ASTM E2611-09
(Test Method)Standard Test Method for Measurement of Normal Incidence Sound Transmission of Acoustical Materials Based on the Transfer Matrix Method
Standard Test Method for Measurement of Normal Incidence Sound Transmission of Acoustical Materials Based on the Transfer Matrix Method
SIGNIFICANCE AND USE
There are several purposes of this test:
For transmission loss: (a) to characterize the sound insulation characteristics of materials in a less expensive and less time consuming approach than Test Method E 90 and ISO 140-3 (“reverberant room methods”), (b) to allow small samples tested when larger samples are impossible to construct or to transport, (c) to allow a rapid technique that does not require an experienced professional to run.
For transfer matrix: (a) to determine additional acoustic properties of the material; (b) to allow calculation of acoustic properties of built-up or composite materials by the combination of their individual transfer matrices.
There are significant differences between this method and that of the more traditional reverberant room method. Specifically, in this approach the sound impinges on the specimen in a perpendicular direction (“normal incidence”) only, compared to the random incidence of traditional methods. Additionally, revereration room methods specify certain minimum sizes for test specimens which may not be practical for all materials. At present the correlation, if any, between the two methods is not known. Even though this method may not replicate the reverberant room methods for measuring the transmission loss of materials, it can provide comparison data for small specimens, something that cannot be done in the reverberant room method. Normal incidence transmission loss may also be useful in certain situations where the material is placed within a small acoustical cavity close to a sound source, for example, a closely-fitted machine enclosure or portable electronic device.
Transmission loss is not only a property of a material, but is also strongly dependent on boundary conditions inherent in the method and details of the way the material is mounted. This must be considered in the interpretation of the results obtained by this test method.
The quantities are measured as a function of frequency with a resolution ...
SCOPE
1.1 This test method covers the use of a tube, four microphones, and a digital frequency analysis system for the measurement of normal incident transmission loss and other important acoustic properties of materials by determination of the acoustic transfer matrix.
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: E2611 − 09
Standard Test Method for
Measurement of Normal Incidence Sound Transmission of
Acoustical Materials Based on the Transfer Matrix Method
This standard is issued under the fixed designation E2611; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3. Terminology
1.1 This test method covers the use of a tube, four 3.1 Definitions—Theacousticalterminologyusedinthistest
microphones, and a digital frequency analysis system for the method is intended to be consistent with the definitions in
measurement of normal incident transmission loss and other Terminology C634.
important acoustic properties of materials by determination of
3.1.1 reference plane—an arbitrary section, perpendicular to
the acoustic transfer matrix.
the longitudinal axis of the tube that is used for the origin of
lineardimensions.Oftenitistheupstream(closesttothesound
1.2 The values stated in SI units are to be regarded as
source) face of the specimen but, when specimen surfaces are
standard. No other units of measurement are included in this
irregular, it may be any convenient plane near the specimen.
standard.
3.1.2 sound transmission coeffıcient, τ—(dimensionless) of
1.3 This standard does not purport to address all of the
a material in a specified frequency band, the fraction of
safety concerns, if any, associated with its use. It is the
airborne sound power incident on a material that is transmitted
responsibility of the user of this standard to establish appro-
by the material and radiated on the other side.
priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use.
W
t
τ 5
W
i
2. Referenced Documents
where:
2.1 ASTM Standards:
W and W = the transmitted and incident sound power.
t i
C634 Terminology Relating to Building and Environmental
3.1.3 sound transmission loss, TL—of a material in a speci-
Acoustics
fied frequency band, ten times the common logarithm of the
E90 Test Method for Laboratory Measurement of Airborne
reciprocal of the sound transmission coefficient. The quantity
Sound Transmission Loss of Building Partitions and
so obtained is expressed in decibels.
Elements
E1050 Test Method for Impedance and Absorption of
W 1
i
TL 5 10 log 5 10 log
S D S D
Acoustical Materials Using aTube,Two Microphones and 10 10
W τ
t
a Digital Frequency Analysis System
3.1.3.1 Discussion—In this standard the symbol TL will be
n
2.2 ISO Standards: applied to sound which impinges at an angle normal to the test
ISO 140-3 Acoustics—Measurement of Sound Insulation in specimen, as opposed to an arbitrary or random angle of
Buildings and of Building Elements—Part 3: Laboratory incidence.
Measurement of Airborne Sound Insulation of Building
3.2 Symbols:
Elements
c = speed of sound, m/s.
ρ = density of air, kg/m .
f = frequency, hertz, (Hz).
ThistestmethodisunderthejurisdictionofASTMCommitteeE33onBuilding
G , G , etc. = auto power spectra (autospectrum) of the
and Environmental Acoustics and is the direct responsibility of Subcommittee 11 22
E33.01 on Sound Absorption. acoustic pressure signal at microphone locations 1, 2, and so
Current edition approved March 1, 2009. Published March 2009. DOI: 10.1520/
on.
