ASTM C384-04(2022)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: C384 − 04 (Reapproved 2022)
Standard Test Method for
Impedance and Absorption of Acoustical Materials by
Impedance Tube Method
This standard is issued under the fixed designation C384; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2.2 ANSI Standards:
S1.6Preferred Frequencies and Band Numbers forAcousti-
1.1 This test method covers the use of an impedance tube,
cal Measurements
alternatively called a standing wave apparatus, for the mea-
surement of impedance ratios and the normal incidence sound 3. Terminology
absorption coefficients of acoustical materials.
3.1 The acoustical terminology used in this test method is
intended to be consistent with the definitions in Terminology
1.2 The values stated in SI units are to be regarded as
C634. In particular, the terms “impedance ratio,” “normal
standard. No other units of measurement are included in this
incidence sound absorption coefficient,” and “specific normal
standard.
acoustic impedance,” appearing in the title and elsewhere in
1.3 This standard does not purport to address all of the
this test method refer to the following, respectively:
safety concerns, if any, associated with its use. It is the
3.2 Definitions:
responsibility of the user of this standard to establish appro-
3.2.1 impedance ratio, z/ρc ≡ r/ρc + jx/ρc;
priate safety, health, and environmental practices and deter-
[dimensionless]—the ratio of the specific normal acoustic
mine the applicability of regulatory limitations prior to use.
impedance at a surface to the characteristic impedance of the
1.4 This international standard was developed in accor-
medium. The real and imaginary components are called,
dance with internationally recognized principles on standard-
respectively, resistance ratio and reactance ratio. C634
ization established in the Decision on Principles for the
3.2.2 normal incidence sound absorption coeffıcient, α ;
n
Development of International Standards, Guides and Recom-
[dimensionless]—of a surface, at a specified frequency, the
mendations issued by the World Trade Organization Technical
fraction of the perpendicularly incident sound power absorbed
Barriers to Trade (TBT) Committee.
or otherwise not reflected. C634
3.2.3 specific normal acoustic impedance, z ≡r+jx;
2. Referenced Documents
-2 -1
[ML T ]; mks rayl (Pa s/m)—at a surface, the complex
2.1 ASTM Standards:
quotient obtained when the sound pressure averaged over the
C423TestMethodforSoundAbsorptionandSoundAbsorp- surface is divided by the component of the particle velocity
tion Coefficients by the Reverberation Room Method
normal to the surface. The real and imaginary components of
C634Terminology Relating to Building and Environmental thespecificnormalacousticimpedancearecalled,respectively,
Acoustics specific normal acoustic resistance and specific normal acous-
tic reactance. C634
E548Guide for General Criteria Used for Evaluating Labo-
ratory Competence (Withdrawn 2002)
4. Summary of Test Method
4.1 A plane wave traveling in one direction down a tube is
reflectedbackbythetestspecimentoproduceastandingwave
ThistestmethodisunderthejurisdictionofASTMCommitteeE33onBuilding
that can be explored with a microphone.The normal incidence
and Environmental Acoustics and is the direct responsibility of Subcommittee
E33.01 on Sound Absorption. sound absorption coefficient, α , is determined from the stand-
n
Current edition approved Oct. 1, 2022. Published October 2022. Originally
ingwaveratioatthefaceofthetestspecimen.Todeterminethe
approved in 1956. Last previous edition approved in 2016 as C384–04 (2016).
impedance ratio, z/ρc, a measurement of the position of the
DOI: 10.1520/C0384-04R22.
standing wave with reference to the face of the specimen is
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
needed.
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.
The last approved version of this historical standard is referenced on Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
www.astm.org. 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C384 − 04 (2022)
4.2 The normal incidence absorption coefficient and imped- where:
ance ratio are functions of frequency. Measurements are made
f = frequency, Hz,
withpuretonesatanumberoffrequencieschosen,unlessthere
c = speed of sound in the tube, m/s, and
arecompellingreasonstodootherwise,fromthosespecifiedin d = diameter of tube, m.
ANSI S1.6.
