哈工程振動噪聲-第6章 噪聲控制的聲學基礎(chǔ)

第6章噪聲控制的聲學基礎(chǔ)Chapter6FundamentalsofAcousticsforNoiseControl6.1TheWaveEquation6.2BasicCharacteristicsofPlaneSoundWave6.3AcousticEnergyinSoundField6.4SoundLevels6.5RadiationofSound

Source6.6SoundFieldinRoomsChapter6FundamentalsofAcousticsforNoiseControl6.1TheWaveEquation(1)SoundPressure（聲壓）Avariationinpressureaboveandbelowatmosphericpressureiscalledsoundpressure(p),inunitsofPascal(Pa)

Theroot-meansquare(rms)pressureChapter6FundamentalsofAcousticsforNoiseControl6.1TheWaveEquationForharmonicwaves,thereareHerepmistheamplitudeofsoundpressure.(3)SpeedofSound（聲速）Thespeedofsoundistherateatwhichasoundwavepropagatesthroughagivenmedium

Foranidealgas,thespeedofsoundisafunctionoftheabsolutetemperatureofthegas

Chapter6FundamentalsofAcousticsforNoiseControl6.1TheWaveEquationTheacousticpressureandparticlevelocityarerelatedbythespecificacousticimpedance（聲阻抗率）:(2)ParticleVelocity（質(zhì)點振速）Theacousticparticlevelocity(u)isdefinedasthelocalmotionofparticlesoffluidasasoundwavepassesthroughthematerial.

Chapter6FundamentalsofAcousticsforNoiseControl6.1TheWaveEquationwhere

isthespecificheatratio（比熱比）,Risthespecificgasconstant（氣體常數(shù)）

forthegas,R=287J/kg-Kforair,andTistheabsolutetemperatureofgasindegreesKelvin,equalto273.15plusthetemperatureindegreesCelsius.Thereciprocalofthefrequencyofapuretoneistheperiodinseconds

(4)FrequencyandPeriodThenumberofpressurevariationspersecondiscalledthefrequencyofthesound,inunitsofHertz(Hz)20Hz–20kHzaudiblesoundsfsound>20kHzcalledultrasounds(超聲波)fsound<20Hzcalledinfrasounds(次聲波）Dolphinsandbatscanemitultrasonicwaves.(5)WavelengthWavelengthisdefinedasthedistancethepure-tonewavetravelsduringafullperiodwavenumber(k)isdefinedasChapter6FundamentalsofAcousticsforNoiseControl6.1TheWaveEquationFromthisequationweknowthathighfrequencysoundshaveshortwavelengthsandlowfrequencysoundshavelongwavelengths.推導(dǎo)理想流體媒質(zhì)中的聲波方程的四個基本假設(shè):1）媒質(zhì)為理想流體，不存在粘性，無能量損耗；2）媒質(zhì)是均勻連續(xù)的，無聲擾動時媒質(zhì)在宏觀上處于靜止狀態(tài)；3）聲波傳播過程是絕熱過程，壓強僅是密度的函數(shù)，可以不考慮溫度的因素。因此可以用聲壓、質(zhì)點振速和密度這三個參數(shù)來描述聲場；4）媒質(zhì)中傳播的是小振幅壓力波，各聲學參量都是一階微量，遠小于平衡狀態(tài)的參數(shù)。Chapter6FundamentalsofAcousticsforNoiseControl6.1TheWaveEquationAcousticdisturbancescanusuallyberegardedassmall-amplitudeperturbationstoanambientstateThemomentumequation(movementequation)Themassconservationequation(continuityequation)

Forthequiescentmedium,neglectingthesecond-orderandhigher-orderacoustictermsyieldsthelinearacousticequations

