10.10,10.4
Received21 February1966
Absorption of Sound in Air versus Humidity and Temperature
CYRIL
•[.
HARRIS
Department
of ElectricalEngineering,
CohtmbiaUniversity,.VewI;ork,.Ve'zo
York 10027
Measurementshave beenmadeof the absorptionof soundin air at «-octavefrequencyintervals from 2000
to 12 500 Hz, as a functionof humidity,at six temperaturesin the rangefrom --0.5 ø to 25.1øCat normal
atmosphericpressure.The resultsof the new study are presentedand comparedwith thoseof past investigations.Then a "best fit" is obtainedto existingdata. The resultinginformationis presentedin both tabular
and graphicalform, usefulfor the solutionsto problemsof the calculationof attenuation of soundpropagated in the atmosphereand the computationof the effectsof air absorptionin problemsof roomacoustics.
These resultshave been extrapolateddownwardin frequencyto 125 Hz and extrapolated to cover the temperaturerangefrom --10 ø to 30øCat normalatmosphericpressure.
INTRODUCTION
study and are describedin detail in that paper.• There-
fore, they are outlinedonly briefly here. Sufficeit to
Nofathe
paper
bythe
author
•inin1963,
values
of soundin air wats
absorption
of sonnd
air measured
were given
as a say that the attenuationcoefficient
function of humidity in the frequencyrange between evaluated from measurements of the decay rate of dif2000and 12 500Hz (cps),at normalatmospheric
pres- fuse soundin a sphericalchamber1.68 m in diameter.
sureand at a temperatureof 20øC.The data presented During measurements,the temperatureof the chamber
heregreatlyextendthe previouswork over a wide tem- was held constant to within 0.1øC. Precautions were
peraturerangeand providemeasuredvalueshaving taken to rid the chamberof contaminationby evacuatgreateraccuracythroughimprovedmethodsof data ing it by meansof vacuumpumps; then the spherical
reduction. A total of 2800 measurements were made at
chamberwasfilled with dry air havinga carbondioxide
i-octavefrequencyintervalsfrom 2000to 12 500 Hz at contentof 300 parts per million, whichis a usualvalue.
eachof six temperatures
in the rangefrom --0.5ø to Randomnoisefrom a sourcein the chamberwaspicked
25.1øC at nmTnalatmosphericpressure.The nexvdata up by a microphone,amplified,and fed through «-oct
are comparedwith thoseof past investigations.Then a filter to a high-speedlevel recorder.When the random
"best fit" is obtained to existing data. These results noise source was turned off, a curve of the decay of
make it possibleto evaluatethe effectsof air absorption sound in the chamber was obtained. The slope of the
overa rangeof environmentalconditionsencountered
in curve determinedthe decay rate in decibelsper second
practical problemsin acousticalengineering,for ex- at the frequencyof the centerof the band to which the
ample:(1) theca.
lculationof theattennationof soundin «-oct analvzer is set. For a singletest condition,three
air owingto air absorption;(2) the calculationof the decay curveswere superposed;then the averageslope
curveswasobtainedto
contributionof air absorptionto the total absorptionin of three suchsetsof snperposed
a large room; (3) the correctionfor air absorptionin determine the decay rate for this condition.This decay
reverberation-timemeasurementsin large auditoriun•s; rate, when correctedfor lossesat the boundariesof the
and (4) the correctionfor air absorptionin the measure- chamber,is a measureof the total absorptionof sound
ment of the sound-absorption
coefficientsof materials in the chamber.
tested in a reverberation chamber. These results have
In determining the magnitude of the absorptionof
been extrapolateddownwardin freqnencyto 125 Hz soundin air from measurementsof the rate of decay of
and extrapolatedto coverthe temperaturerangefrom soundin a chamber,it is necessaryto evaluate the contribution
--10 ø to 30øC.
to decay rate that may be attributed
to losses
The experimental
setupandmeasnrement
techniques in acousticenergy at the botmdariesof the chamber.
usedhere are the sameas thoseemployedin the earlier The techniqueusedhere is to evaluate thesewall losses
• C. M. Harris, J. Acoust.Soc.Am. 35, 11-17 (1963).
directly, by meansof decay-ratedata obtainedwhen
148
Volume40
Number I
1966
ABSORPTION
OF
SOUNI)
IN
the chamberis filled with prepurified
dry nitrogen
(whichexhibitsno anomalous
absorption
in the freqnencyrangeof measurement).The differencebetween
AIR
•max =0.00214
0.002
20øC
hmax = 11.7%
themeasured
valueof therateof decayof soundin the
nitrogen-filled
chamber
and thewduecomputed
from
64
kHz
absorption
data on nitrogen(the nitrogendata of Par-
brookandTempest
=areusedin thiscalcuhttion)
repre-
I
sents the contribution to the decay rate dne to wall
losses.This can be shown as follows. The decay rate of
soundin the chamberthat onemeasures,
R,,,,.
whenit is filledwith nitrogenis givenby
R..........d(x-=)
= Rx=+ R,,.•ndB/sec,
(1)
whereR•H is thedecayratedue to absorption
at the
boundaries
of thechamber,
andwhereRx=is thedecay
ratedueonlyto thenitrogengas.Similarly,whenthe
0.001
chamberis tilled •vith air, the measnreddecay rate
R..............
t(=i, = R•,i•+Rw•udB/sec,
(2)
whereR•.,,ois the decay rate contributedby the wall
lossesand R•i• is the calculated decay rate dne only
air absorption.
The wall-lossterm in theseequations
is approximatelythe same becauseboth gasesare
closelysimilar in molecularweight and characteristic
acousticimpedance.
By combiningEqs. 1 and 2, the
rate of decayof soundin the chamberowingonly to
the absorption
of soundin air is givenby
R:•i•=R............
•(•i•-- •R ...........l(x-o--Rx:• dB/see, (3)
400
600
800
I000
333 LOG•o(IOR.H.)
F•o. 1. Example of a plot of experimentaldata of the molecular
attenuation coefficient per wavelength in air as a function of
humidity. These data are for a temperatureof 20øC and a frequency of 6400 Hz.
wherethe quantityxvithinthe bracketsrepresents
the
contribution
to therateof decayof soundin a ch•tmber
that is dueto walllosses.
Consideration
hasbeengiven to problemsin the propagationof soundin air and room
topossible
wtriationin theboundary
losses
withchanges acoustics in Sec. IV.
in the humiditywithinthe sphere.As pointedout by
I. DATA
REDUCTION
Ewtns and Bazlev:• in discussing
this possibility,the
work of Knudsen,Wilson,and An(lerson• indicatesthat
For a givenconditionof temperatureand humidity,
suchan effectis not significant;their data shmvthat the decay rate of soundin air wits measuredfor the
thereis no appreciable
changein wall absorption
even variousfrequencies.
