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第6章噪聲控制的聲學(xué)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(diǎn)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(gè)基本假設(shè):1)媒質(zhì)為理想流體,不存在粘性,無(wú)能量損耗;2)媒質(zhì)是均勻連續(xù)的,無(wú)聲擾動(dòng)時(shí)媒質(zhì)在宏觀上處于靜止?fàn)顟B(tài);3)聲波傳播過程是絕熱過程,壓強(qiáng)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(diǎn)振速和密度這三個(gè)參數(shù)來描述聲場(chǎng);4)媒質(zhì)中傳播的是小振幅壓力波,各聲學(xué)參量都是一階微量,遠(yuǎn)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(qiáng)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(jí)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(yǔ):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(jī)的聲音:約140分貝。一般認(rèn)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(dòng)方程為rPChapter6FundamentalsofAcousticsforNoiseControl6.5RadiationofSoundSource對(duì)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
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