ASTM E1050-98(2006)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E 1050 – 98 (Reapproved 2006)
Standard Test Method for
Impedance and Absorption of Acoustical Materials Using A
Tube, Two Microphones and A Digital Frequency Analysis
System
This standard is issued under the fixed designation E 1050; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope 3. Terminology
1.1 This test method covers the use of an impedance tube, 3.1 Definitions—The acoustical terminology used in this
two microphone locations, and a digital frequency analysis test method is intended to be consistent with the definitions in
system for the determination of normal incidence sound Terminology C 634.
absorption coefficients and normal specific acoustic impedance
NOTE 1—Historical literature regarding the measurement of normal
ratios of materials.
incidence absorption coefficients referred to “transfer function” measure-
1.2 Laboratory Accreditation—A procedure for accrediting
ments; however, the term arises from Laplace transform theory and is not
a laboratory for performing this test method is given inAnnex
strictly rigorous when the initial conditions have a non-zero value. The
term “frequency response function” arises from more general Fourier
A1.
transform theory (1). This test method shall retain the use of the former
1.3 This standard does not purport to address the safety
term although not technically correct. Users should be aware that modern
concerns, if any, associated with its use. It is the responsibility
FFT analyzers may employ the latter terminology.
of the use of this standard to consult and establish appropriate
3.2 Symbols: The following symbols are used in Section 8
safety and health practices and determine the applicability of
(Procedure):
regulatory limitations prior to use.
3.2.1 brc—normal specific acoustics susceptance ratio.
2. Referenced Documents
3.2.2 c—speed of sound, m/s.
3.2.3 grc—normal specific acoustic conductance ratio.
2.1 ASTM Standards:
3.2.4 G ,G —auto power spectra of the acoustic pressure
C 384 Test Method for Impedance and Absorption of 11 22
signal at microphone locations 1 and 2, respectively.
Acoustical Materials by Impedance Tube Method
3.2.5 G —cross power spectrum of the acoustic pressure
C 634 Terminology Relating to Building and Environmen-
signals at microphones locations 1 and 2.
tal Acoustics
3.2.6 H—transfer function of the two microphone signals
E 548 Guide for General Criteria Used for Evaluating
corrected for microphone response mismatch.
Laboratory Competence
¯
3.2.7 H—measured transfer function of the two micro-
2.2 ISO Standards:
phone signals.
ISO 10534-1 Acoustics—Determination of Sound Absorp-
I II
3.2.8 H,H —calibration transfer functions for the micro-
tion Coefficient and Impedance or Admittance—Part 1:
phones in the standard and switched configurations, respec-
Impedance Tube Method
tively.
ISO 10534–2 Acoustics—Determination of SoundAbsorp-
¯
3.2.9 H —complex microphone calibration factor.
tionCoefficientandImpedanceinImpedanceTubes—Part c
3.2.10 j—equals –1.
2: Transfer-Function Method =
-1
3.2.11 k—equal 2pf/c; wave number, m .
3.2.11.1 Discussion—In general the wave number is com-
This test method is under the jurisdiction of ASTM Committee E33 on
plex where k = k8-jk9.k8 is the real component, 2pf/c and k9
EnvironmentalAcousticsandisthedirectresponsibilityofSubcommitteeE33.01on
is the imaginary component of the wave number, also referred
Absorption.
-1
to as the attenuation constant, Nepers-m .
Current edition approved Sept. 1, 2006. Published September 2006. Originally
approved in 1985. Last previous edition approved in 2000 as E 1050 - 00.
Withdrawn.
3 4
Available from American National Standards Institute (ANSI), 25 W. 43rd St., The boldface numbers in parentheses refer to the list of references at the end of
4th Floor, New York, NY 10036, http://www.ansi.org. this test method.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E 1050 – 98 (2006)
3.2.12 l—distance from the test sample to the centre of the 5.2 Normal incidence sound absorption coefficients can be
nearest microphone, m. quite useful in certain situations where the material is placed
3.2.13 r/rc—normal specific acoustic resistance ratio. within a small acoustical cavity close to a sound source, for
3.2.14 R—complex acoustic reflection coefficient. example a closely-fitted machine enclosure.
3.2.15 s—centre-to-center spacing between microphones, 5.3 This test method allows one to compare relative values
m. of sound absorption when it is impractical to procure large
3.2.16 x/rc—normal specific acoustic reactance ratio. samples for accurate random-incidence measurements in a
3.2.17 yrc—normal specific acoustic admittance ration. reverberation room. Estimates of the random incidence absorp-
3.2.18 z/rc—normal specific acoustic impedance ratio. tion coefficients can be obtained from normal impedance data
3.2.19 a—normal incidence sound absorption coefficient. for locally-reacting materials (2).
