-specular and all specular-diffuse reflections are deterministic,
while remaining reflection combinations are treated randomly. This algorithm is computationally moredemanding and is recommended for room with critical conditions. In the present case, given the very
low scattering coefficients used for large flat surfaces, no significant differences were expected
between the two methods, so the simpler and computationally efficient Algorithm 1 was used.
The geometrical model used for calculations was dimensionally identical to the real room (Figure2), with a volume of 200 m3 , a floor surface of 45 m2 , and an overall surface of 208 m2 excluding
diffusers and other movable elements. Sources and receivers were located in the same positions usedduring the measurements and the sources were assumed to be omni-directional. Calculations were runusing the recommended number of ray which was about 37000, and truncation time (i.e. the length of
the simulated impulse response, was set to equal the longest measured reverberation time under thesame configuration). The Schroeder frequency varied between 430 Hz under empty conditions, and360 Hz when the sample is in place. Thus, results in the lowest two bands are unreliable and otherprediction tools should be used (15). The effect of air absorption was taken into account by properly
setting temperature and relative humidity as measured during the on-site survey, so that the software
could calculate the appropriate coefficients according to ISO 9613-1.
Absorption and scattering coefficients of the different surfaces were assigned starting fromliterature values, and subsequently refining them in order to obtain the best match with measured
results under the same conditions. Given the nature of the simulation, a maximum difference between
measured and predicted values of 1% was considered as acceptable. Reverberation times (T30)
measured under the different conditions as listed in Table 1, as well as under no-diffusers conditions,were used as reference. The resulting absorption coefficients are given in Table 2.
With reference to scattering coefficients, given the smooth nature of the surfaces, the values wereassumed to be independent of frequency and very low. The typical value which is recommended forflat surfaces is 0.1, but, for the above reasons, all the calculations were carried out assuming also avalue of 0.05. No significant variations as a function of scattering coefficients appeared for the empty
room, thus suggesting that diffuse conditions are met in the model even when the lowest scattering
coefficients are used. For diffusers, the “automatic edge diffusion” option was activated to take into
account the diffraction effects at the borders of the panels.
Table 1. Reverberation times measured under the different configurations
Room configuration
Octave band [Hz]
125
250
500
Empty room
10.79 11.05 10.30
Empty room with diffusers
8.68
9.64
8.87
Empty room with diffusers and dampers
5.11
4.06
2.93

1000
8.35
7.83
2.23

2000
6.35
6.15
1.86

2m
Volume:205.8m³ (approx.)

Y
05
A2
03

04
02

01

06

A0
X

Figure 2 – Plan and 3D view of the GA model of the reverberant chamber

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4000
4.02
4.05
1.51

Table 2. Absorption coefficients used in the simulation
Material
Octave band [Hz]125
Marble floor
0.013
Plastered surfaces finished with enamel varnish
0.010
Simple door
0.200
Plexiglas diffusers
0.033
Polyester fiber panel
0.600

250
0.013
0.011
0.120
0.020
0.840

500
0.015
0.011
0.100
0.020
0.940

1000
0.02
0.011
0.080
0.015
0.950

2000
0.02
0.014
0.060
0.012
0.920

4000
0.020
0.014
0.040
0.010
0.960

3. Results
3.1 Measurements
First of all, the results of the measurements of reverberation time (T30) in the empty chamber under
the different conditions are presented (Figure 3a). Results show quite impressive variations,particularly when the damping panels are added to the room, showing nearly halved values underconfig. B and slightly longer T30 values under config. C. As expected, T30 values drop at the highest
frequencies as a consequence of the air absorption. In fact, calculation of the total equivalent
absorbing area (Figure 3b) in which air absorption is subtracted, shows a rather flat response as afunction of frequency. In all the cases total equivalent absorbing area falls below the maximum limit
prescribed by ISO 354 standard (2). Thanks to the corner mounting, the polyester fiber panels provided
a relatively flat increase to absorbing area, allowing a smooth control of the room conditions without
the sample installed.
The absorption coefficients of the test panel were calculated with reference to one-third octave
bands (Figure 4a) and octave bands (Figure 4b). Results showed that both configurations B and C
provided similar results, while config. A yielded lower absorption values, particularly in the highfrequency range, where an underestimation of about 10% appeared.
14
Equivalent sound absorption [m2]12

Reverberation time [s]1086No diffusers

4

Config. A
Config. B

2

Config. C

12

Limit

10

Config. B

Config. A
Config. C

8
6
4
2

0

0
125

250

500
1000
Frequency [Hz]

a)

2000

4000

125

250

500
1000
Frequency [Hz]

b)

2000

4000

Figure 3 – Plot of a) average reverberation time (T30) and b) equivalent sound absorption as a function of

