ASTM-E1050.23685-1

Designation:E1050–98StandardTestMethodforImpedanceandAbsorptionofAcousticalMaterialsUsingATube,TwoMicrophonesandADigitalFrequencyAnalysisSystem1ThisstandardisissuedunderthefixeddesignationE1050;thenumberimmediatelyfollowingthedesignationindicatestheyearoforiginaladoptionor,inthecaseofrevision,theyearoflastrevision.Anumberinparenthesesindicatestheyearoflastreapproval.Asuperscriptepsilon(e)indicatesaneditorialchangesincethelastrevisionorreapproval.1.Scope1.1Thistestmethodcoverstheuseofanimpedancetube,twomicrophonelocations,andadigitalfrequencyanalysissystemforthedeterminationofnormalincidencesoundabsorptioncoefficientsandnormalspecificacousticimpedanceratiosofmaterials.1.2LaboratoryAccreditation—AprocedureforaccreditingalaboratoryforperformingthistestmethodisgiveninAnnexA1.1.3Thisstandarddoesnotpurporttoaddressthesafetyconcerns,ifany,associatedwithitsuse.Itistheresponsibilityoftheuseofthisstandardtoconsultandestablishappropriatesafetyandhealthpracticesanddeterminetheapplicabilityofregulatorylimitationspriortouse.2.ReferencedDocuments2.1ASTMStandards:C384TestMethodforImpedanceandAbsorptionofAcousticalMaterialsbytheImpedanceTubeMethod2C634TerminologyRelatingtoEnvironmentalAcoustics2E548GuideforGeneralCriteriaUsedforEvaluatingLaboratoryCompetence32.2ISOStandards:ISO10534-1Acoustics—DeterminationofSoundAbsorp-tionCoefficientandImpedanceorAdmittance—Part1:ImpedanceTubeMethod4ISO10534–2Acoustics—DeterminationofSoundAbsorp-tionCoefficientandImpedanceinImpedanceTubes—Part2:Transfer-FunctionMethod43.Terminology3.1Definitions—TheacousticalterminologyusedinthistestmethodisintendedtobeconsistentwiththedefinitionsinTerminologyC634.NOTE1—Historicalliteratureregardingthemeasurementofnormalincidenceabsorptioncoefficientsreferredto“transferfunction”measure-ments;however,thetermarisesfromLaplacetransformtheoryandisnotstrictlyrigorouswhentheinitialconditionshaveanon-zerovalue.Theterm“frequencyresponsefunction”arisesfrommoregeneralFouriertransformtheory(1).5Thistestmethodshallretaintheuseoftheformertermalthoughnottechnicallycorrect.UsersshouldbeawarethatmodernFFTanalyzersmayemploythelatterterminology.3.2Symbols:ThefollowingsymbolsareusedinSection8(Procedure):3.2.1brc—normalspecificacousticssusceptanceratio.3.2.2c—speedofsound,m/s.3.2.3grc—normalspecificacousticconductanceratio.3.2.4G11,G22—autopowerspectraoftheacousticpressuresignalatmicrophonelocations1and2,respectively.3.2.5G12—crosspowerspectrumoftheacousticpressuresignalsatmicrophoneslocations1and2.3.2.6H—transferfunctionofthetwomicrophonesignalscorrectedformicrophoneresponsemismatch.3.2.7H¯—measuredtransferfunctionofthetwomicro-phonesignals.3.2.8HI,HII—calibrationtransferfunctionsforthemicro-phonesinthestandardandswitchedconfigurations,respec-tively.3.2.9H¯c—complexmicrophonecalibrationfactor.3.2.10j—equals=–1.3.2.11k—equal2pf/c;wavenumber,m-1.3.2.11.1Discussion—Ingeneralthewavenumberiscom-plexwherek=k8-jk9.k8istherealcomponent,2pf/candk9istheimaginarycomponentofthewavenumber,alsoreferredtoastheattenuationconstant,Nepers-m-1.1ThistestmethodisunderthejurisdictionofASTMCommitteeE-33onEnvironmentalAcousticsandisthedirectresponsibilityofSubcommitteeE33.01onAbsorption.CurrenteditionapprovedJune10,1998.PublishedAugust1998.OriginallypublishedasE1050-85a.LastpreviouseditionE1050-90.2AnnualBookofASTMStandards,Vol04.06.3AnnualBookofASTMStandards,Vol14.02.4AvailablefromAmericanNationalStandardsInstitute,11W.42ndSt.,13thFloor,NewYork,NY10036.5Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendofthistestmethod.1Copyright©ASTMInternational,100BarrHarborDrive,POBoxC700,WestConshohocken,PA19428-2959,UnitedStates.CopyrightbyASTMInt'l(allrightsreserved);ReproductionauthorizedperLicenseAgreementwith3M;FriMar1000:46:19EST20063.2.12l—distancefromthetestsampletothecentreofthenearestmicrophone,m.3.2.13r/rc—normalspecificacousticresistanceratio.3.2.14R—complexacousticreflectioncoefficient.3.2.15s—centre-to-centerspacingbetweenmicrophones,m.3.2.16x/rc—normalspecificacousticreactanceratio.3.2.17yrc—normalspecificacousticadmittanceration.3.2.18z/rc—normalspecificacousticimpedanceratio.3.2.19a—normalincidencesoundabsorptioncoefficient.3.2.20f—phaseofthecomplextransferfunction,radians.3.2.21fR—phaseofthecomplexacousticreflectioncoef-ficient,radians.3.2.22r—densityofair,kg/m3.3.3Subscripts,Superscripts,andOtherNotation—Thefol-lowingsymbols,whichemploythevariableXforillustrativepurposes,areusedinSection8:3.3.1Xc—calibration.3.3.2Xi—imaginarypartofacomplexquantity.3.3.3Xr—realpartofacomplexquantity.3.3.4XI,XII—calibrationquantitiesmeasuredwithmicro-phonesplacedinthestandardandswitchedconfigurations,respectively.3.3.5X¯—measuredquantitypriortocorrectionforampli-tudeandphasemismatch.3.3.6|X|—magnitudeofacomplexquantity.4.SummaryofTestMethod4.1ThistestmethodissimilartoTestMethodC384inthatitalsousesanimpedancetubewithasoundsourceconnectedtooneendandthetestsamplemountedattheotherend.Themeasurementtechniquesforthetwomethodsarefundamen-tallydifferent,however.Inthistestmethod,planewavesaregeneratedinthetubeusingab