Transfer function method for measuring characteristic impedance
and propagation constant of porous materials
HideoUtsuno,
a)Toshimitsu
Tanaka,andTakeshiFujikawa
MechanicalEngineering
Research
Laboratories,
KobeSteel,Ltd., TakatsukadaiI-chomeNishi-ku,Kobe,
673-02,Japan
A.F. Soybert
Department
ofMechanicalEngineering,
University
ofKentucky,Lexington,
Kentucky40506-0046
(Received12December1988;accepted
forpublication
3 April 1989)
A methodfor measuring
thecharacteristic
impedance
andpropagation
constantof porous
materialsis described
in thispaper.Measurements
wereperformedbasedon a surface
impedance
methodthat requireda setof distinctacoustic
impedances
derivedat thematerial
surface.This requirement
is satisfied
by arbitrarilychangingthe air spacedepthbehindthe
material,andthena new formulationis derivedsothat a recentlydevelopedmethodof
determination,calledthe transferfunctionmethod,canbeapplied.An appropriatesetof air
spacedepthsis alsodiscussed.
Glasswoolandporousaluminumwereusedto assess
the
usefulness
of the presentmethod.The normalacousticimpedance
andnormalabsorption
coefficient
of the testmaterialswith arbitrarythicknesses
or with an arbitraryair spacedepth
behindthemwerecalculatedfrom the obtainedcharacteristic
impedanceand propagation
constant
andwerecompared
withthemeasured
valuesthatwereobtained
directlyby usingthe
transferfunctionmethod.The goodagreement
achievedsuggests
that the presentmethodis
reliableandeffective
enoughto measure
thecharacteristic
impedance
andpropagation
constantovera broadbandfrequencyrange.
PACS numbers: 43.55.Ev, 43.20.Mv
INTRODUCTION
assumingthe surfaceof the porousmaterial is not locally
Porousmaterials,suchasglasswoolor foam,are generally usedto attenuatenoise.In addition to thesewell-known
materials,new materialssuchas porousmetal, Kevlar, or
ceramichavebeendeveloped
to satisfytheneedfor a porous
material that can be usedat high temperatures,can be exposedto high-speed
air flow,or whosephysicalcharacteristicswill remainunchanged
whenexposedto a chemicalgas
atmosphere.
The mostfundamental
acousticpropertyof theseporousmaterialsis their soundabsorptioncoefficient.
This
maybemeasured
by usingan acoustic
impedance
tube.Sev-
eralpaperst-3
havereported
usingarelatively
recently
developedtransferfunctionmethodratherthan the conventional
reacting?
In thatcase,theporous
materialcanbecharacterized not by the normalacousticimpedance,but by the characteristicimpedanceand the propagationconstant.Evenif
the surfaceis assumedto belocallyreacting,theseproperties
are usefulbecausethe soundabsorptioncoefficientand the
acousticimpedancecanbe calculatedfrom them.
As mentionedabove,it is importantto obtainboth the
characteristicimpedanceand propagationconstant.Two
approachesare usedto obtain theseproperties.One is to
establishan appropriatedescriptionof the porousmaterial
from the first principle: the propagation of the sound
through it. The characteristics of sound propagation
throughporousmaterialshavebeeninvestigated
by several
•-• butmostnotablyby ZwikkerandKosten.
6
standing
waveratiomethodto measure
thesoundabsorp- researchers,
To utilizethetheoryin Ref. 6, it isnecessary
to obtaincertain
parameters,
such
as
flow
resistance
and
structure
factor,that
signalasa soundsource,sothatthenormalsoundabsorpare
measured
by
means
of
nonacoustical
experimentation.
tion coefficient
and normalacousticimpedance
are meaAnother approachinvolvesmeasuringtheseproperties
suredin a shorttime overa broadband
frequency
range.
directly
usingan acousticalexperiment.The moststraightThough the soundabsorptioncoefficientand acousticimforward
methodwasdeveloped
by Scott.•- His technique
is
pedanceare measuredmoreefficientlyby thisnew method,
based
on
measuring
the
attenuation
and
phase
change
of
an
to obtainthemis not sufficient
in orderto usethe porous
materialeffectively.
Further,it is moreimportantto obtain incidentsoundwaveinsidethe porousmaterial.The materithe characteristic
impedance
and propagation
constantof al was thick enoughto preventthe wavefrom reflectingin
theporous
materialbecause
thematerialmightessentially
be the impedancetube.
The surfaceimpedancemeasurement
methodwasstudcharacterized
by theseproperties.