For rectangular tubes, with d used as a symbol for the larger
cross section dimension, the upper limit is:
5. Significance and Use
f,0.500 c/d (2)
5.1 The acoustical impedance properties of a sound absorp-
tive material are related to its physical properties, such as
It is best to work well below these limits whether the tube is
airflowresistance,porosity,elasticity,anddensity.Assuch,the
circularorrectangular.Atfrequenciesabovetheselimits,cross
measurements described in this test method are useful in basic
modesmaydevelopandtheincidentandreflectedwavesinthe
research and product development of sound absorptive mate-
tubearenotlikelytobeplanewaves.Ifsoundwithafrequency
rials.
below the limiting value enters the tube as a non-plane wave,
itwillbecomeaplanewaveaftertravelingashortdistance.For
5.2 Normal incidence sound absorption coefficients are
this reason, no measurement should be made closer than one
more useful than random incidence coefficients in certain
tube diameter to the source end of the tube.
situations. They are used, for example, to predict the effect of
6.1.1.3 Length—The length of the tube is also related to the
placing material in a small enclosed space, such as inside a
frequencies at which measurements are made. The tube must
machine.
belongenoughtocontainthatpartofthestandingwavepattern
5.3 Estimates of the random incidence or statistical absorp-
needed for measurement. That is, it must be long enough to
tion coefficients for materials can be obtained from normal
containatleastoneandpreferablytwosoundpressureminima.
incidence impedance data. For materials that are locally
Toensurethatatleasttwominimacanbeobservedinthetube,
reacting, that is, without sound propagation inside the material
its length should be such that:
parallel to its surface, statistical absorption coefficients can be
f.0.75 c/ l 2 d (3)
~ !
estimated from specific normal acoustic impedance values
using an expression derived by London (1). Locally reacting
where:
materials include those with high internal losses parallel with
l = length of tube, m.
the surface such as porous or fibrous materials of high density
If, for example, the tube is1min length and 0.1 m in
or materials that are backed by partitioned cavities such as a
diameter and the speed of sound is 343 m/s, the frequency
honeycomb core. Formulas for estimating random incidence
should exceed 286 Hz if two sound pressure minima are to be
sound absorption properties for both locally and bulk-reacting
observed.
materials, as well as for multilayer systems with and without
6.1.2 Test Specimen Holder—The specimen holder, a de-
air spaces have also been developed (2).
tachable extension of the tube, must make an airtight fit with
6. Apparatus the end of the tube opposite the sound source. Provision must
be made for containing the specimen with its face in a known
6.1 The apparatus is essentially a tube with a test specimen
position. The interior cross-sectional shape of the specimen
at one end and a loudspeaker at the other.Aprobe microphone
holder must be the same as the tube itself. Provision must be
that can be moved along the length of the tube is used to
made for backing the specimen with a metal backing plate that
explore the standing wave in the tube. The signal from the
forms a seal with the interior of the specimen holder. A
microphone is filtered, amplified, and recorded.
recommended backing is a solid steel plate with a thickness of
6.1.1 Tube:
not less than 2 cm. The sample holder may be constructed in
6.1.1.1 Construction—The tube may be made of metal,
such a way that a variable depth air space can be provided
plastic, portland cement, or other suitable material that has
between the back of the test specimen and the surface of the
inherently low sound absorption properties. Its interior cross
metal backing plate. Provision must be made for substituting
section may be circular or rectangular but must be uniform
the metal backing plate for the specimen for calibration
from end to end. The tube must be straight and its inside
purposes.
surfacemustbesmooth,nonporousandfreeofdusttokeepthe
6.1.3 Sound Source:
sound attenuation with distance low. The interior of the tube
6.1.3.1 Kind and Placement—The sound source may be a
may be sealed with paint, epoxy, or other coating material to
loudspeaker or a horn-driver coupled to a short exponential
ensure low sound absorption of the interior surface. The tube
horn. The source may face directly into the tube or, to avoid
wallsmustbemassiveandrigidenoughsothatthepropagation
interference with the probe microphone, it may be placed to
of sound energy through them by vibration is negligible.
oneside.Sincethesourcediametermaybelargerthanthetube
6.1.1.2 Diameter—For circular tubes, the upper limit (3) of
diameter,itisbesttomountthesourceinanenclosuretowhich
frequency is:
the tube is connected.
f,0.586 c/d (1)
6.1.3.2 Precautions—Precautions should be taken to avoid
direct transmission of vibration from the sound source to the
probe microphone where it enters the tube or to the tube itself.
