This work investigates the use of the initial decay time to obtain the Sabine absorption coefficient from measurements conducted in a reverberation chamber. Due to non-uniform distribution of sound absorption in the test chamber, measured energy decay functions exhibit multiple slopes, which cannot be evaluated unambiguously using linear regression as prescribed in the current standard (ISO 354, International Organization for Standardization, Geneva, Switzerland, 2003). As an alternative, this study proposes a Bayesian framework that allows estimating multiple decay parameters, hence capturing more accurately the energy decay features. Measurements are carried out in a reverberation chamber with and without diffusing elements to investigate the influence of diffusers on the absorption coefficient and on the decay process. Measured absorption coefficients of a porous sample are compared to theoretical values estimated with a transfer matrix model. The results show that the Sabine absorption coefficient calculated using the shortest decay time agrees well with the size-corrected theoretical absorption coefficient.

1.
ISO 354:2003
, “
Acoustics—Measurement of sound absorption in a reverberation room
” (International Organization for Standardization, Geneva, Switzerland,
2003
).
2.
W.
Sabine
,
Collected Papers on Acoustics
(
Harvard University Press
,
Cambridge
,
1922
), pp.
3
68
.
3.
F. V.
Hunt
,
L. L.
Beranek
, and
D. Y.
Maa
, “
Analysis of sound decay in rectangular rooms
,”
J. Acoust. Soc. Am.
11
(
1
),
80
94
(
1939
).
4.
H.
Kuttruff
, “
Eigenschaften und Auswertung von Nachhallkurven (Characteristics and analysis of decay curves)
,”
Acta Acust. Acust.
8
(
4
),
273
280
(
1958
).
5.
E.
Nilsson
, “
Decay processes in rooms with non-diffuse sound fields. Part I: Ceiling treatment with absorbing material
,”
Build. Acoust.
11
(
1
),
39
60
(
2004
).
6.
W.
Davern
and
P.
Dubout
, “
First report on Australasian comparison measurements of sound absorption coefficients
,” DBR Special Report, CSIRO Division of Building Research, Highett (
1980
).
7.
ASTM
, “
Interlaboratory study to establish precision statements for ASTM C423
,” Research Report E33-1010 (
2006
).
8.
A.-C.
Thysell
, “
Test codes for suspended ceilings—Sound absorption RRT
,” Tyrens AB project no. 224628, Tyrens, A. B. Sweden (
2011
).
9.
L.
Savioja
and
U. P.
Svensson
, “
Overview of geometrical room acoustic modeling techniques
,”
J. Acoust. Soc. Am.
138
(
2
),
708
730
(
2015
).
10.
M.
Vorländer
, “
Computer simulations in room acoustics: Concepts and uncertainties
,”
J. Acoust. Soc. Am.
133
(
3
),
1203
1213
(
2013
).
11.
J.
Allard
,
Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials
(
Elsevier Science Publishers
,
Essex, England
,
1993
), p.
38
.
12.
Y.
Miki
, “
Acoustical properties of porous materials. Modifications of Delany-Bazley models
,”
J. Acoust. Soc. Am.
11
(
1
),
19
24
(
1990
).
13.
S.-I.
Thomasson
, “
On the absorption coefficient
,”
Acta Acust. Acust.
44
(
4
),
265
273
(
1980
).
14.
M. R.
Schroeder
, “
New method of measuring reverberation time
,”
J. Acoust. Soc. Am.
37
(
3
),
409
412
(
1965
).
15.
P.
Bruel
, “
The enigma of sound power measurements at low frequencies
,”
Bruel & Kjaer Tech. Rev.
34
,
3
40
(
1978
).
16.
F.
Jacobsen
,
Fundamentals of General Linear Acoustics
(
John Wiley & Sons
,
United Kingdom
,
2013
), pp.
151
153
.
17.
F.
Jacobsen
, “
Decay rates and wall absorption at low frequencies
,”
J. Sound Vib.
81
(
3
),
405
412
(
1982
).
18.
ISO 3382-2:2008
, “
Acoustics—Measurement of room acoustic parameters—Part 2: Reverberation time in ordinary rooms
” (International Organization for Standardization, Geneva, Switzerland,
2008
).
19.
E.
Nilsson
, “
Decay processes in rooms with non-diffuse sound fields. Part II: Effect of irregularities
,”
Build. Acoust.
11
(
2
),
133
143
(
2004
).
20.
J.
Balint
,
F.
Muralter
,
M.
Nolan
, and
C.-H.
Jeong
, “
Energy decay curves in reverberation chambers and the influence of scattering objects on the absorption coefficient of a sample
,” in
Conference Proceedings Euronoise 2018
,
Crete, Greece
(
2018
), pp.
2025
2030
.
21.
J.
Balint
and
G.
Graber
, “
Gekruemmte Abklingkurven in Hallräumen (Curved energy decays in reverberation rooms)
,” in
Proceedings of the 44th Annual Meeting for Acoustics DAGA
,
Munich, Germany
(
2018
).
22.
N.
Xiang
and
P. M.
Goggans
, “
Evaluation of decay times in coupled spaces: Bayesian parameter estimation
,”
J. Acoust. Soc. Am.
110
(
3
),
1415
1424
(
2001
).