The resultof eachdecay-ratemeaswhen moisture condenses on the wall surface.
The valueof R,irin decibels
persecond
givenby Eq. 3,
urementwas punchedon an IBM card along with the
followinginformation:(1) temperature;(2) fi'equency;
(3) valueof classical
absorption
m•for theseconditions;
of soundin a chamberor roomcausedby air absorp- (4) humidity; (5) wavelength}, of soundfor thesecontion, may be convertedto the attenuation coe•cient ditions, computedfrom sound-velocitydata given in
m per meteras expressed
in the equation/= Ioe-'"' by Tables compiledby the National Bureau of Standardsa;
which representsthe contribution to the rate of decay
the relation
m= R•i•/(4.343c)meters
-t,
(4)
and (6) the value of wall lossesfor theseconditions.
From the above input data, a computer program
wherec is thevelocityof soundin metersper second. providedfor the printout of the followingresults:(1)
total attenuation coefficientm= m,,+m• (i.e., the sum
The methodsof dam reductionthat wereemployed of the attenuation toeflrelents due to molecular and
to determine the values of m for wtrious conditions in
this study itre described in detail in the next Section. A
classicalattenuation) corrected for wall losses; (2)
molecular
attenuationcoefficient,
m,,,;and (3) molecular
comparisonof the new data for air with earlier studies
attenuation
coefficient
per
wavelength
u=m,,,X. The
is given in Sec. II. Then a best fit is obtained.The new
resultsare presented
in Sec.III. Then lhev are applied results provided by thbscomputer program were a•.a-
lvzed
asindicated
i;•thisSection.
Thena computational
• H. D. Parbrookand W. Tempest,Acustica8,345-350 (1958).
a E. J. Evansand E. N. Bazley, Acustica6, 238 245 (1956).
• V. O. Knudsen,V. Wilso,, and N. S. A,derson,J. Acoust.Soc.
Am. 20, 849-857 (1948).
procednrewas clevelopedfor evaluating the total ataj. Hillsenrathet al., "Table of Thermal Propertiesof Gases,"
Natl. Bur. Std. (U.S.) Cite. No. 564 (1 Nov. 1955).
The Jeurnal of the AcousticalSocietyof America
149
C .
M
H A P. R I S
DELSASSO
+ LEONARD
22'C
•
2
HARRIS 963
Fl. 2. P,elaxation
frequency
asa functionof theconcentration
of watervaporin air expressed
in gm/m:'.The relationship
usedin the
resultspresentedin this paperis shownas the solidcurve.
tenuation coefficientfor auv temperatore, frequency, wheref .... is the frequencyin kilohertz corresponding
peak at h (expressed
in gramsper cubic
or hnmidity xvithinthe range over which the experi- to absorption
centimeter).The valuesof h given by this solid curve
mentaldata may be extrapolatedwith confidence.
wereusedin calculatingthe absorptioncurvespresented
A. Values of h ......
in Sec. III. There is a marked disagreementbetween
For a giventemperatureandfrequency,themolecular this curve and the theoreticalrelationshipof Kneser,7
absorptionm,• varieswith the moisturecontentof the
air. For a given frequency,the value of humidity at
whichthe molecularabsorptionis maximumis defined
ash...... The measuredvalueof h......may be determined
from plotsof the molecularattenuationper wavelength
whichpredictsthat f ..... variesas hø-,as indicatedby
the dashedcurve. In contrast,there is reasonablygood
agreement
with themorerecenttheoreticalrelationship
given by Hendersonand Herzfelds for a temperature
of 20øC.
In consideringthe relationship between f, .... and h,
the water-vapor content h is usually expressedeither
in terms of tool fractions (or percent molar concentrau against333logO0R.H.) ratherthanagainstlog(R.H.) tion) of water or in terms of the weight of the water in
directly.• For example,the original data points for gramsper cubicmeter (as in Fig. 2). The temperature
soundhavinga freqnencyof 6400Hz in air havinga tem- dependencyof the relationshipbetweenf ......and h deperatureof 20øCareplottedin Fig. 1. Heretheresulting pendson the units in which h is expressed.According
value of h...... is 11.7•. A total of 54 such plots was to the experimentaldata of Knotzel,• the relationship
made, i.e., one for eachof six differentvaluesof tem- betweenf ..... and h is relatively independentof temversnsthe logarithm of the relative humidity, such as
the one shownin Fig. 1. [Here, becausean automatic
plotting devicewas employed,it was convenientto plot
in gramsper
perature(--0.5ø,5.6ø, 10.2ø, 14.8ø,20.0ø,and25.1øC) peratureif the water vaporis expressed
at nine differentfrequencies
(2.0, 2.5, 3.2, 4.0, 5.0, 6.4, cubicmeter.If wemake thisassumptionandnowobtain
8.0, 10.0, and 12.5 kHz). From theseplots, an experi- an equivalentrelationshipin whichthe water vapor is
mentally determinedvalue of h......for eachfrequency, expressedin tool fractions,then f ..... increasesas the
and at each temperature,was obtained.These data are temperaturedecreases!Such an "inverse" relationship
shownin Fig. 2, where the wdues of h...... are expressed has been observedexperimentallyfor other gasesconin gramsper cubicmeter, alongwith similardata from taining water vapor? Accordingto data of Ref. 9, the
other studies.The solid curve representsa best fit to relationship,where h is expressedin grams per cubic
the data at 20øCfrom this and previousdata obtained meter, is not actually constant;instead,at high conwith the same experimentalsetup,•.• as well as data centrationsof water vapor, as the temperaturedecreases
obtained by other experimentersas weightedby the the value of f ...... increases,thereby accentuatingthe
author. This solidcnrve,in the frequencyrangebetween
125 and 12 500 Hz, may be expressed
bv the equation
f ......= 0.79h2+1.47h--0.15,
(5)
• C. M. Harris and W. Tempest,J. Acoust.Soc. Am. 36, 2390-
Volume 40
(1949).
s M. C. Hendersonand K. F. Herzfeld, J. Acoust.Soc.Am. 37.
986-988 (1965).
• H. Knotzet, Akust. Z. $, 245-256 (1940).
2394 (1964).
150
7 H. O. Kneser, J. Acoust. Soc. Am. $, 122-126 (1933); also,
Akust. Z. $, 256 257 (1940); Ergeb. Exakt. Naturwiss. 22, 121-185
Number 1
1966
:\ BS;O R PTIO
N
O1:
SO UN
1•
I N
.\I
1.0
1.'•6. 3. Plot of exl)erimental data of the molecular attenuation
coefficient
in air versus humidity.
These data are presented
in the uorma]ized form,
m/m .... vs h/h..... for comparison with the theoretical
relationship of Kneser
shown by the dashed line.