1

1.0

0.9

0.9

0.8

0.8

Absorption coefficient

Absorption coefficientdifferent configurations including ISO 354 limits

0.7
0.6
0.5
0.4
0.3
Config. A
Config. B
Config. C

0.2
0.1

One-third octave band [Hz]

5000

4000

3150

2500

2000

1600

1250

800

1000

630

500

400

315

250

200

160

125

a)

0.6
0.5
0.4
0.3

Config. A

0.2

Config. B

0.1

Config. C

0.0

100

0

0.7

125

b)

250

500

1000

2000

4000

Octave band [Hz]Figure 4 – Plot of ISO 354 absorption coefficients as a function of frequency and of different configurationsin a) one-third octave bands and b) octave bands

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This behavior could be explained as a consequence of the position of the sample on the floor surface
and of the fact that all lateral walls were vertical and without any scattering element, so that slowly
decaying reflection paths moving at grazing incidence over the floor, could barely interact with thesample to be tested. Conversely, the presence of sound absorbers and of additional diffusing elements
along the vertical surfaces close to the floor contributed to dampen that slowly decaying paths. Thus,
the location of damping or diffusing elements close to the floor but on vertical surfaces, a portion of
the space which is typically left untreated to ease sample placement and source and receiver movement,
actually proved to be effective in obtaining more diffuse conditions and more reliable results.
3.2 GA models
Taking into account the above results, the GA model was used in order to answer the following
questions:
1) Is it possible to better explain the differences between config. A and the others?
2) Does the GA model respond correctly to changes in room configuration?
3) How could GA models help to improve measurement accuracy?
With reference to the first question, starting from the calibrated model of config. A, the absorption
coefficients of the test sample were iteratively changed until the lowest possible difference (below 1%)
was found between measured and simulated values. The results of the iterative adjustment procedure
were shown in Table 3, suggesting that when the scattering coefficient of the flat surfaces was set to0.05 an error below 1% was obtained adopting sound absorption values that were in close agreementwith those obtained from measurements under config. B and C. If the scattering coefficient assigned toflat surfaces was increased to 0.10 (the default value) a slight decrease in the absorption coefficients ofthe sample was observed, but they remained fairly close to those measured in configs. B and C,
confirming that GA modelling may provide more reliable results than just using Sabine’s formula.
Finally, in order to define a unique scattering coefficient to be used in the subsequent calculations, theabsorption coefficients measured under config. C were used to feed the GA model, and the scattering
was changed until a good match between predictions and measurements was found. A value of 0.07 at
frequencies from 500 Hz to 1 kHz, and of 0.06 at the remaining bands, was finally assigned. Low
frequencies were not included in the optimization and a default value of 0.10 was assigned.
Table 3. Comparison between measured and simulated reverberation times under config. A
Material
Octave band [Hz]
125
250
500
1000
2000
4000
Measured T30
6.97
6.14
4.08
2.83
2.28
1.80
Predicted T30 (scattering coefficient set to 0.05)
6.93
6.11
4.08
2.81
2.26
1.79
% Error-0.5% -0.5% 0.0% -0.6% -0.7% -0.3%
Sample absorption coefficient
0.10
0.19
0.41
0.71
0.88
0.99
Predicted T30 (scattering coefficient set to 0.10)
6.92
6.09
4.04
2.81
2.25
1.78
% Error-0.6% -0.8% -1.0% -0.6% -0.9% -0.9%
Sample absorption coefficient
0.10
0.19
0.41
0.69
0.85
0.96
To answer question 2, starting from the calibrated model (including measured absorption
coefficients of the sample, and optimized scattering coefficients), reverberation times referred toconfigurations B and C without and with samples were analyzed and the respective errors calculated.
Results, summarized in Table 4, showed that for all the configurations, at frequencies above
Schroeder’s limit, the errors were typically very small (around 1%) with some exceptions in which
errors never exceeded 2.5%. No systematic behavior could be seen in these errors, as they had different
signs, took place at different frequencies in different configurations. However, on average, in presenceof the sample, slightly larger errors were found, even though they were mostly at lower frequencies,
where diffusers are less effective and modal behavior affects measurements. At high frequencies,
where the largest variations in measured absorption coefficients were found, with respect to thedifferent analyzed configurations, results were very good. This was an important result, also
considering uncertainties related to air absorption, which in the software is computed according to ISO
9613-1 (13) based on actual values of temperature and relative humidity. So, after all, the GA model
proved to be a reliable approximation of the room behavior above Schroeder’s frequency.