For example,previous
ied
by
¾aniv.
•3
The
characteristic
impedance
andpropagawork4hasshownthattheporous
materialitselfmustbecontion constant were calculated from a set of distinct acoustic
sideredas a medium in which the soundwave transmits,
impchancesderivedby measurements
takenat the surfaceof
the
porous
material.
The
distinct
impedances
wereachieved
Visiting
scholar,
Department
ofMechanical
Engineering,
University
of
Kentucky,Lexington,KY 40506-0046.
by changingthe air spacedepthbehindthe porousmaterial:
tion coefficient.This new method usesa broadband random
637
J. Acoust.$oc. Am. 86 (2), August1989
0001-4966/89/080637-07500.80
@ 1989 AcousticalSocietyof America
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( 1) porousmaterialbackedby a rigid wall and (2) porous
material backed by one-quarter wavelengthair spaceterminatedin the rigid wall.
Smithand Parrott'4 achievedthe distinctimpedances
by using two different thicknessesof material backedby a
rigid wall. They called their method the "two-thickness
method" and referredto Yaniv's methodas the "two-cavity
method." They measuredacousticimpedancesby usingthe
conventionalstandingwaveratio method.
Terao15usedthe two-thicknessmethod,where acoustic
impedanceswere measured using the transfer function
½al
method.
The work reported here is an attempt to improve the
two-cavity method, which was initially describedin Ref. 6
and wasstudiedfurtherby Yaniv.'3 Previously,the twocavity methodrequiredthe acousticimpedances
behindthe
material to be zero and infinity. The latter is easilyachieved
by a rigid wall. The former is achievedat eachfrequencyby
changingthe air spacedepthto one-quarterwavelength,terminatedby a rigid wall. This meansthat the air spacedepth
mustbe changedat everyfrequencyof interest.
In this paper,a new formulationis derivedto calculate
the characteristicimpedance and propagation constant
when the porousmaterial is backedby an arbitrary impedance.Consideringthe acousticimpedancebehindthe material asa closed-tubeimpedancethat can beobtainedtheoretically, it becomesunnecessaryto changethe air spacedepth
at every frequencyaccordingto the new formulation.This
meansthat the transferfunctionmethodcanalsobe applied
to the two-cavity method.
As comparedwith the two-thicknessmethod,the improvedtwo-cavitymethodhastheadvantageof reducingthe
numberof timesof mountingtestmaterials,aswell aselimination of the variationassociatedwith test-piecemounting
and the variation
of the material
/
/
l•ic.B
Hic.A
Speaker
Referenceplane --•
Porous
Hovable piston
eaterial
A i r sl•ce
FIG. 1. (a) Experimentalapparatususedto measurethe characteristicimpedanceand propagatiouconstant;(b) block diagram of the impedance
tube and accessoryequipment.
itself between two test
SolvingEqs.(2) and (3) forZc and ?'gives
pieces.
I. FORMULATION
FOR A NEW TWO-CAVITY
METHOD
follows6:
Zo= Z •
Z I cosh(yd) + Zc sinh(yd)
Z msinh(yd) + Zc cosh(yd)
(1)
= exp(2j?'d).
--
Zo-ZcZ,+Zc
(5)
wherethesignin Eq. (4) isselected
soasto let therealpart
of Z• bepositive.UsingEqs.(4) and (5), Z½and?'canbe
calculatedfrom the measuredimpedances
Zo and Z• and
the impedances
of a closedtubewith depthL andL ', i.e.,
--jZ.i r cot(kL),
jZ,,
cot(kL'),
(6)
(7)
wherek isthewavenumber
of air andZ,•, isthecharacteris-
The right sideof Eq. (2) is a functionofd and y. While the
thicknessremainsconstant,the same equation is obtained
evenifZo and Zmare changedto other values.Let anotherbe
representedby ('); then Zo and Z, are replacedby Zg and
Z •, respectively.We obtain
Zo+ZcZ,-Z
(zo-z•)
I ln(Zo+ZcZ,--Zc•,
?'= 2jr
z, zd
Z; =
(2)
(z,-z;)
(4)
Zi:
Then, Eq. ( 1) yields
Zo+ZZ,-Z
-Zo-ZZm
+
Z½
=.qL
(ZoZ•(Zi
--Z•)--ZiZ
•(Zo-Z•))1'2,
\
A layer of homogeneous
porousmaterialis considered,
asshownin Fig. 1(b). The acousticimpedanceZ o at a referencesurfacecan be related to the characteristicimpedance
Z o the propagationconstanty, the acousticimpedancebehind the porousmaterialZl, and the materialthicknessd, as
638
(b) !!• A
--
z;-zc
zi,-zcz;+z
J. Acoust.Soc.Am.,Vol.86, No.2, August1989
(3)
tic impedanceof air.