0.4
0.2
0
O
I
2
3
4
5
6
7
8
9
IO
12
13
NORMALIZED HUMIOITY h/hind x
"invcrsi(m" effect. The data obtained in this stu(lv at
for it frcqncncyf was obtainedby dividing the value of
differenttemperaturesshowan even morepronounced • ......for the temperatureby the w•tvelengthcorrespondtrend in this direction, which would accentuate the ing to that frequencyat temperatureT. For example,
inversioneffect. However, it shouldt)c noted that the for a temperature
of 31)ø(•,themaximumabsorption
at
accuracyof determira\\ion
of f ......is greatestat 20øC 10000 Hz wasdctcrmilmdby dividingthe wtlueof • ......
and that it is progressively
lessat lowertemperatures. for 30øC (0.00258)by ,5 for this freqnencyand temperThis pointbearsfnrtherinvcstig•ttionand may resultin ature, obhtining a wdue of m...... equal to 0.0740 m-L
a modificationof the aboveEq. 5 at lowertemperatures. The correspondingvalue at 101)0 Hz is equal to
I).0074 m •, etc.
B. Maximum Value of Molecular Absorption
versus Frequency
l:or at given temperatureand frequency,the maxi
C. Normalized Curves of Molecular Absorption
versus Humidity
]'he data pointsfor catchcurveof molecnlarabsorprepresentedby m....... Accordingto theory, the maxi- tion versushumidity at constantfrequencywere normum valuesof molecularabsorptionincreaselinearly realizedin the followingway. At a given temperature,
with frequency.
TMSincem......=• ......;/X,xvemay obtain the value of the molccnlarcoefficient(m,,,)for eachdata
wdues of both u...... and m...... from plots of • versus point xvasdividedby themaxhmlmwdueof the molecuhumidity, suchas the oneshownin l:ig. 1. For example, lar attenuation coefficientfor that temperatnre; this
in this illustration, • ......=0.00214; dividing by the ratio is deiined here as m/m ....... Shqfilarly, the correwavelengthfor at frequencyof 6400 Hz at 2{)ø(', we pondingvalue of relativehnmiditv h for the data point
obtain the maximrim wdue of molecuhtrabsorptionat wasdividedby h.......Accordingto the theor),of Kneser,
data for variousfrequencies
this freqncncy and temperature, i.e., (t.(1399m •. The absorptiol•-versus-humi(lity
wducsof • .......measuredat the variousfrc({ucncics
were that are so nomutlized should all fall along a single
averaged, obtaining the following wtlues of /•..... at cnrvc, which is shownby dashedlines in Fig. 3. This
procedure
rest\Its
the temperaturesindicated:-0.5øC, 0.(X)152;5.6øC, studyshowsthat sncha nom•alization
0.00170; 10.2øC, 0.(X)187; 14.gøC, 0.00205; 20.0C, in a singlecurve.l:or example,thedatapointsfor 20øC
0.00214; 25.1øC, 0.00247. These values, which are are shownin Fig..3 and the best lit thronghthesedata,
, is represented
by the
higher than similar data obtainedin past studieswith obtZned at differentfre(lnencies
this experimentalsetup,were averagedwith the earlier solidcnrvc.This solidcurve indicatesthat theor)' does
clara.t.• A smooth curve drawn throngh the res\firing not fit the measnrcdvalues of absorptionbelow and
wtluesof • ......yieldswduesthat are clo>,cto thosepre- abovethe maximumwtlue of absorption a result that
has beenobservedin the past when the data of earlie•
dicted by theory.
investigators
werepresentedin normalizedform.n This
The follo•vingwtlnes of/• ...... were employed,at the
temperatnresindicated, in the computerprogram for is becausethe above theory assumedthat the angular
determining the wftues of m......: -10øC, 0.(}0114; relaxationfreqnencywtrieswith h'",as indicatedby the
iHtln/ wtlue of molecular attenuation coefficient m,, is
--.5øC, 0.00128; 0øC, 0.00143; .5ø(7, 0.001.59; 1()ø(•,
0.00176; 15øC, 0.00194; 20øC, 0.00214; 21øC, 0.00218;
22øC, 0.(X)223; 23øC, 0.00227; 24øC, 0.00231; 25ø(7,
0.00235; 30øC, 0.00258.Thns, at a given temperature
T, the maximum wdnc of the molecularabsol'ptiol•m,,,
dashed curve of Fig. 2, xvhercasthe experimental data
l"K. l"JHerzfeld
an(lT. :\. Litovitz,
_Ibsorplion
andDispersion
of I;ltrasonicIf'aves(.\cademicPressInc., New York, 1959).
n W. I,. Nyborg and l). Mintzer, x3,'rightAir Development
Center, Wright-Patterson :\["B, WADC Tech. Rcpt. No. 54-602
(May 1955), Sec. 1.2.4.
The Journalof the AcousticalSocietyof America
151
C.
M.
HARRIS
A. Evaluation
showthat the relationshipis morecomplex.The present
study indicatesthat the value of m/m..... is slightly
below•).2 at highvaluesof humidity.Knudsen'sdatap'
showmuchgreaterdiscrepancies
betweenmeasuredand
theoreticalvaluesof m/m......at highvaluesof humidity.
In contrast,the studyof Delsasso
andLeonard•ashows
muchcloseragreementwith the presentdata shownin
Fig. 2.
Althoughthe above theory doesnot fit the experimental data, it is important to note that a singlecurve
is obtainedby rationalizingabsorptiondata at all frequencies
and tenrperatures
asindicatedabove,and that
this solidcurve representsa bestfit throughthe experimental data, and that the data collapseto a singlecurve
within the limits of experimentalmeasurement.Thus
one may concludethat it is possibleto measurethe
value of h..... and m......for variousfrequenciesand for
various conditionsof temperature.Then one can use
the solid curve shownin Fig. 3, in combinationwith
thesemeasuredvalues,to computecurvesof molecular
absorption
versushumidityfor variousfrequencies
and
temperatures.
This procedure
wasfollowed,employing
a high-speeddigital computer that had been programreedto calculatethe curvesof molecularabsorption versushumidity,usingthe data from exper/mental
measurements
as inpnt information.In the computer,
the classicalabsorptionwits added to the molecular
absorptionto yield the total value of the attenuation
coefficient.The advantageof this evaluationprocedure
is that it providesa convenientmeansof determining
soundabsorptionat frequenciesand temperaturesother
of Wall
Losses
In order to achievehigheraccuracyin the measurementof the absorptionof soundin air by the reverberationmethod(or the"intensity"method),it isnecessary
to evaluatewall losseswith precision.The greater the
wall losses,the more important is this sourceof error.
Becausethe decay rate that is measureddependsupon
the sum of the absorptionsby the walls and the air,
the wall lossesshouldbe small comparedwith the air
losses.Therefore, the lossesof acousticenergyat the
walls of the test chamber
minimum.
should be reduced to a bare
For the above reasons,a sphericalchamber was employed in this stud)', becauseit presentsthe smallest
wall surfacearea for a given volume and becauseits
shapemakesit possibleto achievea very highvalue of
acousticalimpedanceat the boundaries.