E2611-09.
2 G , G , etc. = cross power spectrum (cross spectrum) of
For referenced ASTM standards, visit the ASTM website, www.astm.org, or 21 32
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM the acoustic pressure signals at location 2 relative to location 1,
Standards volume information, refer to the standard’s Document Summary page on
3 relative to 1, and so on. In general, a complex value.
the ASTM website.
¯ ¯
H ,H , etc. = measured transfer function of the acoustic
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 21 31
4th Floor, New York, NY 10036, http://www.ansi.org. pressure signals at location 2 relative to location 1, 3 relative to
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2611 − 09
1, and so on. In general, a complex value. Note that H is valued in general. The following may be useful in evaluating
purely real and equal to 1. the defining equations:
I II
H , H = calibration transfer functions for the microphones
jω
e 5 cos ω 1jsin ω
~ ! ~ !
in the standard and switched configurations, respectively. See
~A1jB! 3~C1jD! 5 ~AC1BD!1j~AD1BD!
8.4.
2 2 2 2
c
1/~A1jB! 5 A/~A 1B ! 2 jB/~A 1B !
H = complex microphone calibration factor accounting for
microphone response mismatch.
4. Summary of Test Method
H , H , etc. = transfer function of two microphone signals
21 31
corrected for microphone response mismatch. In general, a 4.1 This test method is similar toTest Method E1050 in that
complex value. it also uses a tube with a sound source connected to one end
and the test sample mounted in the tube. For transmission loss,
NOTE 1—In this context, the term “transfer function” refers to the
four microphones, at two locations on each side of the sample,
complex ratio of the Fourier transform of two signals. The term “fre-
aremountedsothediaphragmsareflushwiththeinsidesurface
quency response function” arises from more general linear system theory
(1). This test method shall retain the use of the former term. Users should
of the tube perimeter. Plane waves are generated in the tube
be aware that modern FFT analyzers might employ the latter terminology.
using a broadband signal from a noise source. The resulting
standing wave pattern is decomposed into forward- and
j = =21
-1 backward-traveling components by measuring sound pressure
k=2πf/c; wave number in air, m .
simultaneously at the four locations and examining their
r i r
NOTE 2—In general the wave number is complex wherek’=k –jk. k
relative amplitude and phase. The acoustic transfer matrix is
i
is the real component, 2π f/c, and k is the imaginary component of the
calculated from the pressure and particle velocity, or equiva-
wave number, also referred to as the attenuation constant, nepers/m. This
lently the acoustic impedance, of the traveling waves on either
accounts for the effects of viscous and thermal dissipation in the
side of the specimen. The transmission loss, as well as several
oscillatory, thermoviscous boundary layer that forms on the inner surface
of the duct, (2). The wave number k’ of the propagating wave interior to
other important acoustic properties of the material, including
the material being tested is generally different from that in air, and may be
the normal incidence sound absorption coefficient, is extracted
calculated in certain cases from the acoustic transfer matrix.
from the transfer matrix.
d = thickness of the specimen in meters; see Fig. 4.
11, 12 = distance in meters from the reference plane (test 5. Significance and Use
sample front face) to the center of the nearest microphone on
5.1 There are several purposes of this test:
the upstream and downstream side of the specimen; see Fig. 4.
5.1.1 For transmission loss: (a) to characterize the sound
s1, s2 = – center-to-center spacing in meters between micro-
insulation characteristics of materials in a less expensive and
phone pairs on the upstream and downstream side of the
less time consuming approach than Test Method E90 and ISO
specimen; see Fig. 4.
140-3 (“reverberant room methods”), (b) to allow small
R = complex acoustic reflection coefficient.
samples tested when larger samples are impossible to construct
α = normal incidence sound absorption coefficient.
or to transport, (c) to allow a rapid technique that does not
TL = normal incidence transmission loss.
n
require an experienced professional to run.
k’ = complex wavenumber of propagation in the material,
5.1.2 For transfer matrix: (a) to determine additional acous-
-1
m .
tic properties of the material; (b) to allow calculation of
Z = characteristic impedance of propagation in the material,
acoustic properties of built-up or composite materials by the
rayls.
combination of their individual transfer matrices.
3.3 Subscripts, Superscripts, and Other Notation—The fol-
5.2 There are significant differences between this method
lowing symbols, which employ the variable X for illustrative
and that of the more traditional reverberant room method.
purposes, are used in Section 8:
Specifically, in this approach the sound impinges on the
Xc = calibration.
specimen in a perpendicular direction (“normal incidence”)
XI, XII = calibration quantities measured with microphones
only,comparedtotherandomincidenceoftraditionalmethods.
placed in the standard and switched configurations, respec-
Additionally, revereration room methods specify certain mini-
tively.
mumsizesfortestspecimenswhichmaynotbepracticalforall
¯
X = measured quantity prior to correction for amplitude and
materials. At present the correlation, if any, between the two
phase mismatch.
methods is not known. Even though this method may not
|X| = magnitude of a complex quantity.
replicate the reverberant room methods for measuring the
φ = phase of a complex quantity in radians.
transmission loss of materials, it can provide comparison data
Xi = imaginary part of a complex quantity.
for small specimens, something that cannot be done in the
Xr = real part of a complex quantity.
reverberant room method. Normal incidence transmission loss
may also be useful in certain situations where the material is
3.4 Summary of Complex Arithmetic—The quantities in this
placed within a small acoustical cavity close to a sound source,
standard, especially the transfer function spectra, are complex-
for example, a closely-fitted machine enclosure or portable
electronic device.