To summarize, Eqs. (4) and (5) are derived without
assuming
Zm to bezeroandZ; to be infinity.Considering
themas theoreticalclosed-tube
impedances
and measuring
the referencesurfaceacousticimpedancetwice usingthe
transferfunction method permit the determinationof the
characteristic
impedanceand propagationconstantovera
broadbandfrequencyrange.
Utsunoet at: Transferfunctionmeasurement
of porousmaterials
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aluminum). The dimensions of the test materials and air
spacedepthsusedare shownin Table I. The glasswool test
material was 50 mm thick, while the porousaluminum test
material
was 20 mm thick. In order to calculate
the charac-
teristic impedanceand propagationconstant,it would be
sufficientto measurethe impedancesbasedon two different
air spacedepths,but in this paper the impedanceswith six
differentair spacedepthsweremeasuredindividuallyto investigatewhetherthecombinationof air spacedepthsaffected the experimentalaccuracywhenthe presentmethodwas
used.
FIG. 2. Porousaluminumabsorbingmaterial.
III. EXPERIMENTAL
II. EXPERIMENTAL
PROCEDURE
Measuringthe acousticimpedanceusingthe random
I--3
excitationtechniqueiswell documentedin severalpapers.
In this paper,we describethe experimentalapparatusutilized to mount the porousmaterial to accomplishan arbitrary air spacedepth.
The experimental
apparatusis shownin Fig. 1(a) and
(b). The impedancetube, havingan internal diameterof
87.5mm anda lengthof 1 m, is terminatedby a loudspeaker
and a movablebrasspiston.The impedancetubecanbe separated at cross section A-A. The test material was cut into
circular slices with flat faces and attached to the tube so that
onereferenceplanewasaccuratelyestablished
at crosssection A-A, and anotherwas"flush"againstthe surfaceof the
movablepiston.After visualinspectionof the mountedtest
material, the tubeswere connected.Then, the piston was
movedbackwardto createthe arbitrary air spacedepth.The
air spacedepthL wasmeasured
by thescaleattachedto the
tube. The distance Lx between the reference surface and mi-
crophoneA wassetat 17 mm, and the distanceDx between
the two microphones
wassetat either70 or 300 mm, according to the frequencyrangeof interest.
A randomsignalwasgeneratedfrom the loudspeaker,
and the transfer function H betweenthe two microphones
was measuredusinga two-channelfast Fourier transform.
The acousticimpedancewasobtainedfrom
Z o =JZair
-- H sin(kLx) q- sin[k(Lx q- Dx) ]
Hcos(kLx) -- cos[k(Lx + Dx) ]
(8)
After measuringZo with air spacedepth L, the pistonwas
movedto anotherdepthL ', andZ• wasmeasuredusingthe
sameprocedure.
Two differenttest materialswere usedfor the experiment:one,a glasswool;and the other,a porousaluminum
absorbingmaterial(Fig. 2, hereafterreferredto asa porous
RESULTS
The measuredcharacteristicimpedanceof the glass
wool is shownin Fig. 3(a). These resultsare normalizedby
the characteristicimpedanceof the air, Z• r. The solid lines
representthe complexcharacteristicimpedance.The experimentalresultswerepresentedovera frequencyrangeof from
300 Hz to 2 kHz, wherethe experimentalerror causedby the
distanceof separationbetweenthe microphonesmight be
negligible.It is possibleto measurethecharacteristicimpedanceoverhigheror lower frequencyrangesby shorteningor
lengtheningthe distancebetweenthe microphones.
The complexpropagation
constant(rad/m) of theglass
wool is shownin Fig. 3 (b) overthe samefrequencyrangeas
the characteristicimpedance.The measureddata shownin
Fig. 3(a) and (b) were obtained usingdistinct setsof air
spacedepths:(L, L ') = (20 mm, 40 mm), (20, 70), (20,
100), (40, 70), (40, 100), and (70, 100). From the graph, it
can be seenthat there is very goodagreementamongthe six
distinct measured values.
On the other hand, Fig. 4 showsthe characteristicimpedanceof glasswoolcalculatedfromsetsof air spacedepths
different than those usedfor the data shown in Fig. 3(a).