By usingvery
heavy walls in the presentexperimentalsetup, it was
possibleto achievea reverberationtime in dry air of
43 secat 1000 Hz. This is very many timeslongerthan
the comparablevaluesin earlierstudies,and the associated boundary lossesare significantlylower. In determining the attenuation coefficients
for air, the effects
of wall lossesweresubtractedout, asindicatedby Eq. 3.
In the "two-chamber"method employedby Knudsen,•= it was assumedthat the absorptioncoefficients
of both chamberswere the same.Althoughhis chamber
wallswereof steeland werereinforcedwith spot-welded
angleirons,it is nnlikely that the boundary conditions
in the chambers
were identical
because the walls were
only 4.8 mm thick. Intercomparisonsbetween three or
than the exact values at which the measurements were
more
similarly fabricatedmodel chambershave shown
made,by interpolationor extrapolation.
This procednre
that it is difficult to achieveidentical boundary condiwas followedto obtain the resultspresentedin Sec. III.
tionsin chambersof different sizes.In contrast, the steel
II. DISCUSSION
AND
OTHER
COMPARISON
WITH
STUDIES
In this Section,a comparisonis made betweenthe
presentresnltsand thoseobtainedin otherinvestiga-
walls of the sphereusedin the presentstudy were 16
nnn thick, and the boundarylosseswere evaluatedin
the same chamber
in which
the measurements
were
carried out.
tions. In most of thesestudies,the reverberation-chamIn the study by Evans and Baztey, a singlechamber
ber method has been employed,in which the rate of was employed,but becauseof physicallimitations it
decayof soundin air has beenmeasuredfor various wasimpracticalto sealthe chamberand fill it with a gas,
humidityconditions
at a constantvalueof frequency. such as nitrogen, for the purposeof calibrating wall
Laboratorymeasurements
of the absorptionof sound losses.Hence, the)' used the followingindirect evaluain air are subject to severalmajor sourcesof error tion procedure,which affordedgreateropportunityfor
(systematic
or random)resultingfrom (1) an inability error. They computedtheir wall lossesand curves of
to evaluatewith precisionlossesin acousticenergyin- absorptionversushumidity from the followingequation
troduced bv the walls of the test chamber; (2) the lack andonly a singlesetof experimental
measurements
(i.e.,
of adequatecontrolof the test-chamberenvironment, measurementsof the reverberationtime of an empty reincludingtemperatureand gas composition;and (3) verberationchamberfor varioushumidity conditions):
the lack of precisionin humidity measurement,either
as a result of instrumentation error or as a result of
137.2fX 10-4
1-4.6(/)IX 10-=
absorption
of moistureby the wallsof the testchamber.
Thesesourcesof errorare considered
belowin comparing
the results of the various studies.
1=V. O. Knudsen,J. Acoust.Soc.Am. 5, 112-121 (1933).
n L. P. Delsassoand R. W. Leonard, "The Atteuuation of
Sound in the Atmosphere," Univ. Calif., Los Angeles, Rept.
USAF contract W-28-099-AC-228 (25 l:eb. 1953).
152
Volume40
Number1
1966
molecular
ideal surface
(6)
classical
ABSORPTi'ON
OF
SOUND
where.! is the total absorptionof soundin the chamber
in squaremeters,./' is the frequencyin Hertz, k is the
angularrelaxationfrequency(2rf,,,,•), • represents
the
IN
AIR
CIRCULATION
PUMP•
GATEVALVE• •----LOUDSPEAKER
difference between the actual wall losses and the values
predictedby theory, and the numericalconstantsare
dependenton the physicalcharacteristicsof the room.
The firsttermhada nmximumvalueof 68.6fX 10-L The
singlesetof data,obtainedovera periodof two years,
wascorrected
to a temperature
of 20øCand the above
eqnationwas usedto (I) evaluatetheir wall losses;(2)
determinethe angularrelaxationfrequencyk; (3) deter
mine the magnitudeof the molecuhtrabsorption; (4)
computethe total absorption,i.e., molccnlarplus clas-
SATURATOR
ELEMENTS
I"m. 4. Simplifiedschematicdiagramof the air-circulationsystem. Air is recirculatedcontinuouslythrough the sphericalchamber. The saturator either takes away moisture from the air or
addsmoistureto it, dependingon the relative temperaturesof the
sphericalchamber and the saturator.
sicalabsorption;
and (5) checktheirresults.Sincephysicallimitationsof themeasurement
setupmadeit imposMble to provide any independentmeansof measuring ment that had been employedby earlier investigators.
the aboveparameters,includingthe effectsof wall losses, One method was to weight the amount of water that
the check was one of self-consistcncv.•Since
present
theory is not adequate for predicting the value of
molecularabsorptionaccuratelyfor wtrioustemperaluresand humidities,the first term iu Eq. 6, whichindudesthe term "k" (k=2•f ......), is opento question.
wasevaporatedin the test chamberprior to the establishmentof a givenhumidity condition.It wasdemonstrated that this technktuecan lead to seriouserror
plus a constantin the form shown in Eq. 6.
thepltst),themeasurement
valuedoesnot representthe
humidity within the chamberbecauseof absorptionor
sincea significantfraction of the water that enters the
chambermay be absorbedby the wltllsof the chamber.
Further, it has not been establishedthat the room ab- Similarly,if the humidity of tlneair that entersor leaves
sorption,in a nonidealsituationsuchas their reverbera- the test chamberis measured(which is another techtion chamber,can be representedby the secundterm niquethat has beenemployedby someinvestigatorsin
B.
Control
of Environment
of Test
Chamber
emission of moisture by the walls of the test chalnber--
tinlessa steady-statehumidity conditionis achieved.To
In the presentstudy, the test chamberwascompletely avoid these errors, the humidity control and measuresurroundedby 1 2 ft of fiberglassto provide thermal ment systemshownin Fig. 4 was constructed.Air •vas
insulation.A refrigerationsystemmaintainedthe tem- recirculated until a steadv-state condition of humidity
peratureof the chamberto within0.1øC.In contrast was achieved;often, this requiredits muchas « hour of
to this anti the controls employed in other studies, no
recirculation.
Then
the humidity
was determined
by
temperatnrecontrolwasemployedin the chamberused electric h.vgromelersensingelements as describedin
by Ewtns and Bazlev. As at result, the standard devia-
Ref.
1.
tion of the room temperature at which measurements
A determinationof the relationshipbetweenrelaxawere made was 2.1øC. tt was necessaryfor them to rely
tion
frequencyand humidity requireshighly accurate
on tlneorv
to correcttheirrestilLs
to 20øCandtinademeasurementof humidity, particuhirly at low concenquate theoreticaltreatmentof how absorptionwtries trationsof water wipor ,vherethe accuracyof measure-
with temperaturehalsyet to be established.