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Table 4. Comparison between measured and simulated reverberation times under config. B and C
Material
Octave band
125
250
500
1000
2000
4000
[Hz]
Measured T30 (Config. B, empty)
5.84
5.53
5.03
4.69
4.09
3.02
Predicted T30 (Config. B, empty)
5.87
5.52
5.04
4.64
4.04
2.97
Error (%)
0.51% -0.18% 0.20% -1.07% -1.22% -1.66%
Measured T30 (Config. B, full)
5.11
4.06
2.94
2.23
1.86
1.51
Predicted T30 (Config. B, full)
5.30
4.18
2.94
2.17
1.85
1.51
Error (%)
3.72% 2.96% 0.00% -2.69% -0.54% 0.00%
Measured T30 (Config. C, empty)
6.38
6.25
5.90
5.42
4.60
3.19
Predicted T30 (Config. C, empty)
6.57
6.45
5.91
5.47
4.57
3.14
Error (%)
2.98% 3.20% 0.17% 0.92% -0.65% -1.57%
Measured T30 (Config. C, full)
5.62
4.57
3.18
2.42
1.97
1.55
Predicted T30 (Config. C, full)
5.90
4.69
3.26
2.40
1.95
1.53
Error (%)
4.98% 2.63% 2.52% -0.83% -1.02% -1.29%
In order to answer the last question there are several aspects that could be considered. First of all, it
is possible to take advantage of the potential offered by the GA modelling tool to visualize the soundfield and, in particular, the position of the image sources (up to the 9 th order). Figure 5 compares the
distribution pertaining to configurations A and C, as a function of source positions. In all the cases
there is a large number of image sources that lay close to the horizontal plane, but in case A their
number is larger than in case C, confirming the important role played by grazing sound, and that of theelements that may contribute to absorb or break those paths. The position of the source on the floor
also seems to contribute significantly to reduce the spatial distribution of the image sources, while theposition off the floor (Figure 5c) makes a much more scattered cloud of image sources, but theconcentration of sources along planes parallel to the floor remains and is even more evident (anddoubled because of floor reflections).
So, as the increase in scattering coefficient of flat surfaces clearly shortened the reverberation time
under fully occupied room, while the empty room proved to be immune as the lengthy reverberation
contributed to further diffuse the reflections, a possible use of the GA model could be that of
optimizing the distribution of reflectors/diffusers, so to improve diffuse field conditions.

Order
0
1
2
3
A001

4
5

01 A1

6
7
8

a)

b)

354_isolm_d7

354_isolm_d7

01 A2

A001

c)

d)

draft_full_d7

draft_full_d7

Figure 5 – Plot of the image source distribution as a function of source position and different room
configuration: a) Config. A, S-A; b) Config. A, S-B; c) Config. C, S-A; d) Config. C, S-B

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A001

a)

01 A1

b)

extra_empty_d7

extra_em pty_d7

Figure 6 – Plot of the image source distribution (up to 9th order) as a function of source position for theconfiguration with alternate diffuser placement: a) S-A; b) S-B.
Table 5. Comparison between measured and simulated reverberation times under the optimized diffusers
configuration
Material
Octave band [Hz]125250
Predicted T30 (empty)
8.22
9.27
Predicted T30 (full)
7.19
6.1
Absorption coeff. (calculated from Sabine)
0.05
0.17

500
8.67
4.04
0.40

1000
7.82
2.83
0.68

2000
6.07
2.23
0.86

4000
3.82
1.71
0.98

As an example, two more 1.3 m square diffusers have been added on the walls located at 0 and 0.65
m from the floor in order to intercept and disrupt persistent and nearly-horizontal paths. The plot of theimage source distribution (Figure 6) shows a significant improvement, with a more even distributionof the points and a reduction of those laying on the same plane. In terms of predicted reverberation
times, they show in both empty and full configuration an almost perfect agreement with those
calculated using Sabine’s formula and the resulting absorption coefficients (Table 5) are almost
coincident with those used in the model (which are those resulting from measurements in config. B and
C). So, controlling reflection paths, without adding any damping material, it was possible to overcome
the limitations observed when configuration A was adopted.

4. CONCLUSIONS
Geometrical acoustic simulation can be a valid help to support and complement measurements ofsound absorption coefficient in a reverberant chamber according to ISO 354 standard. In fact, sounddiffusers are typically mounted far from the areas where the sample to be tested must be located, inorder to avoid interferences with sources, microphones and operators. However, this leaves room topersistent horizontal reflection paths which may result in an underestimation of the absorption
coefficient in certain situations (e.g. when the sample is very thin). Adoption of damping andscattering elements located along the plane parallel to the floor prove to be beneficial to obtaining
more accurate measurements. A comparison between the results obtained using different roomarrangements and those obtained by geometrical acoustic simulation showed that the latter contributed
to immediately obtain the correct sound absorption coefficient even when the results of the less diffuse
configuration were used to feed the model. Conversely, using the absorption coefficients resulting
from the more diffusing configurations to feed the geometrical acoustic model resulted in very
accurate reverberation time prediction under all the analyzed combinations. Finally, taking advantageof the good performance shown by the method, it was used to propose alternative configurations
capable of overcoming the observed limitations without the use of damping elements. Further
investigations are under way in order to take into account different and thicker samples.

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