ThemassconservationequationThemomentumequationChapter6FundamentalsofAcousticsforNoiseControl6.1TheWaveEquationThestateequation:Theacousticdisturbancesinidealgasesareidealizedasadiabaticprocess.ThestatevariablessatisfytheisentropicityequationThegroupingresultsfromaTaylor-seriesexpansioninandneglectingthesecond-orderandhigher-orderacousticterms,leadstoSubmittingthestateequationofidealgasesintothespeedfunctionofsoundwaveChapter6FundamentalsofAcousticsforNoiseControl6.1TheWaveEquationThemassconservationequationThemomentumequationThestateequationTheWaveEquation

TheLaplacinoperatorforthree-dimensionalproblemsisgivenChapter6FundamentalsofAcousticsforNoiseControl6.1TheWaveEquationThemassconservationequationThemomentumequationThestateequation

The1-DWaveEquation

Chapter6FundamentalsofAcousticsforNoiseControl6.2BasicCharacteristicsofPlaneSoundWaveSolutionsoftheone-dimensionalwaveequationIfthetimedependenceisassumedtobetheharmonicandthesolutionofone-dimensionalwaveequationmaybeexpressedasTheone-dimensionalHelmholtzequationThesolutionofone-dimensionalHelmholtzequationmaybeexpressedasacombinationofsineandcosine,orcomplexexponentialformasChapter6FundamentalsofAcousticsforNoiseControl6.2BasicCharacteristicsofPlaneSoundWaverepresentssuperpositionoftwoprogressivewaveswithamplitudesAandBmovinginoppositedirections

SubstitutingthesolutioninthemomentumequationyieldsSolutionsoftheone-dimensionalwaveequationChapter6FundamentalsofAcousticsforNoiseControl6.2BasicCharacteristicsofPlaneSoundWaveSubstitutingthefirsttermofsoundpressureexpressionintotheaboveexpressionyields

Characteristicsoftheplanewavesoundequation,so.Itmeansthatthefirsttermofsoundpressureexpressionrepresentsthetravelingwaveinthepositivexdirection.Velocityofsoundpropagation,orspeedofsoundTheparticledisplacementatthepositionChapter6FundamentalsofAcousticsforNoiseControl6.2BasicCharacteristicsofPlaneSoundWaveKineticenergyofavolumeV01AcousticenergyandacousticenergydensityPotentialenergyTotalenergyChapter6FundamentalsofAcousticsforNoiseControl6.3AcousticEnergyinSoundFieldTheacousticenergydensityFortheplanetravelingwaveTheaverageacousticenergydensity1AcousticenergyandacousticenergydensityChapter6FundamentalsofAcousticsforNoiseControl6.3AcousticEnergyinSoundFieldTheacousticenergyradiatedbyasoundsourceperunittimeiscalledsoundpower,denotedasWandtheunitisthewatt(W).Soundintensityisdefinedasameasureoftheacousticenergypassingthroughaunitareaperpendiculartothedirectioninwhichthewaveistravelingperunit,denotedasIandtheunitis.2SoundpowerandsoundintensityChapter6FundamentalsofAcousticsforNoiseControl6.3AcousticEnergyinSoundField聲強的定義式Theaveragesoundintensity2SoundpowerandsoundintensityChapter6FundamentalsofAcousticsforNoiseControl6.3AcousticEnergyinSoundFieldTherelationshipbetweensoundintensityandaveragesoundenergydensity3SoundpowerandsoundintensityforplanesoundwaveFortheplanesoundwavetravelinginthepositivexdirectionwhereandaretheeffectivesoundpressureandparticlevelocities,respectively.Chapter6FundamentalsofAcousticsforNoiseControl6.3AcousticEnergyinSoundFieldAnotherreasonisthatthehumanearhearslogarithmically,thatis,itjudgestherelativeloudnessofsoundsaccordingtotheratiooftheirpressure.Theimportantthingtorememberaboutthedecibelisthatitrepresentsarelativemeasurement,orratio.Ahealthyhumanearcandetectpressuresaslowasabout20