The air spacesusedfor the caseshownin Fig. 4 were: (L,
L')
----(20, 150), (20, 170), (40, 150), (40, 170), and (70,
170). In general, the figuresshow the same trend as was
evidentin Fig. 3(a), but significantsystematicdiscrepancies
appearin the 1100-to 1700-Hz frequencyrange.The reason
for this will be discussedlater. The resultssuggestedthat
there is an ideal setof air spacedepthsof which the characteristicimpedanceandpropagationconstantcanbecalculated correctly.
Figure 5(a) and (b) showsthe characteristicimpedanceand propagationconstantof the porousaluminum.Becauseporousaluminumhasattractiveacousticcharacteristics at low frequencies,it was measuredover a range of
frequencies
of from 100 to 450 Hz. This wasaccomplished
by spacingthe microphones300 mm apart.The testmaterial
TABLE I. Propertiesof the materialstested.
Sample
Glass wool
Porous aluminum
639
Density
Diameter
Thickness
Air spacedepth
(kg/m•)
(mm)
d (mm)
L (mm)
30
87.5
50
20, 40, 70, 100, 150, 170
250
87.5
20
20, 40, 70, 100, 150
J. Acoust.Sec. Am., Vol. 86, No. 2, August 1989
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,-
2
Ca)
5a
(b)
40
30
Re[Zc/Zai r]
20
I
I
I
I
I
I
-IO
-38
o
i
i
i
500
1000
1500
Frequency
-s6
2000
o
i
i
i
500
1000
1500
CHz]
Frequency
2000
CHz3
FIG. 3. (a) Thecharacteristic
impedance
ofglass
woolnormalized
byair;(b) thepropagation
constant
ofglass
wool,wherebothproperties
wereobtained
at
d = 50 mm and (L, L ') = (20 mm, 40 ram), (20, 70), (20, 100), (40, 70), (40, 100), and (70, 100).
was20 mm thick,andfivesetsof air spacedepthswereused:
(L, L ') = (20, 40), (20, 70), (20, 100), (40,70), and (40,
100). The characteristic
impedance
wasnormalizedby that
of air. It canbeseenthatthereisgoodagreement
amongthe
measuredvaluesobtainedfrom distinctsetsof air space
depthsovera frequencyrangeof from 150to 400 Hz. While
thereare slightdiscrepancies
below150Hz and above400
describes
two factors:( 1) the selectionof an appropriateset
of air spacedepthsand (2} the verificationof measured
acousticproperties.
A. The selection of an appropriate set of air space
depths
Hz, a consistenttrend is observed.
If Z• approaches
Z; in Eq. (4), thenZ, approaches
+ Z•; i.e.,thecharacteristic
impedance
of theporousmateIV. DISCUSSIONS
rial is equalto the acousticimpedanceof the closedtube.
Thecharacteristic
impedance
andpropagation
constant This incorrectconclusionis causedby eliminationof the
weremeasured
for glasswool,a traditionalporousmaterial, terms(Zo - Z• ) in Eq. (4), and that situationariseswhen
and for porousaluminum,a newlydevelopedmetallicab- theairspaces
L, L' andthefrequency
f satisfythefollowing
equation:
sorbingmaterial. In the aboveexperimentalresults,it is
shownthat bothpropertiescanbe measuredwhenutilizing
f(L -- L ') = no/2,
(9)
an appropriatesetof air spacedepths.The discussion
below
wherec is the speedof soundin the air and n = 1, 2, 3.....
Thefrequencies
of thedistinctive
peaks,•-f4, shownin Fig.
4, arein completeagreement
with thefrequencies
calculated
,.
2
fromEq. (9), sotheappropriate
setof air spacedepthsmust
be selectedsoasto not satisfyEq. (9).
B. The verification of measured acoustic properties
The presentinvestigationwasinitiatedto improvethe
two-cavity method so as to calculatethe characteristicimpedanceand propagationconstant,evenif the acousticimfi:l150
fe:1325
-2
pedancesZ• and Z • are not zero and infinity, respectively.
fa:1565
-1
I
500
I
1000
Frequency
I
f4:1715
I
1500
2000
CHz3
FIG. 4. The characteristicimpedanceof glasswool normalizedby air,
where it was obtainedat d = 50 mm and ( L, L' ) = ( 20 ram, 150 m m ), (20,
170), (40, 150), (40, 170), and (70, 170).