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this standard. Such vibrational transmission will be evidenced by a smaller
C384 − 04 (2022)
standing wave ratio (higher normal incidence sound absorp- pressure ratios are required for the computations in this test
tion) than would be expected for the material under test. method, it is not necessary that the sound pressure measure-
Vibration isolation material, such as polymeric foam, may be ment system be calibrated to a known, reference sound
placed between the sound source and tube or the microphone pressure level or to a known voltage.
probe, or both, to minimize this effect. Interaction between the 6.1.8 Temperature Indicator—A thermometer or other am-
soundfieldwithinthetubeandtheloudspeakerdiaphragmmay bienttemperaturesensingdeviceshallbelocatedinthevicinity
cause the frequency response of the loudspeaker to be nonlin- of the impedance tube. This device should indicate air tem-
ear. Although this has no effect on measurement accuracy, it perature inside the tube to within 62°C.
does require awkward changes in amplifier gain settings when 6.1.9 Monitoring Oscilloscope—While not required for any
switching between test frequencies. This effect can be mini- actual measurement purpose, it is recommended that an oscil-
mized by lining the interior of the tube near the sound source loscope be used to monitor both the voltage driving the sound
with a porous, absorbent material. source and the output of the amplifier. Observing the oscillo-
scope trace is useful in locating the exact position of pressure
6.1.4 Microphone—If the microphone is small enough, it
minima within the tube as well as in detecting distortion,
maybeplacedinsidetheimpedancetubeconnectedtoarodor
excess noise, and other possible problems in the voltage
otherdevicethatcanbeusedtomoveitalongthelengthofthe
signals.
tube. If the microphone is placed within the tube, the total
cross-sectional area of the microphone and microphone sup-
7. Sampling
ports shall be less than 5% of the total cross-sectional area of
thetube.Inmostapplications,themicrophoneisontheoutside
7.1 At least three specimens, preferably more if the sample
connected to a hollow probe tube that is inserted through the
is not uniform, should be cut from the sample for the test.
source end of the apparatus and is aligned with the central axis
Whenthesamplehasasurfacethatisnotuniform(forexample
ofthetube.Inprinciple,thesensingelementofthemicrophone
a fissured acoustical tile), each specimen should be chosen to
orofthemicrophoneprobemaybepositionedanywherewithin
include, in proper proportion, the different kinds of surfaces
thetubecross-sectionalarea.Inpractice,themicrophoneorthe
existing in the larger sample.
end of the probe tube must be supported by a spider or other
device to maintain its position on the central axis of the
8. Test Specimen Preparation and Mounting
impedance tube or at a constant distance from the central axis.
8.1 The measured impedance properties can be strongly
6.1.5 Microphone Position Indicator—Ascale shall be pro-
influenced by the specimen mounting conditions. Therefore,
vided to measure the position of the microphone with respect
the following guidelines for the preparation and mounting of
to the specimen face. It is not necessary that zero on the scale
specimens are provided.
correspondtothepositionofthespecimenface.Theresolution
8.2 The specimen must have the same shape and area as the
of this scale should be such that microphone position can be
tubecrosssection,neithermorenorless.Thespecimenmustfit
measured to the nearest 1.0 mm or, if a vernier is used, to the
snugly into the specimen holder, fitting not so tightly that it
nearest 0.1 mm.
bulgesinthecenter,norsolooselythatthereisaspacebetween
6.1.6 Test Signal:
its edge and the holder. Movement of the specimen as a whole
6.1.6.1 Frequency—The test signal shall be provided by a
and spaces between the specimen perimeter and sample holder
sinewaveoscillatorgeneratingapuretonechosenfromthelist
can result in anomalous values of normal incidence sound
of preferred band center frequencies listed in ANSI S1.6. The
absorption. Specimen movement can be minimized by the use
test frequency shall be controlled to within 61% during the
ofthin,double-sidedadhesivetapeappliedbetweenthebackof
course of a measurement. If a digital frequency synthesizer is
the specimen and the metal backing plate. Spaces at the
used,thetestsignalmaybeassumedtoagreewiththesetpoint
specimen perimeter can be sealed with petroleum jelly.
within the required 61%.
8.3 The specimen must have a relatively flat surface since
6.1.6.2 Frequency Counter—It may be necessary, and is
the reflected wave from a very uneven surface may not have
usually advisable, to measure the frequency of the signal with
become a plane wave at the position of the first minimum. If
an electronic counter rather than to rely on the calibration and
the specimen is an anechoic wedge, or an array of wedges,
indicated setting of the frequency generator. Frequency should
refer to Annex A1.
be indicated to the nearest 1 Hz.
8.4 When the specimen has a very uneven back, a layer of
6.1.7 Output-Measuring Equipment:
putty-like material should be placed between it and the metal
6.1.7.1 Filter—The microphone output should be filtered to
backing plate to seal the back of the specimen and to add
remove any harmonics and to reduce the adverse effect of
enough thickness to make the back of the specimen parallel to
ambientnoise.Thefilterwidthmustbenowiderthanone-third
the front. Otherwise, the unknown airspace may be the
octave, but a one-tenth octave or narrower filter bandwidth is
dominant factor in the measured results.
preferable.