23.
N.
Xiang
and
P. M.
Goggans
, “
Evaluation of decay times in coupled spaces: Bayesian decay model selection
,”
J. Acoust. Soc. Am.
113
(
5
),
2685
2697
(
2003
).
24.
N.
Xiang
and
T.
Jasa
, “
Evaluation of decay times in coupled spaces: An efficient search algorithm within the Bayesian framework
,”
J. Acoust. Soc. Am.
120
(
6
),
3744
3749
(
2006
).
25.
N.
Xiang
,
P.
Goggans
,
T.
Jasa
, and
P.
Robinson
, “
Bayesian characterization of multiple-slope sound energy decays in coupled-volume systems
,”
J. Acoust. Soc. Am.
129
(
2
),
741
752
(
2011
).
26.
A.
Shukla
,
M.
Peter
, and
L.
Hoffmann
, “
Analysis of positron lifetime spectra using quantified maximum entropy and a general linear filter
,”
Nuclear Instrum. Methods Phys. Res. A
335
,
310
317
(
1993
).
27.
A.
Shukla
,
L.
Hoffmann
,
A.
Manuel
, and
M.
Peter
, “
Bayesian methods for lifetime analysis
,”
Mater. Sci. Forum
175–178
,
939
946
(
1995
).
28.
A.
Shukla
,
L.
Hoffmann
,
A.
Manuel
, and
M.
Peter
, “
Melt 4.0a a Program for Positron Lifetime Analysis
,”
Mater. Sci. Forum
255–257
,
233
237
(
1997
).
29.
L.
Hoffmann
,
A.
Shukla
,
M.
Peter
,
B.
Barbiellini
, and
A.
Manuel
, “
Linear and non-linear approaches to solve the inverse problem: Applications to positron annihilation experiments
,”
Nuclear Instrum. Methods Phys. Res. Sec. A
335
(
1–2
),
276
287
(
1993
).
30.
C.-H.
Jeong
,
S.-H.
Choi
, and
I.
Lee
, “
Bayesian inference of the flow resistivity of a sound absorber and the room's influence on the Sabine absorption coefficients
,”
J. Acoust. Soc. Am.
141
(
3
),
1711
1714
(
2017
).
31.
N.
Xiang
and
C.
Landschoot
Bayesian inference for acoustic direction of arrival analysis using spherical harmonics
,”
Entropy
21
(
579
),
2
21
(
2019
).
32.
S. F.
Gull
and
J.
Skilling
, “
Maximum entropy method in image processing
,”
IEE Proc. F
131
(
6
),
646
659
(
1984
).
33.
R. K.
Bryan
,
Maximum Entropy and Bayesian Methods
, edited by
P. F.
Fougere
(
Kluwer
,
Dordrecht
,
1990
), Vol.
127
(
6
), pp.
221
232
.
34.
H.
Kuttruff
,
Room Acoustics
(
CRC Press
,
Boca Raton, FL
,
2016
), p.
302
.
35.
C.-H.
Jeong
, “
Non-uniform sound intensity distributions when measuring absorption coefficients in reverberation chambers using a phased beam tracing
,”
J. Acoust. Soc. Am.
127
(
6
),
3560
3568
(
2010
).
36.
C.-H.
Jeong
, “
Converting Sabine absorption coefficients to random incidence absorption coefficients
,”
J. Acoust. Soc. Am.
133
(
6
),
3951
3962
(
2013
).
37.
J.
Brunskog
, “
The forced sound transmission of finite single leaf walls using a variational technique
,”
J. Acoust. Soc. Am.
132
(
3
),
1482
1493
(
2012
).
38.
J.
Brunskog
, “
Sound radiation from finite surfaces
,”
J. Acoust. Soc. Am.
133
(
5
),
3385
3385
(
2013
).
39.
M. E.
Delany
and
E. N.
Bazley
, “
Acoustical properties of fibrous absorbent materials
,”
Appl. Acoust.
3
(2),
105
116
(
1970
).
40.
M.
Berzborn
and
M.
Vorländer
, “
Investigations on the directional energy decay curves in reverberation rooms
,” in
Conference Proceedings Euronoise 2018
,
Crete, Greece
(
2018
), pp.
2005
2010
.
41.
M.
Nolan
,
E.
Fernandez-Grande
,
J.
Brunskog
, and
C.-H.
Jeong
, “
A wavenumber approach to quantifying the isotropy of the sound field in reverberant spaces
,”
J. Acoust. Soc. Am.
143
(
4
),
2514
2526
(
2018
).
42.
D. T.
Bradley
and
L. M.
Wang
, “
Quantifying the double slope effect in coupled volume room systems
,”
Build. Acoust.
16
(
2
),
105
123
(
2009
).
43.
F.
Muralter
and
J.
Balint
, “
Analysis tools for multi-exponential energy decay curves in room acoustics
,” in
Proceedings of the 45th Annual Meeting for Acoustics DAGA
,
Rostock, Germany
(
2019
).
44.
J.
Skilling
, “
Quantified maximum entropy
,” in
Maximum Entropy and Bayesian Methods
(
Springer
,
New York
,
1990
), pp.
341
350
.
You do not currently have access to this content.