The measurements
fiescribedin this paper weremade
usinga closedair circulationsystem,shownin Fig. 4
and describedin Ref. 1. To lowerthe humidity, moisture
was taken from the test chamberand depositedin the
mentisrelatively
poor.
Although
a humidlily
measure-
%aturator"; to raise the humidity, the processwatsre-
in determiningthe value of h....... For this reason,there
hits been considerablediscrepancybetween such data
versed. Thus all measurements
were made on the same
air, of known chemicalcontent.This systemavoidsthe
ment error may have a s•nalleffecton the peak value
of the absorptioncurve, a small error in measuring
humidity can have a significanteffect in shifting the
positionof thepeak alongthe humidityscaleand, hence,
measuredby various investigators.Comparisonsare
shownin Fig. 2 of the resultsof severalair-absorption
studiesin termsof the relaxationfrequencyf ..... versus
concentration
of watervapor (h, expressed
in gramsper
cubic centimeter) at which the maximnm absorption
the addition of acousticabsorptioninto the measure- ix achievedfor the frequency.
ment system,whichsucha drying techniqueintroduces.
Knudsen's data, represented by the three experi-
possibilityof contamination
of the air undertest,either
by smogor by chemicaldrying agentssuch as those
employedby Evans and Bazlev to redneethe wdue of
humidity in their test chamber.Furthermore,it avoids
mental pointsat 20øC,do not providesufficientdata
for an explicit relationshipbetweenthe relaxationfreUsing the present experimentalsettip, the author quencyand concentrationof water vapor. Ewms and
tried several different methodsof hnmidity measure- Bazleyreportedthat the relaxationfrequencyvariesas
C. Humidity Measurements;f
...... versus h......
The Journalof the AcousticalSocietyof America
15:t
C.
M.
HARRIS
TanrE I. Values of the product 4m at a frequencyof 2000 Hz
for various temperaturesand values of relative humidity. The
TABLEIV. Valuesof the product 4m at a frequencyof 4000 Hz
for various temperaturesand values of relative humidity. The
attenuation coefficientm is expressedin ft-L
attenuation coefficientm is expressedin meters-L
R.H.
TEMPERATURE
20øC
25 øC
(5'•:)
(59.0ø[:)
(68.0øI:)
(77.0øF)
(86.0ø1:)
30
40
45
46
47
48
49
50
51
52
53
54
55
60
70
80
0.00436
0.00338
0.00317
0.00312
0.00308
0.00305
0.00302
0.00300
0.00298
0.00296
0.00294
0.00292
0.00291
0.00282
0.00267
0.00255
0.00362
0.00316
0.00303
0.00301
0.00299
0.00297
0.00294
0.00292
0.00290
0.00289
0.00287
0.00285
0.00283
0.00274
0.00259
0.00246
0.00346
0.00313
0.00300
0.00298
0.00296
0.00294
0.00291
0.00289
0.00287
0.00285
0.00283
0.00281
0.00279
0.00269
0.00255
0.00244
0.00339
0.00305
0.00291
0.00288
0.00286
0.00285
0.00283
0.00281
0.00279
0.00277
0.00275
0.00274
0.00272
0.00264
0.00250
0.00239
15 øC
20øC
25øC
((•)
(59.0ø1:)
(68.0øF)
(77.0øI,')
(86.0øF)
30
40
45
46
47
48
49
50
51
52
53
54
55
60
70
80
0.04861
0.03577
0.03178
0.03107
0.03040
0.02974
0.02914
0.02861
0.02809
0.02759
0.02714
0.02670
0.02632
0.02444
0.02227
0.02086
0.03794
0.02870
0.02603
0.02564
0.02527
0.02499
0.02472
0.02444
0.02419
0.02397
0.02371
0.02343
0.02321
0.02243
0.02131
0.02042
0.03130
0.02570
0.02435
0.02417
0.02401
0.02385
0.02369
0.02353
0.02337
0.02321
0.02306
0.02293
0.02280
0.02216
0.02107
0.02014
0.02814
0.02506
0.02413
0.02395
0.02377
0.02362
0.02347
0.02332
0.02317
0.02301
0.02286
0.02271
0.02257
0.02192
0.02072
0.01979
30øC
TABLEII. Valuesof the product 4m at a frequencyof 2000 Hz
for various temperatures and values of relative humidity. The
attenuation coefficientm is expressedin meters L
R.H.
TEMPERATURE
R.tI.
15 øC
TABLEV. Valuesof the product 4m at a frequencyof 6300 Hz
for various temperaturesand values of relative humidity. q'he
attenuation coefficientm is expressedin ft •.
R.H.
TEMPERATURE
15 øC
20øC
25øC
30øC
(%)
(59.0øI:)
(68.0ø[:)
(77.0ø1:
')
(86.0øI?)
30
40
45
0.01432
0.01110
0.01040
0.01187
0.01037
0.00996
0.01136
0.01029
0.00986
46
47
48
49
50
51
0.01026
0.01013
0.01003
0.00993
0.00986
0.00979
0.00989
0.00982
0.00974
0.00967
0.00960
0.00954
52
53
54
55
60
70
80
0.00972
0.00966
0.00960
0.00954
0.00925
0.00878
0.00838
0.00948
0.00942
0.00936
0.00930
0.00901
0.00851
0.00807
30øC
TEMPEnATURE
15øC
20øC
25øC
30øC
(Sk)
(59.0øF)
(68.0øI:)
(77.0øF)
(86.0øF)
0.01113
0.01002
0.00955
30
0.03217
0.02559
0.02088
0.01718
40
45
0.02412
0.02131
0.01901
0.01695
0.01589
0.01444
0.01416
0.01340
0.00979
0.00972
0.00964
0.00957
0.00950
0.00943
0.00947
0.00941
0.00935
0.00928
0.00922
0.00916
46
47
48
49
50
51
0.02078
0.02033
0.01991
0.01948
0.01908
0.01871
0.01659
0.01623
0.01591
0.01561
0.01534
0.01507
0.01421
0.01401
0.01382
0.01368
0.01354
0.01340
0.01330
0.01322
0.01313
0.01305
0.01297
0.01289
0.00936
0.00929
0.00922
0.00916
(}.00884
0.00839
0.00803
0.00910
0.00904
0.00899
0.00893
0.00868
0.00823
0.00784
52
0.01836
0.01483
0.01327
0.01280
53
54
55
6(}
70
80
0.01802
0.01770
0.01739
0.01599
0.01384
0.01242
0.01459
0.01438
0.01419
0.01322
0.01215
0.01145
0.01316
0.01302
0.01288
0.01242
0.01183
0.01136
0.01272
0.01265
0.01258
0.01225
0.01168
0.01119
TABLE III. Values of the product 4m at a frequency of 4000 Hz
'/'A•LE VI. Values of the product 4m at a frequencyof 6300 Hz
for various temperaturesand values of relative humidity. The
attenuation coefficientm is expressedin ft-L
for various temperaturesand valuesof relative humidity. The
R.H.