3.2.20 f—phase of the complex transfer function, radians. 5.4 Measurements described in this test method can be
3.2.21 f —phase of the complex acoustic reflection coef- made with high precision, but these measurements may be
R
ficient, radians. misleading.Uncertaintiesofgreatermagnitudethanthosefrom
3.2.22 r—density of air, kg/m . the measurements may occur from other sources. Care should
3.3 Subscripts, Superscripts, and Other Notation—The fol- be exercised to sample nonuniform materials adequately (see
lowing symbols, which employ the variable X for illustrative 11.1).
purposes, are used in Section 8:
6. Apparatus
3.3.1 X —calibration.
c
3.3.2 X—imaginary part of a complex quantity. 6.1 The apparatus is a hallow cylinder, or tube, with a test
i
3.3.3 X —real part of a complex quantity.
sample holder at one end and a sound source at the other.
r
I II
3.3.4 X,X —calibration quantities measured with micro- Microphone ports are mounted at two or more locations along
phones placed in the standard and switched configurations,
the wall of the tube. A two channel digital frequency analysis
respectively. system is used for data acquisition and processing.
¯
3.3.5 X—measured quantity prior to correction for ampli-
6.2 Tube:
tude and phase mismatch. 6.2.1 Construction—The interior section of the tube may be
3.3.6 |X|—magnitude of a complex quantity.
circular or rectangular with a constant dimension from end-to-
end. The tube shall be straight and its inside surface shall be
4. Summary of Test Method
smooth, nonporous, and free of dust to maintain low sound
4.1 This test method is similar to Test Method C 384 in that
attenuation. The tube construction shall be massive so sound
it also uses an impedance tube with a sound source connected
transmission through the tube wall is negligible.
to one end and the test sample mounted at the other end. The
6.2.2 Working Frequency Range—The working frequency
measurement techniques for the two methods are fundamen-
range is:
tally different, however. In this test method, plane waves are
f , f , f (1)
l u
generated in the tube using a broad band signal from a noise
source rather than a discrete sinusoid from an oscillator. The where:
decomposition of the stationary sound wave pattern into f = operating frequency, hertz,
f = lower working frequency of the tube, hertz, and
forward- and backward-traveling components is achieved by
l
f = upper working frequency of the tube, hertz.
measuring sound pressures simultaneously at two spaced u
6.2.2.1 The lower frequency limit depends on the spacing of
locations in the tube’s side wall. Calculations of the normal-
the microphones and the accuracy of the analysis system. It is
incidence absorption coefficients for the acoustical material are
recommended that the microphone spacing exceed one percent
performed by processing an array of complex data from the
of the wavelength corresponding to the lower frequency of
measured transfer function.
interest.
4.2 The quantities are determined as functions of frequency
6.2.2.2 The upper frequency limit, f , and the corresponding
with a resolution determined by the sampling rate of a digital
u
wavelength, l , depends on the diameter of the tube and upon
frequency analysis system. The usable frequency range de-
u
the speed of sound.
pends on the diameter of the tube and the spacing between the
6.2.3 Diameter—In order to maintain plane wave propaga-
microphone positions. An extended frequency range may be
tion, the upper frequency limit (4) is defined as follows:
obtained by using tubes with various diameters and micro-
phones spacings.
f ,Kc /dord ,Kc / f (2)
u u
4.3 This test method is intended to provide a much faster
where:
measurement technique than that of Test Method C 384.
5. Significance and Use
5.1 This test method can be applied to measure sound 5
The classification, “locally-reacting” includes fibrous materials having high
absorption coefficients of absorptive materials at normal inci-
internal losses. Formulas have been developed for converting sound absorption
properties from normal incidence to random incidence, for both locally-reacting and
dence, that is, 0°. It also can be used to determine specific
bulk-reacing materials (3).
impedance and admittance ratios. The properties measured
The tube can be constructed from materials including metal, plastic, cement, or
with this test method are useful in basic research and product
wood. It may be necessary to seal the interior walls with a smooth coating in order
development of sound absorptive materials. to maintain low sound attenuation for plane waves.