Pa,comparedtothenormalatmospherepressure(1.013x105Pa)aroundwhichisvaries,afractionalvariationof2x10-10.Amazingly,theearcantoleratesoundpressuresuptomorethanonemilliontimeshigher.Inordertocompressthelargerangeoftypicalsoundpressuresintoasmaller,moreunderstandablescale,thesoundlevelsaredescribedonalogarithmicscaleinunitscalleddecibels(dB).Chapter6FundamentalsofAcousticsforNoiseControl6.4SoundLevelsSoundPressureLevelwhereisthestandardreferencepressureinair.SoundPowerLevelwhere(W)isthestandardreferencesoundpowerSoundIntensityLevelwhere(W/m2)isthestandardreferencesoundintensityChapter6FundamentalsofAcousticsforNoiseControl6.4SoundLevelsChapter6FundamentalsofAcousticsforNoiseControl6.4SoundLevels關(guān)于聲壓級的一些典型例子：人耳剛剛能聽到的聲音:０至１０分貝；手表聲、落葉的沙沙聲：２０分貝；兩人的輕聲耳語：３０分貝；一般居室里的聲音：４0分貝；公共汽車的響聲、鬧市區(qū)的聲音：80至90分貝；織布車間：不低于100分貝；噴氣式飛機的聲音：約140分貝。一般認為超過60分貝的聲音是噪聲。HomeWorksPage195Questions:7-1、7-2Chapter6FundamentalsofAcousticsforNoiseControl波陣面保持為S不變的波動方程為rPChapter6FundamentalsofAcousticsforNoiseControl6.5RadiationofSoundSource對于球面波，

S=4πr2代入上式后方程化為rPChapter6FundamentalsofAcousticsforNoiseControl6.5RadiationofSoundSourceConsideronlywavesmovingradiallyoutwardfromthesourceorthecasefornowavesreflectedbacktowardtheorigin,wemusthaveB=0Forsphericalsoundfield,thewaveequationisSolutionofthewaveequationofsphericalsoundwaveisIntegratingthemomentumequationleadstotheexpressionofparticlevelocity

ThespecificacousticimpedanceThemagnitudeofthesphericalacousticimpedanceisThephaseanglebetweentheacousticpressureandparticlevelocityisChapter6FundamentalsofAcousticsforNoiseControl6.5RadiationofSoundSourceTheconstantAinp(r,t)andu(r,t)maybedetermined,byassumingthevibrationvelocityatthespheresurfaceisknownasConsider,anddenoting(thesourcestrength)TheaveragesoundintensityThesoundpowerradiatedfromthesoundsourceChapter6FundamentalsofAcousticsforNoiseControl6.5RadiationofSoundSourceThesoundpressuremaybeexpressedasTheeffectivesoundpressureTherelationbetweensoundintensityandsoundpressureChapter6FundamentalsofAcousticsforNoiseControl6.5RadiationofSoundSourceItisthesameasinplanesoundfields.Chapter6FundamentalsofAcousticsforNoiseControl6.5RadiationofSoundSourceForasphericalsoundfield,therelationshipbetweenthesoundintensitylevelandsoundpowerlevelmaybeestablishedasbelow.sofortheairmediumatroomtemperature,whichleadstoThesoundpressurelevellowers6dBifthedistanceisdoubled.

Chapter6FundamentalsofAcousticsforNoiseControl6.5RadiationofSoundSourceBecauseLet’sconsiderthevalueofSIL,ifr=r2=2r1,thenfromtheequationabove,wemaygetDipolesource:TwoclosedsmalloscillatingspheresourceswithsamevibrationamplitudeandoppositephaseSoundpressureradiatedfromthedipolesourcemaybeexpressedas:Chapter6FundamentalsofAcousticsforNoiseControl6.5RadiationofSoundSourcer1rr2lPθIfismuchlessthanr,thenonemaygetChapter6FundamentalsofAcousticsforNoiseControl6.5RadiationofSoundSourceSoConsider,thatmeansSowehaver1rr2lPθSoundpressureradiatedfromthedipolesourceinthefarfieldisloweredasthed