This work presents an analysis of the effect of some uncertainties encountered when measuring absorption or scattering coefficients in the reverberation chamber according to International Organization for Standardization/American Society for Testing and Materials standards. This especially relates to the uncertainty due to spatial fluctuations of the sound field. By analyzing the mathematical definition of the respective coefficient, a relationship between the properties of the chamber and the test specimen and the uncertainty in the measured quantity is determined and analyzed. The validation of the established equations is presented through comparisons with measurement data. This study analytically explains the main sources of error and provides a method to obtain the product of the necessary minimum number of measurement positions and the band center frequency to achieve a given maximum uncertainty in the desired quantity. It is shown that this number depends on the ratio of room volume to sample surface area and the reverberation time of the empty chamber.

1.
ISO 354:2003,
Acoustics—Measurement of sound absorption in a reverberation room
(
International Organization for Standardization
,
Geneva, Switzerland
,
2003
).
2.
ASTM C423:2009,
Acoustics—Standard test method for sound absorption and sound absorption coefficients by the reverberation room method
(
American Society for Testing and Materials
,
Conshohocken, PA
,
2009
).
3.
ISO 17497-1:2004,
Acoustics—Sound-scattering properties of surfaces—Part 1: Measurement of the random-incidence scattering coefficient in a reverberation room
(
International Organization for Standardization
,
Geneva, Switzerland
,
2004
).
4.
M.
Vorländer
, “
Computer simulations in room acoustics: Concepts and uncertainties
,”
J. Acoust. Soc. Am.
133
(
3
),
1203
1213
(
2013
).
5.
W. C.
Sabine
,
Collected Papers on Acoustics
(
Harvard University Press
,
Cambridge, MA
,
1923
).
6.
C. W.
Kosten
, “
International comparison measurements in the reverberation room
,”
Acustica
10
,
400
411
(
1960
).
7.
Y.
Makita
,
M.
Koyasu
,
M.
Nagata
, and
S.
Kimura
, “
Investigations into the precision of measurement of sound absorption coefficients in a reverberation room (ii), experimental studies on the method of measurement of the reverberation time and the 4th round robin test
,”
J. Acoust. Soc. Jpn.
24
,
393
402
(
1968
) (in Japanese) [Australia, CSIRO Translation (English), No. 10821].
8.
R.
Ohlan
, “
Nordic comparison measurements of absorption coefficient
,” SP-RAPP13, Swedish National Testing and Research Institute (
1977
).
9.
H.
Myncke
,
D.
Cops
, and
D.
DeVries
, “
The measurement of the sound absorption coefficient in reverberation rooms and results of a recent round robin test
,” in
Third Symposium of the Federation of Acoustical Societies of Europe
,
Yugoslavia
(
1979
), pp.
259
272
.
10.
W. A.
Davern
and
P.
Dubout
,
First Report on Australasian Comparison Measurements of Sound Absorption Coefficients
(
Commonwealth Scientific and Industrial Research Organization, Division of Building Research
,
Highett, Victoria, Australia
,
1980
).
11.
U.
Kath
and
W.
Kuhl
, “
Einfluss von Streufläche und Hallraumdimensionen auf den gemessenen Schallabsorptionsgrad” (“Influence of the scattering surface and reverberation chamber dimensions on the measured sound absorption coefficient
”),
Acustica
11
,
50
64
(
1961
).
12.
E.
Toyoda
,
S.
Sakamoto
, and
H.
Tachibana
, “
Effects of room shape and diffusing treatment on the measurement of sound absorption coefficient in a reverberation room
,”
Acoust. Sci. Technol.
25
(
4
),
255
266
(
2004
).
13.
A.
Cops
,
J.
Vanhaecht
, and
K.
Leppens
, “
Sound absorption in a reverberation room: Causes of discrepancies on measurement results
,”
Appl. Acoust.
46
(
3
),
215
232
(
1995
).
14.
A. C. C.
Warnock
, “
Some practical aspects of absorption measurements in reverberation rooms
,”
J. Acoust. Soc. Am.
74
(
5
),
1422
1432
(
1983
).
15.
W.
Kuhl
, “
Der Einfluß der Kanten auf die Schallabsorption poröser Materialien” (“The influence of edges on the sound absorption of porous materials
”),
Acustica
10
,
264
276
(
1960
).
16.
A.
de Bruijn
, “
A mathematical analysis concerning the edge effect of sound absorbing materials
,”
Acta Acust. Acust.
28
(
1
),
33
44
(
1973
).
17.
T. W.
Bartel
, “
Effect of absorber geometry on apparent absorption coefficients as measured in a reverberation chamber
,”
J. Acoust. Soc. Am.
69
(
4
),
1065
1074
(
1981
).
18.
C. G.
Balachandran
, “
Random sound field in reverberation chambers
,”
J. Acoust. Soc. Am.
31
(
10
),
1319
1321
(
1959
).
19.
G.
Venzke
and
P.
Dämmig
, “
Measurement of diffuseness in reverberation chambers with absorbing material
,”
J. Acoust. Soc. Am.
33
(
12
),
1687
1689
(
1961
).
20.
R. V.
Waterhouse
, “
Statistical properties of reverberant sound fields
,”
J. Acoust. Soc. Am.
43
(
6
),
1436
1444
(
1968
).
21.
T. F. W.
Embleton
, “
Absorption coefficients of surfaces calculated from decaying sound fields
,”
J. Acoust. Soc. Am.
49
(
1A
),
99
(
1971
).