5.3 Transmission loss is not only a property of a material,
The boldface numbers in parentheses refer to the list of references at the end of
this standard. but is also strongly dependent on boundary conditions inherent
E2611 − 09
in the method and details of the way the material is mounted. 6.2.4.1 Diameter—In order to maintain plane wave
This must be considered in the interpretation of the results propagation, the upper frequency limit (3) is defined as
obtained by this test method. follows:
Kc Kc
5.4 The quantities are measured as a function of frequency
f , or d, (2)
u
d f
with a resolution determined by the sampling rate, transform
u
size, and other parameters of a digital frequency analysis
where:
system.Theusablefrequencyrangedependsonthediameterof
f = upper frequency limit, Hz,
u
the tube and the spacing between the microphone positions.An
c = speed of sound in the tube, m/s,
extended frequency range may be obtained by using tubes with
d = diameter of the tube, m, and
various diameters and microphone spacings.
K = 0.586.
5.5 The application of materials into acoustical system
6.2.5 For rectangular tubes, d is defined as the largest
elements will probably not be similar to this test method and
section dimension of the tube and K is defined as 0.500.
therefore results obtained by this method may not correlate
Extreme aspect ratios greater than 2:1 or less than 1:2 should
with performance in-situ.
be avoided. A square cross-section is recommended.
6.2.6 Conduct the plane wave measurements within these
6. Apparatus
frequency limits established by Eq 1 in order to avoid
6.1 The apparatus is a set of two tubes of equal internal area
cross-modes that occur at higher frequencies, when the acous-
that can be connected to either end of a test sample holder.The
tical wave length approaches the sectional dimension of the
number of sets of tubes depends on the frequency range to be
tube.
tested.Awider frequency range may require multiple measure-
6.2.7 Length—The tube should be sufficiently long for plane
ments on a set of several tubes. At one end of one tube is a
waves to be fully developed before reaching the microphones
loudspeaker sound source. Microphone ports are mounted at
and test specimen.Aminimum of three tube diameters must be
two locations along the wall of each tube. A two- or four-
allowed between sound source and the nearest microphone.
channel digital frequency analysis system, or a computer that
The sound source may generate non-plane waves along with
can effectively do the same calculations, is used for data
desired plane waves.The non-plane waves usually will subside
acquisition and processing.
at a distance equivalent to three tube diameters from the
source. If measurements are conducted over a wide frequency
6.2 Tube:
range, it may be desirable to use a tube, which provides
6.2.1 Construction—The interior section of the tube may be
multiple microphone spacing, or to employ separate tubes.The
circularorrectangularandshallhaveaconstantcross-sectional
overall tube length also must be chosen to satisfy the require-
dimension from end-to-end. The tube shall be straight and its
ments of 6.5.3 and 6.5.5.
inside surface shall be smooth, nonporous, and free of dust, in
order to maintain low sound attenuation.The tube construction 6.2.8 Tube Termination—The termination of the tube is
shall be sufficiently massive so sound transmission through the arbitrary in principle, but experience has found that the most
tube wall is negligible compared with transmission though the usefulterminationisatleastweaklyanechoic,causingminimal
sample. See Note 3. Compliant feet or mounts must be used to reflection of the sound wave back down the tube.Aconvenient
attenuate extraneous vibration entering the tube structure from way of providing this is to install a wedge or pyramidal shaped
the work surface. section of some sound absorbing material such as glass fiber,
about 30 cm long, in the open end of the tube.As the two-load
NOTE 3—The tube can be constructed from materials including metal,
method requires a second measurement with a different tube
plastic, concrete, or wood. It may be necessary to seal the interior walls
termimation, the wedge should be easily removable so that an
withasmoothcoatinginordertomaintainlowsoundattenuationforplane
open or closed termination may be provided.
waves.
6.2.9 Tube Venting—Some tube designs cause large tempo-
6.2.2 Working Frequency Range—The working frequency
rary pressure variations to be generated during installation or
range is:
removal of the test specimen. This may induce microphone
f ,f,f (1)
l u
diaphragmdeflection.Byincludingapressurereliefopeningof
some type, the potential for damage to a microphone dia-
where:
phragm due to excessive deflection may be reduced. One way
f = operating frequency, Hz,
to
...
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