640
J. Acoust.Soc. Am., Vol. 86, No. 2, August1989
The previoustwo-cavity methodhasbeenverifiedin studies
by Yaniv and Smith and Parrott and comparedwith that
obtained using Scott'smethod or the theoretical model due
to Beranek.In this paper,a comparisonis madebetweenthe
calculatedand measurednormal acousticimpedanceand
absorptioncoefficient.Substitutingthe measuredZ, and •'
into Eq. ( 1), the normalacousticimpedancecanbecalculated. A subsequentcalculationis made to determinethe absorptioncoefficient.Both of thesequantitiesare also mea-
suredby usingthe transferfunctionmethoddirectly.
Utsunoeta/.: Transfer functionmeasurementof porousmaterials
640
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,-
(b)
18
,m
•\
8
•
40
Re[Zc/Zai r ]
f,..
I
I
I
•
I
o
7•zc/za
ir]
•-lfa
I
I
I
I
I
I
I
I
-20
-an
-40
,,%-8
I
I
I
i
Frequency [Hz]
Frequency [Hz]
FIG. 5. (a) Thecharacteristic
impedance
ofporous
aluminum
normalized
byair;(b) thepropagation
constant
ofporous
aluminum,
wherebothproperties
wereobtainedat d = 20 mm and (L, L ') = (20 ram,40 ram), (20, 70), (20, 100), (40, 70), and (40, 100).
I. 0
(a)
.....
(b)
õ
L=100
•:
Re[Zo/Za
i••!••l•l•4amum
i•[Zoa•l
r]--•
---'•'•
L:150
ß
c / L=O
-4
i
0. a
Frequency
i
-5
,
I
[Hz]
t
Frequency
I
[Hz]
FIG. 6. (a) Comparison
between
calculated
(--) andmeasured
(71)normalabsorption
coefficient
for50-ram-thick
glass
woolwithanairspace
depthof
L = 0,40,100,and150ram;(b) comparison
between
calculated
(--) andmeasured
(n) normalacoustic
impedance
for50-mm-thick
glass
woolwitha 100mmair spacedepth,wherethecalculation
wasbasedon theproperties
thatwereobtained
at d = :50mmand(L, L.') = (20 mm,70 mm).
1.0
(a)
5
I
500
I
1000
F-r'equency
I
1500
[Hz]
2080
(b)
•Ir•Zø/Z
Frequency
œHz]
FIG.7. (a) Comparison
between
calculated
(--) andmeasured
(71)normal
absorption
coefficient
for25-,75-,and125-mm-thick
glass
woolbacked
bya
rigidwall;(b) comparison
between
calculated
(--) andmeasured
(71)normal
acoustic
impedance
for25-ram-thick
glass
woolbacked
byarigidwall,where
thecalculation
wasbased
ontheproperties
thatwereobtained
at d = 50mmand(L, L ') = (20 ram,70mm).
641
d.A½oust.
Soc.Am.,Vol.86,No.2, August
1989
Utsuno
etaL:Transfer
function
measurement
ofporous
materials
641
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1.9
(b)
(a)
L=100
.8
L=I•O
••
•a•le[Zo/7ai
r]I I
509
FIG. 8. (a) Comparison
between
calculated
(--) andmeasured
(I-1)normalabsorption
coefficient
for 20-mm-thick
porousaluminumwithair spacedepths
ofL = 40, 100,and150ram;(b) comparison
between
calculated
(--) andmeasured
([]) normalacoustic
impedance
for20-ram-thick
porous
aluminum
with a 100-ramair spacedepth,wherethecalculationwasbasedon theproperties
thatwereobtainedat d = 20 mm and (L, L ') = (20 mm, 70 mm).
Figure6(a) showsthe normalsoundabsorptioncoeffi- ficientfor 25-, 75-, and 125-mm-thickglasswooltestmatericientfor 50-mm-thickglasswoolwith an air spacedepthof alsbackedbya rigidwallandthenormalacoustic
impedance
L = 0, 40, 100,and 150ram, respectively.