22.
T. J.
Schultz
, “
Diffusion in reverberation rooms
,”
J. Sound Vib.
16
(
1
),
17
28
(
1971
).
23.
H. G.
Andres
and
D.
Brodhun
, “
Zur Genauigkeit von Schallabsorptionsgradsmessungen im Hallraum” (“On the accuracy of sound absorption coefficient measurements in the reverberation chamber
”),
Acustica
10
,
330
335
(
1960
).
24.
E.
Meyer
and
H.
Kuttruff
, “
Akustische Modellversuche zum Aufbau eines Hallraums” (“Acoustical model experiments on the setup of a reverberation chamber
”),
Nachr. Akad. Wiss. Göttingen
6
(
1958
),
97
114
(
1958
).
25.
G.
Venzke
, “
Die schallzerstreuende Wirkung von Kugel-und Zylindersegmenten auf Hallraumwänden” (“The sound scattering effect of spherical and cylindrical segments on the walls of reverberation chambers
”),
Acustica
10
,
170
172
(
1960
).
26.
T. W.
Bartel
and
E. B.
Magrab
, “
Studies on the spatial variation of decaying sound fields
,”
J. Acoust. Soc. Am.
63
(
6
),
1841
1850
(
1978
).
27.
S.
Müller
and
P.
Massarani
, “
Transfer-function measurement with sweeps
,”
J. Audio Eng. Soc.
49
(
6
),
443
471
(
2001
).
28.
ISO 18233:2006,
Acoustics—Application of new measurement methods in building and room acoustics
(
International Organization for Standardization
,
Geneva, Switzerland
,
2006
).
29.
S. J.
Kline
and
F. A.
McClintock
, “
Describing uncertainties in single-sample experiments
,”
Mech. Eng.
75
(
1
),
3
8
(
1953
).
30.
R. J.
Moffat
, “
Describing the uncertainties in experimental results
,”
Exp. Therm. Fluid Sci.
1
(
1
),
3
17
(
1988
).
31.
A.
Lundeby
,
T. E.
Vigran
,
H.
Bietz
, and
M.
Vorländer
, “
Uncertainties of measurements in room acoustics
,”
Acta Acust. Acust.
81
(
4
),
344
355
(
1995
).
32.
M.
Guski
and
M.
Vorländer
, “
Comparison of noise compensation methods for room acoustic impulse response evaluations
,”
Acta Acust. Acust.
100
(
2
),
320
327
(
2014
).
33.
V.
Wittstock
, “
On the uncertainty of single-number quantities for rating airborne sound insulation
,”
Acta Acust. Acust.
93
(
3
),
375
386
(
2007
).
34.
P.
Dämmig
and
H.
Deicke
, “
Measurement uncertainty in the determination of the sound absorption in a reverberation room at low frequencies
,”
Acustica
33
,
249
256
(
1975
).
35.
H. H.
Ku
, “
Notes on the use of propagation of error formulas
,”
J. Res. Nat. Bur. Standards
70
(
4
),
263
273
(
1966
).
36.
JCGM 100:2008,
Evaluation of measurement data—Guide to the expression of uncertainty in measurement
(
Joint Committee for Guides on Metrology
,
Sevres Cedex, France
,
2008
).
37.
ISO 9613-1:1993,
Acoustics—Attenuation of sound during propagation outdoors – Part 1: Calculation of the absorption of sound by the atmosphere
(
International Organization for Standardization
,
Geneva, Switzerland
,
1993
).
38.
J. L.
Davy
,
I. P.
Dunn
, and
P.
Dubout
, “
The variance of decay rates in reverberation rooms
,”
Acustica
43
(
1
),
12
25
(
1979
).
39.
J. L.
Davy
, “
The variance of impulse decays
,”
Acta Acust. Acust.
44
(
1
),
51
56
(
1980
).
40.
J. L.
Davy
, “
The variance of decay rates at low frequencies
,”
Appl. Acoust.
23
(
1
),
63
79
(
1988
).
41.
J. L.
Davy
and
I. P.
Dunn
, “
The statistical bandwidth of Butterworth filters
,”
J. Sound Vib.
115
(
3
),
539
549
(
1987
).
42.
IEC 61260:1995,
Electroacoustics—Octave-band and fractional-octave-band filters
(
International Electrotechnical Commission
,
Geneva, Switzerland
,
1995
).
43.
M. R.
Schroeder
, “
New method of measuring reverberation time
,”
J. Acoust. Soc. Am.
37
(
3
),
409
412
(
1965
).
44.
ISO 3741:2010,
Acoustics—Determination of sound power levels and sound energy levels of noise sources using sound pressure—Precision methods for reverberation test rooms
(
International Organization for Standardization
,
Geneva, Switzerland
,
2010
).
45.
ISO 10140-2:2010,
Acoustics—Laboratory measurement of sound insulation of building elements—Part 2: Measurement of airborne sound insulation
(
International Organization for Standardization
,
Geneva, Switzerland
,
2010
).
46.
ASTM E90:2009,
Acoustics—Standard test method for laboratory measurement of airborne sound transmission loss of building partitions and elements
(
American Society for Testing and Materials
,
Conshohocken, PA
,
2009
).
47.
J. L.
Davy
, “
The relative variance of the transmission function of a reverberation room
,”
J. Sound Vib.
77
(
4
),
455
479
(
1981
).
48.
www.ita-toolbox.org (Last viewed November 4, 2014).
You do not currently have access to this content.