機(jī)械波的種類

機(jī)械波

MechanicalWavesMechanicalwaveisadisturbancethattravelsthroughsomematerialorsubstancecalledthemediumforwave.TransversewaveisthewavethatthedisplacementofthemediumareperpendicularortransversetothedirectionoftravelofthewavealongthemediumLongitudinalwaveisthewavethatthemotionsofparticlesisthesameasthedirectionofwave.1機(jī)械波的種類2單位因次分析（DimensionalAnalysis）和波速有關(guān)的物理量有繩子單位長(zhǎng)度的質(zhì)量m及繩上之張力τ←單位因次唯一可能 其中C為一無(wú)單位之常數(shù)。繩波的速度3力學(xué)分析45WaveEquation6MathematicalDescriptionofaWavesinusoidalwavemovingin+x-directionPhase7EnergyinWaveMotionTheinstantaneousrateofdoingworkatthepointxandtime

tisForsinusoidalwavewithwavefunctiongivenas8MaximumPoweraveragepower,sinusoidalwaveonastring

9inverse-squarelawforintensityAverageintensity10WaveInterferenceBoundaryConditionsandSuperposition11Overlap

oftwowavepulses12standingwaveonastring,fixedendatx=013NormalModesofaString14傅立葉分析(FourierAnalysis)f(t)是週期性函數(shù)注意事項(xiàng)：稱為基頻(fundamentalfrequency)

T為f(t)之週期。稱為基頻項(xiàng)或基頻分量，

其他項(xiàng)稱為諧波(harmonics)n次諧波項(xiàng)：15若f(t)為t之奇函數(shù)若f(t)為t之偶函數(shù)作業(yè):以下列函數(shù)近似鋸齒波(sawtoothwave)利用電腦繪出(1)n=3(2)n=7之圖形16SoundWavesSoundisalongitudinalwaveinamediumAudiblerangeofhumanearis20to20000Hz17Gaugepressure18Gaugepressure1920Inasinusoidalsoundwavethemaxpressurevariationsare3.0*10-2Paabovetheatmosphericpressure.Findthemaxdisplacementiffrequencyis1000Hz.Givenspeedofsoundis344m/sandbulkmodulusis1.42*105Pa21TheAnatomyofHumanEarAeardrum=43mm2

Astirrup=3.2mm2Vfluid=1500m/s22intensityofasinusoidalsoundwavedefinitionofsoundintensitylevelSoundVelocityandGaugePressure2324空氣的bulkmodulus若為等溫過(guò)程，pV=nRT，用此結(jié)果代入所得之聲速較實(shí)際值小。在聲音的傳遞，速度很快，空氣和周圍來(lái)不及做熱交換，要考慮絕熱過(guò)程，即。2526He在STP，M0=4.00kg/kmole,g=5/3＊＊吸一口He氣體，講話音調(diào)會(huì)變高，為什麼？求在0℃的聲速27BasicPrincipleofDopplerFlowmeter2816.8TheDopplereffectMovinglistenerandstationarysource29Movingsourceandmovinglistener302smcosw't拍音可利用來(lái)做樂(lè)器的調(diào)音。人類可感覺(jué)之拍音約<7HzBeats拍音31PeopleusedDopplerflowmetertomeasurethebloodflowrates.Thespeedofsoundinbloodisknowntobe1570m/sandatypicalredbloodcellhasaradiusof5μm.Pleaseestimatewhatwouldbethefrequencyfortheflowmeter?IfthefrequencyshiftmeasuredbytheDopplerflowmeteris100Hz(themeterwasoperatedat107Hz),pleasefindtheaveragevelocityofbloodflow.1.5cm/s32ShackWave(SonicBoom)33橫波(transversewave)彈性體所產(chǎn)生之形變?yōu)榧魬?yīng)變(shearstrain)34縱波(longitudinalwave)彈性體所產(chǎn)生之形變?yōu)槔鞈?yīng)變(tensilestrain)恢復(fù)力為拉伸應(yīng)力(tensilestress)