In thegraph,the for a 25-mm-thickglasswool backedby the rigid wall is
opensquarerepresents
themeasured
valuesderivedby using shown.From thesegraphs,it canbeseenthat the calculated
the transferfunctionmethod, while the solidline represents valuesarein goodagreement
with themeasured
valueswhen
the thickness of the test material is a variable.
the calculatedvaluesderivedfrom measuredvaluesof Zc
and y that wereobtainedat d = 50 mm and (L, L ') = (20
Using the characteristicimpedanceand propagation
constant obtained at d = 20 mm and (L, L ') = (20 ram, 70
mm, 70 mm). The normal acousticimpedanceis shownin
Fig. 6 (b) for 50-ram-thickglasswoolwith anair spacedepth mm) in Fig. 5, the normal absorptioncoefficientand the
of 100min. The measuredacousticimpedanceis represented normal acousticimpedancewere calculatedfor 20-mmby theopensquare,whilethecalculatedacousticimpedance thick porousaluminumwith an air spacedepthof L ----40,
100,and 150 ram. Thesedata and corresponding
measured
is represented
by thesolidline.The realandimaginaryparts
of theacousticimpedances
arenormalizedby thecharacter- data obtainedusingthe transferfunctionmethoddirectly
isticimpedance
of theair. As maybeseen,thecalculatedand
are shownin Fig. 8(a) and (b). The calculatedand meameasureddata showexcellentagreement.
surednormalabsorptioncoefficient
andnormalacousticimIn Fig. 7(a) and (b), thenormalsoundabsorptioncoef- pedance
arealsoshownin Fig. 9(a) and (b) for 10-,30-,and
1.9
(a)
20
•
N
(b)
to
Re[Zo/Zair]
d=•
I
d=•
9.91•
IO9
299
399
Frequency
499
[H=)
599
-29
•99
I
i•[•
399
Frequency
490
œHz3
FIG. 9. (a) Comparison
between
calculated
(--) andmeasured
([3) normalabsorption
coefficient
for 10-,30-,and40-mm-thick
porous
aluminum
test
materials
backed
bya rigidwall;(b) comparison
between
calculated
(--) andmeasured
(VI)normal
acoustic
impedance
for30-mm-thick
porous
aluminum
backed
bya rigidwall,wherethecalculation
wasbased
ontheproperties
thatwereobtained
at d = 20mmand(L, L ') = (20mm,70ram).
642
J. Acoust.
Soc.Am.,VoL86, No.2, August1989
UtsunoetaL:Transferfunction
measurement
of porousmaterials
642
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40-mm-thickporousaluminumtest materialsbackedby a
rigid wall. It canbe seenthat the calculatedvaluesfor the
porousaluminumarein goodagreement
with themeasured
Acoust. $oc. Am. 61, 1362-1370 (1977).
2j. y. ChungandD. A. Blaser,"TransferFunctionMethodof Measuring
In-ductAcousticProperties.I. Theory,"J. Acoust.Soc.Am. 68, 907-913
(1980).
3J.Y. ChungandD. A. Blaser,"Transfer
FunctionMethodof Measuring
ones.
From theseresults,it can be concludedthat the sound
absorption
characteristics
of a porousmaterialcanbedetermined accuratelyfrom the measuredcharacteristicimpedanceandthe propagationconstant.It alsoindicatesthat the
soundabsorption
characteristics
of a porousmaterialcanbe
predicted
easilyusingthepresentmethod.
In-duct AcousticProperties.II. Experiment,"J. Acoust.Soc.Am. 68,
913-921 (1980).
4R.A. Scott,"ThePropagation
ofSoundBetween
WallsofPorousMaterial," Proc. Phys.Soc.London58, 358-368 (1946).
•K. U. Ingard,"LocallyandNonlocally
ReactingFlexiblePorousLayers;
A Comparison
of AcousticalProperties,"ASME Trans.J. Eng.Ind. 103,
302-313 (1981).
6C. ZwikkerandC. Kosten,SoundAbsorbing
Materials(Elsevier,New
York, 1949).
7L.L. Beranek,
"Acoustic
Properties
of Homogeneous
PorousMedium
V. SUMMARY
In this paper,an improvedtwo-cavitymethodto measurethe characteristicimpedanceand propagationconstant
of porousmaterialswasappliedexperimentally
to two different porousmaterials.The characteristicimpedanceand
propagationconstantcanbe measuredeasilyovera broad
frequencyrangeby usingthetransferfunctionmethod.The
selectionof an appropriateset of air spacedepthsis discussed,
andit is shownthat the soundabsorptioncoefficient
andacoustic
impedance
of porousmaterialswith arbitrary
thickness
or with an arbitraryair spacedepthmay be predictedaccuratelyusingthe measured
characteristic
impedanceandpropagation
constant.
Thisresultindicates
thatthe
presentmethodis usefulin predictingthe soundabsorbing
capabilityof acousticalmaterialsin practicalapplications.
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Utsuno oraL: Transfer function measurement of porous materials
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