TEMPERATURE
15øc
20øc
25oc
R.H.
30oc
15oc
20oc
(• i )
(59.0øF)
(68.0øF)
0.00954
0.00857
30
0.10556
0.00783
0.00742
0.00736
0.00732
0.00763
0.00735
0.00730
0.00724
40
45
46
47
48
49
50
51
0.07914
0.06993
0.06819
0.06672
0.06532
0.06392
0.06261
0.06139
52
53
54
0.06024
0.05912
0.05807
55
60
70
80
0.05707
0.05247
0.04542
0.04075
(59.0ø1:)
(68.0øF)
30
0.01481
0.01156
40
45
46
47
0.01090
0.00968
0.00947
0.00926
0.00874
0.00793
0.00781
0.00770
48
49
50
5i
52
53
54
55
60
70
80
0.00906
0.00888
0.00872
0.00856
0.00841
0.00827
0.00813
0.00802
0.00744
0.00678
0.00635
0.00761
0.00753
0.00745
0.00737
0.00730
0.00722
0.00714
0.00707
0.00683
0.00649
0.00622
0.00727
0.00722
0.00717
0.00712
0.00707
0.00703
0.00699
0.00695
0.00675
0.00642
0.00613
0.00720
0.00715
0.00710
0.00706
0.00701
0.00696
0.00692
0.00687
0.00668
0.00631
0.00603
Volume40
Number1
TEMPERATURE
(86.0ø[:)
(5•)
154
attenuation coefficieutm is expressedin meters'L
(77.0øF)
1966
25oc
30oc
(77.0øF)
(86.0øF)
0.08398
0.06852
0.05637
0,06238
0.05561
0.05444
0.05327
0.05220
0.05124
0.05033
0.04945
0.05215
0.04738
0.04664
0.04599
0.04537
0.04490
0.04443
0.04397
0.04648
0.04397
0.04366
0.04337
0.04310
0.04283
0.04256
0.04229
0.04867
0.04789
0.04721
0.04656
0.04340
0.03988
0.03757
0.04355
0.04317
0.04274
0.04202
0.04175
0.04150
0.04129
0.04021
0.03833
0.03672
0.04228
0.04075
0.03883
0.03729
ABSO
RI'TIt)
N
I N
O1,'
.\ I l(
0.09
0.08
0.07
006
0,05
FIG. 5. Values of the total attcnuati(m
coelficientm versuspercentP,.H. for air at
20øC and normal atmosphericpressurefor
004
frequencies
between2.0 and 12.5 kHz at
l-oct intervals.
0.03
12.5 KHz
0.02
I0,0
8,0
o
0
IO
20
;50
40
RELATIVE
50
60
70
80
90
I00
HUMIDITY , PERCENT
shownin iFig.2 of Ref. 14
h•.a.Thisisshownasa dashedcurvein Fig. 2. The 20øC indicatedby the comparison
data of the presentstudyare •vithin the measurement (alsosee Fig. 3 o• Ref. 16). In contrast,the resultsof
accuracy
of the earlierdataof Refs.1 and6. I/kewise, Knudsen and ()bert '" for oxygenare in substantialdisthe data of Knotzel also could be represenledb3' the
solid curve of Eq..5.
D. Comparisonof Data for Oxygen Containing
Water Vapor
agreementwith thesemore recentdata. A comparison
of this type couldnot be made by Evans and Bazleva
since their experimentalsetnp did not permit them to
make sound-absorptionmeasurementsin gasesother
than air.
Iii,
RESULTS
Onemeansof providingan independent
checkon the
over-allmeasurement
system
fortheabsorption
ofsound Employingthe abovedata-reduction
procedures,
the
in air is to usethe systemto measurethe absorption attenuationcoefficients
of sotrodin air at normalpresofsound
in oxygen
andthento compare
thesedatawith surehave beenevaluatedfor the followingconditions:
resultsobtainedby a differentmeasurementtechnique (1) at the temperatures
of --10 ø, --5 ø,0ø,5ø,10ø,15ø,
that is not subjectto thesametypesof errors.Suchan 20ø, 21ø, 22ø, 23ø, 24ø, 25ø, and 30øC; (2) at relative
independent
check
hasbeenmadeat 20øC.Theexperi- humidities of 5cy• 100% in incrementsof 5• R.H.
mentalsetupusedfor sound-absorption
datapresented Eexceptin the r;mgcfrom45• to ,55%R.H., wherethe
here was used to measurethe absorptionof soundin increments
are 1%•; and (3) for frequencies
of 12,5,
oxygenasa functionof water-vapor
content.
'4The re- 250, ,500,1000, 2(}00,2,500,320(I, 4000, 5000, `5940,6300,
suitssoobtainedagreeveryclosely
with recentdatafor 8000, 10 000, and 12 `500Hz. Values in the frequency
oxygenobtained
by Henderson,
•:"•c'
whoemployed
it range from 12,5to 1000 Hz were detemxinedby extraresonant
pressure-chamber
measurement
system,
•7using polarion from the data at higher frequenciesby the
a measurement
techniquethat avoidsthe useof a hy-
procedureindicatedin Sec.1. Data for the full tempera-
grometer,
whichma5' introduce
oneof the principle ture and humidity rangeslisted aboveare tabulated, in
sourcesof error. Also, theserestiltsare in closeagree- both the metric and English systemsof tinits, in a Namentwith theoxygendataof KnotzelandKnotzelfisas tional Aeronauticsand Space Administration report=ø
•4C. M. Harrisand W. Tempest,J. Acoust.•qoc.Am..•6, 24162417 (1964).
now in publication.Excerptsof someof thesedata, over
restrictedtemperatureand humidity ranges,are given
in Tables [ and I[ for 2000 Hz, Tables Iii and tV for
is M. C. Henderson,
J. Acoust.Soc.:\m. 34,349 350 (1962).
•r,,I. C. Henderson,A. V. Clark, and P. 14.15ntz,J. Acoust.
Soc. Am. 37, 456 463 (1965).
17.•I. C. Hendersonand J. O. l)onnelly,J. :\coust.Soc.Am.
34, 779-784 (1962).
l• H. Knotzeland L. Knotzel,Ann. Phys.2,393 403 (1948).
19•/, (). Knudsenand 1.. Obert, J, Acoust.Soc.Am. 7, 249-253
(1936).
•('(?. M. Harris, "AI)sorl)tion of Sound in Air versus Humidity
and Temperature," X.\SA Contractor Rel)t. (to tie I)ublished).