E 1050 – 98 (2006)
men and the backing plate. One such arrangement may be to
f = upper frequency limit, hertz,
u
simulate a suspended ceiling tile.
c = speed of sound in the tube, m/s,
d = diameter of the tube, m, and
6.3.2 Detachable Holder—As a detachable unit, the holder
K = 0.586.
must make an airtight fit with the end of the tube opposite the
6.2.3.1 For rectangular tubes, d is defined as the largest
sound source. The holder must conform with the interior shape
section dimension the tube and K is defined as 0.500. Extreme
and dimensions of the main part of the impedance tube. The
aspect rations greater than 2:1 or less than 1:2 should be
connecting joint must be finished carefully and the use of a
avoided. A square cross-section is recommended.
sealant, such as petroleum jelly or silicone grease, is recom-
6.2.3.2 It is best to conduct the plane wave measurements
mended for sealing.
well within these frequency limits in order to avoid cross-
6.3.3 Integral Holder—If the sample holder is in an integral
modes that occur at higher frequencies when the acoustical
part of the impedance tube, it is recommended to make the
wave length approaches the sectional dimension of the tube.
installation section of the tube accessible for mounting of the
6.2.4 Length—The tube should be sufficiently long as plane
specimen by a removable cover. The mating surfaces must be
waves are fully developed before reaching the microphones
finished carefully, and the use of a sealant is recommended for
and test specimen.Aminimum of three tube diameters must be
sealing.
allowed between sound source and the nearest microphone.
6.3.4 Circular Holder—For circular tubes, it is recom-
The sound source may generate nonplane waves along with
mended to make the specimen accessible from both the front
desired plane waves. The nonplane waves usually will subside
and back end of the sample holder. It is possible then to check
at a distance equivalent to three tube diameters from the
the position and flatness of the front surface and back position.
source. If measurements are conducted over a wide frequency
Holders may be constructed from a rigid, clear material, such
range, it may be desirable to use a tube which provides
as acrylic, to facilitate inspection.
multiplemicrophonespacingsortoemployseparatetubes.The
overall tube length also must be chosen to satisfy the require-
6.3.5 Rectangular Holder—With rectangular tubes, it is
ments of 6.4.3, 6.5.3, and 6.5.4. recommended to install the specimen from the side, making it
6.2.5 Tube Venting—Some tube designs are such that, dur- possible to check the fitting and the position of the specimen in
ing during installation or removal of the test specimen, large
the tube and to check the position and flatness of the front
temporary pressure variation may be generated. This may
surface.
induce microphone diaphragm deflection. The potential for
6.3.6 Backing Plate—The backing plate of the sample
damagetoamicrophonediaphragmduetoexcessivedeflection
holder shall be rigid and shall be fixed tightly to the tube since
may be reduced including a pressure relief opening in the tube.
it serves to provide a sound-reflective termination in many
This may be accomplished by drilling a small hole, 1 to 2 mm
measurements. A metal plate having a minimum thickness of
through the wall of the tube. It is recommended to locate the
20 mm is recommended.
tube vent near the sound source, away from microphone
6.4 Sound Source:
locations, and to seal the vent during acoustic measurements.
6.4.1 Kind and Placement—The sound sources should have
6.3 Test Specimen Holder:
a uniform power response over the frequency range of interest.
6.3.1 General Features—The specimen holder may either
It may either be coaxial with the main tube or joined to the
be integrated with the impedance tube or may be a separate,
main tube by means of a transition having a straight, tapered,
detachable extension of the tube. Provision must be made for
or exponential section (see Fig. 1).
mounting the specimen with its face in a known position along
6.4.2 Isolation—The sound source and transition shall be
the tube axis and for placing a heavy backing plate behind the
specimen. For some measurements it may be desirable to sealed and isolated from the tube to minimize structure-borne
maintain an airspace of known dimensions between the speci- sound excitation of the impedance tube. If a direct radiator
FIG. 1 Sound Source Configurations
E 1050 – 98 (2006)
loudspeaker is utilized, it shall be contained in a sound- through the preamplifier. Sealing may be accomplished either
isolating enclosure in order to avoid airborne flanking trans- against the rear of the microphone cartridge barrel or against
mission to the microphones (see Fig. 1). the protection grid. If the
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