6.1.7.2 Amplifier—The signal-to-noise ratio of the measur-
9. Description of Standing Wave Pattern in Tube
ing amplifier must be at least 50 dB.The amplified signal may
be read and recorded as a voltage or as a sound pressure level 9.1 Fig. 1 represents microphone voltages that might be
(dB). It is presumed in Sections 9 and 10 of this test method measuredinatubeatvariousdistancesfromthespecimenface.
that voltages rather than dB levels are being used. As only That is, Fig. 1 is a standing wave pattern, in this case for a
C384 − 04 (2022)
minimum microphone voltages actually measured in the tube.
Section 10 of this test method describes several methods for
performing the extrapolation depending on the number of
maxima and minima observed.
9.5 Tube Attenuation—Losses within a tube can generally
be described by:
2ζx
p x 5 p e (5)
~ !
where:
p = the pressure at some reference position,
x = the absolute distance traveled by the wave from the
reference position, and
ζ = the attenuation constant.
Kirchhoff (see Ref. 4) developed and Beranek (5) subse-
quently modified a formula for estimating the attenuation
FIG. 1 Microphone Voltage in 1.0 m Tube Driven at 500 Hz
constant as:
1/2
ζ 50.02203 f /~cd! (6)
where:
reflective specimen installed in a one-metre tube with the tube
−1
driven at 500 Hz. The minimum points at x,x , and x on the ζ = attenuation constant, m .
1 2 3
standing wave pattern are spaced half a wavelength apart and
For this purpose, the equivalent diameter of a tube with
positioned midway between the maxima. It should be noted
rectangular cross section is four times the area of the cross
that the data shown in Fig. 1 are plotted as voltage versus
section divided by its perimeter.
distance rather than voltage level (in dB) versus distance.
9.2 The standing wave pattern generally contains a finite
10. Procedure
number of discrete minima (for example, x,x,x in Fig. 1)
1 2 3
10.1 Calculation of Velocity of Sound, c—The velocity of
andthelocusformedbytheseindividualminimummicrophone
sound in air is computed from the measured temperature
voltages defines a continuous V (x) function as shown by the
min
according to:
lower dotted line on Fig. 1. Similarly, the locus of maximum
1/2
voltages can be used to define a continuous V (x) function, c 520.05 T1273.1 (7)
~ !
max
shownastheupperdottedlineonFig.1.Astandingwaveratio,
where:
SWR, also a function of x, can be formed according to:
T = air temperature, °C.
SWR x 5 V x /V x (4)
~ ! ~ ! ~ !
max min
10.2 Calculation of Wavelength, λ—The wavelength of
where:
sound at each test frequency is computed from the speed of
SWR(x) = standing wave ratio at location x, dimensionless.
sound and the test frequency according to:
λ 5 c/f (8)
Note that SWR(x) will be a positive, real number equal to or
where:
greater than one.
λ = wavelength, m.
9.3 ThevariousmaximaofthestandingwavepatternofFig.
are nearly equal in magnitude. Thus V (x) is very nearly a
1 10.3 Correction Factor:
max
straight, horizontal line. The minimum microphone voltages,
10.3.1 To define the standing wave pattern within the tube,
however, form a V (x) locus with a noticeable slope. It is not
min it is necessary to know the distance from the sample face at
the absorption at the sample face but rather the attenuation
which each pressure is being measured. The exact location of
within the tube itself that causes V (x) to exhibit this slope.
min the face of the mounted sample within the tube can be
Indeed, if there were no attenuation of incident and reflected
determined by gently advancing the probe until it makes
waves as they propagated back and forth in the tube, V (x)
min contactwiththesamplefaceandnotingthescalereadingatthe
and V (x) could both be represented as horizontal lines and
max point of contact. The exact location of a measured pressure,
SWR(x) would be the same everywhere along the length of the
however, requires applying a correction factor to the observed
tube.Attenuation within the tube, however, while having only
scale reading at the point where the pressure is measured.This
a slight effect on the individual maxima, causes the individual
is due to the fact that the acoustic center of a microphone or
voltage minima to increase with increasing distance from the
microphone probe does not necessarily correspond with its
face of the specimen.
geometric center.
9.4 The primary purpose for making the measurements 10.3.2 The correction factor is computed based on the
described in this test method is to find the standing wave ratio assumption that, with a highly reflective metal backing plate
atthefaceofthespecimen,thatis, SWR(0).Thisdetermination mounted in the tube, a sound pressure minimum will occur at
must be done indirectly by extrapolation of the maximum and precisely λ/4 from the surface of the plate. For each test
C384 − 04 (2022)
frequency the correction factor is thus determined with the 10.5.1 Two o
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