The Journalof the AcousticalSocietyof America
155
C.
M.
HARRIS
value of relative humidity as the temperatureincreases.
l"igure8 showscurvesof absorptionversustemperature
for constant values of frequency--all for a relative
above temperatures(20ø('). This informalion is pre~ l]nmidity of 50%.
sentedin anotherform for other valuesof temperature
IV. APPLICATION
OF RESULTS
TO ROOM
ACOUSTICS
and humidity in Fig. 6.
AND PROPAGATION
PROBLEMS
The effectof temperatureon curvesof soundabsorpLionversushumidityat constantfrequencyis illustrated
A. Propagation of Sound in Air
in Fig. 7, which presentsabsorptiondata for a freFor problemsconcernedwith the propagationof
quencyof 4000 Hz. Here the total attenuationcoefficient m is plotted as a function of humidity for differ- soundin air, it is convenientto expressattenuationof
4000 Hz, and Tables V and VI for 6300 Hz. Figure 5
shoxvs the result• of this study of total attenuation
coellicient versu.• humidity for •ound in air at one of the
ent valuesof temperature.Note that (1) the maximum soundin terln• of decibelsper unit distance.Valuesof
value of absorptionincreaseswith increasingtemperature, and (2) the peak in the curvesshifts to a lower
0.20
0.18
0.6
0.16
0.14
•
0.12
•E
0
_0 0.10
(c)
Z.Z
0.08
2.0
0.06
1.8
0.04
1.6
0.02
1.4
0
-I0
-5
0
5
TEMPERATURE,
IO
15
20
25
30
OEGREES CENTIGRADE
(a)
0.5
0.4
0.6
I
0.4
0.2
OJ
0
0
-io
-5
0
5
i0
15
20
25
TEMPERATURE
, DEGREESCENTIGRADE
(b)
30
-i0
-5
0
5
[0
15
20
25
50
TEMPERATURE, DEGREESCENTIGRADE
(d)
FIG. 6. Attenuation of soundin air versu* temperaturefor various values of relative humidity. The attenuation is given in
dB/100 meters.
156
Volume 40
Number 1
1966
ABSORPTION
OF
SOUND
IN
AIR
attenuation
in decibels
permeterareobtainedby multi- the source,so that it is sometimesreferredto as "excess
plying the total attenuationcoefficientby 4.343. This attenuation." It does not include losses due to other
information has been tabulated in full in Ref. 20, both factorssucha.• scattering.
in themetricand Englishsystemsof units.Someof these
B. Calculation of Reverberation
Time
data are plotted in Fig. 6, which givesthe attenuation
in decibelsper 100 metersas a functionof temperature
In calculating the reverberationtime of a room, the
for variousvaluesof relative humidity. This represents
the attenuationof a planewavein a homogeneous
me
dium owingonly to air absorption.This ix the attenuation in excessof the lossdue to sphericaldivergence,
xvhichis 6 dB for each doublingof the distancefrom
total absorptionin the roomis required.This total is
the sum of the absorptionsdue to the lossesat the
boundaries,to the furnishingsin the room, and to air
absorption.The absorptiondue to lossesin air usually
is importantonly in large roomsand/or at high frequencies,
andis givenby 4reV.This termrepresents
the
areaof a perfectlyabsorptivesurfacethat is equivalent
to the absorptionof soundin air in a room of volume
V. The product4m is givenin Tables I throughVI in
the metric and Englishsystemsof units for 2000, 4000,
and 6300 Hz. Thesevaluesneedonly be multipliedby
the vohtme of the r(tom to determine
the values of air
absorption.
Example. Snppose that a room has a volume of
1 000000 ft :• (28 320 ma) and is at a temperatnreof
20ø(3anda relativehumidityof 47%. Find the absorp-I0
-5
0
5
I0
Iõ
20
25
30
TEMPERATURE , DEGREE CENTIGRADE
tion in the roomowingto air at a frequencyof 4000 Hz.
From Table l II, the product 4m for these conditions
e(luals0.(/077ft • L Multiplying by the volume1 000 000
ft ;*, xveobtain a total absorptionof 7700 sabins.An
equiwtlentrestLitix obtainedin the metricsystemfrom
(e)
12
Table IV if we usea valueof 4m eqna}to 0.0253n1-1
and lnultiply by a volume of 28 320 m• to obtain the
total absorptionin metric sabins.
l0
C. Corrections
to Reverberation-Time
Measurements
As indicated by the data of Tables 1 VI, the contri-
bution to the rate of decay of soundin a large room
owingto air absorptionis significantat higherfrequenciesand it varieswith humidity and temperature.One
sourceof discrepancyin the measuredvaluesof rever-
•?
beration time of the same auditorium
by different in-
vestigators
maytie attril)utedto differences,
duringthe
measurements,
of temperature
andhumidityconditions.
The following procedureis suggestedto correct this
possiblesourceof discrepancy,and to provide an improved basisfor the comparisonof reverberation-time
data for various large halls at higher frequencies.
presenli•zg
reverberalio,-lime
dalafor largeaudiloriums,
irrespective
of lhe humidily a•td lemperahtreat which
measuremeldsare made, carreel lhe reverbera!io•tlime so
lha! il represcnls
lhe reverberalio,.
lime lha! •c,
ouldhave
bee, oblai,ed if lhemeasureme•zIs
hadbee• madeal a rela-
tivehumidilyof50%anda lemperahtre
of20øC,i.e.,sla•zdard conditions.This correctionmay be made as follows.
0
-I0
-5
0
5
TEMPERATURE
I0
, DEGREES
15
20
CENTIGRADE
25
30
Subtractthe decayrate due to :/it' absorptionfor the
actualmeasurement
conditions
from the ,'ateof decay
at 20øCand 50% R.H. This difference
is to be addedto
the measuredwtlue of the rate of decayof soundin the
The Journal of the AcousticalSocietyof America
157
C.
M.
HARRIS
0.03
0.02
/\
ø I
'
'
ooo Hz
Fro. 7. Values of total attenuation
coefficient
m vcrushumidity for a frequencyof 4000 Hz at
temperaturesof -10 ø, 0 ø, 10ø, 20ø, and 30øC.
IO
20
I
i
50
40
50
RELATIVE
•
,
I
I
60
70
80
90
room. From this correcteddecay rate, compute the
corrected
reverberation
I00
HUMIDITY , PERCENT
time.
Example. Supposethat reverberation-timemeasurementsare made in an auditoriumat a temperatureof
Step3: Add the valueof R• obtainedin Step2 to
the measuredrate of decay.This representsthe
decay rate correctedto normal conditions.
= R.........a+R•= 28.57dB/sec--1.54dB/sec
25øCand a relativehumidityof 800•o.At 4000Hz, the R....'eeted
= 27.03 dB/sec
(s)
condition"(20øC,50•0 R.H.)?
measured value of the reverberation time is 2.10 sec.
