机械波的种类

機械波

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

tisForsinusoidalwavewithwavefunctiongivenas8MaximumPoweraveragepower,sinusoidalwaveonastring

9inverse-squarelawforintensityAverageintensity10WaveInterferenceBoundaryConditionsandSuperposition11Overlap

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

T為f(t)之週期。稱為基頻項或基頻分量，

其他項稱為諧波(harmonics)n次諧波項：15若f(t)為t之奇函數若f(t)為t之偶函數作業:以下列函數近似鋸齒波(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若為等溫過程，pV=nRT，用此結果代入所得之聲速較實際值小。在聲音的傳遞，速度很快，空氣和周圍來不及做熱交換，要考慮絕熱過程，即。2526He在STP，M0=4.00kg/kmole,g=5/3＊＊吸一口He氣體，講話音調會變高，為什麼？求在0℃的聲速27BasicPrincipleofDopplerFlowmeter2816.8TheDopplereffectMovinglistenerandstationarysource29Movingsourceandmovinglistener302smcosw't拍音可利用來做樂器的調音。人類可感覺之拍音約<7HzBeats拍音31PeopleusedDopplerflowmetertomeasurethebloodflowrates.Thespeedofsoundinbloodisknowntobe1570m/sandatypicalredbloodcellhasaradiusof5μm.Pleaseestimatewhatwouldbethefrequencyfortheflowmeter?IfthefrequencyshiftmeasuredbytheDopplerflowmeteris100Hz(themeterwasoperatedat107Hz),pleasefindtheaveragevelocityofbloodflow.1.5cm/s32ShackWave(SonicBoom)33橫波(transversewave)彈性體所產生之形變為剪應變(shearstrain)34縱波(longitudinalwave)彈性體所產生之形變為拉伸應變(tensilestrain)恢復力為拉伸應力(tensilestress)