What wound the reverberation time be under "standard
Therefore, the reverberationtime under standard conditions is
Step1: Calculatethe measureddecayrate:
R......... d=60 dB/2.10 sec=28.57dB/sec.
(7)
t•o=60 dB/27.03dB/'secm2.2
sec.
(9)
Slep 2: Subtract the decayrate due to air absorpto Measurementsof Sound-Absorption
tion at a relative humdity of 50% and a tempera- D. Corrections
Coefficients
ture of 20øC(obtainedfi'omTablesVII, VIii, and
IX) from the decay rate due to air absorption According
to Eq. 2, therateof decayof soundin a test
under measurementconditions.For a frequencyof chamber(or a room)may be represented
as thesumof
4000 Hz, the rate of decaydue to air absorptionat two terms:(1) therate of decayof soundowingto air
25øCand 80% R.H. is 7.57 dB/sec; at "standard absorption,
and(2) therateof decayof soundresulting
conditions"
of 20øC,50% R.H., the correspondingfromabsorption
at the boundaries.
Thns,if measurevalue is 9.11 dB/sec. Subtracting,the difference ments of the absorptioncoefficients
of an acoustical
R• is --1.54 dB/sec.
materialaremadein •[rew'.rberation
chamber,
at higher
0.07
[ _.
....
C 0.06
50%R.H.
0.05
•-
0.04
l,'lo. 8. Values of total attenuation coelticient m versus
temperaturefor constantvaluesof frequency.All data are
for a relative humidity of 50%.
LL
•-
0.03
•3 0,02
L•
0.01
0
I0
15
20
TEMPERATURE
158
Volume 40
25
, DEGREES
Number I
1966
CENTIGRADE
3O
ABSORPTION
OF
SOUND
IN
AIR
'I'AurEVII. Valuesof the decayrate of soundin a roomowing
TABLEIX. Valuesof the decayrate of soundin a roomowing
to the contributionof air absorption,at variousvaluesof tem- to the contrilmtionof air absorption,at variousvaluesof temperatureand relativehumidity.Thesedata, expressed
in dB/sec, peratureand relativehumklity.Thesedata, expressed
in dB/sec,
are for a frequencyof 2000 Hz.
are for a frequencyof 6300 llz.
R.H.
TEMVEItA TUIIE
B.H.
15øC
20øC
25oc
3oø(2
(',.•)
(59.0ø1
.')
(68.0ø1
;'
(77.0ø1
,')
(86.0ø1:
)
30
40
45
46
47
48
5.29
4.10
3.85
3.79
3.75
3.71
3.67
3.64
3.62
3.59
3.57
3.55
3.53
3.42
3.25
3.10
4.43
3.87
3.71
3.69
3.66
3.63
4.27
3.87
3.71
3.68
3.65
3.63
3.60
3.57
3.55
3.52
3.49
3.47
3.44
3.33
3.16
3.02
49
50
51
52
53
54
55
60
7(I
80
3.61
3.58
3.56
3.53
3.51
3.49
3.47
3.36
3.17
3.01
4.22
3.80
3.62
3.59
3.57
3.54
3.52
3.50
3.47
3.45
3.43
3.41
3.39
3.29
3.12
2.97
frcqueilcies where air absorptmn is significant an
errorin evaluatingthe absorptioncoefficients
will result
unlessthc contributionto the total decay causedby
air absorptionis subtractedout. If this correctionis
made,thenoneshouldobtain the samevalueof absorption
coefiqcient for
the
material
under
test even
if
TABLEVIII. Valuesof the decay rate of soundin a room owing
to the contributionof air absorption,at various values of temlmrature and relative humidity. These data, expressedin dB/sec,
are for a frequencyof 4000 Hz.
TEMPERATURE
(5/•)
15øC
20øC
25øC
(59.0ø1:
)
(68.0øF)
(77.0øI:)
30oc
(186.0ø1:
)
30
40
45
46
47
48
49
50
5l
52
53
54
55
611
39.01
29.24
25.84
25.20
24.65
24.14
23.62
23.14
22.68
22.26
21.85
21.46
21.09
19.39
31.30
23.25
20.73
20.29
19.85
19.46
19.10
18.76
18.43
18.14
17.85
17.59
17.35
16.18
25.76
19.60
17.81
17.53
17.29
17. (15
16.88
16.70
16.53
16.37
16.23
16.(}7
15.89
15.32
21.37
17.62
16.67
16.55
16.44
16.34
16.23
16.13
16.03
15.93
15.82
15.73
15.65
15.24
70
811
16.78
15.06
14.87
14.00
14.60
14.02
14.53
13.92
measureduuder differcut conditionsof humidity and
temperature. Such a correction can be made conven-
iently by the useof TablesVII IX. For example,suppose that measurementsat 4000 Hz are made in a re-
verberationchamberat a tetnperatureof 25øC and
a relativehumidityof 80%. Accordingto Table VHI,
the rate of decaydue to soundabsorptionin air R,•, is
7.57 dB/sec.Accordingto Eq. 2, the measured
decay
rate is equal to the sum of the decayrate due to absorptionat the boundariesof the room and due to air
absorption.Thus, if the measuredvalue of the rate of
R.H.
TEMPERATURE
15 øC
20øC
25 øC
311ø(2
((•&)
(59.0øF)
(68.0øF)
(77.0øF)
(86.0øF)
30
40
45
46
47
48
49
50
51
52
53
54
55
60
70
80
17.96
13.22
i 1.74
11.48
11.24
10.99
10.77
10.57
111.38
10.20
10.03
9.87
9.73
9.03
8.23
7.71
14.14
10.70
9.70
9.56
9.42
9.32
9.21
9.11
9.02
8.94
8.84
8.73
8.65
8.36
7.94
7.61
11.77
9.66
9.15
9.07
9.03
8.97
8.91
8.85
8.79
8.73
8.67
8.62
8.57
8.33
7.92
7.57
10.67
9.50
9.15
9.08
9.01
8.95
8.90
8.84
8.78
8.72
8.67
8.61
8.55
8.31
7.85
7.50
decayis 22.10dB/sec, the actualdecayrate corrected
for air absorptionis (22.10-7.571•13.5 dB/sec. Thus
it is possibleto correctfor air absorptionin measuring
the absorptioncoefficientof a material in a reverberation chamber.Such tt procedurehas been proposedin
CommitteeC-20 of the AmericanSocietyfor Testing
Materials. 2
ACKNOWLEDGMENT
This research was supported by the George C.
Marshal[ Space Flight Center, National Aeronautics
and Sp;tceAdministration.The author •tppreciatesthe
assistanceof H;trry Gong, in the measurements,
and
Beth Alberty, in the cktta reduction.
o.•R. Huntley, personalcommunication.
The Journalof the AcousticalSocietyof America
]59