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1、機械波 Mechanical WavesMechanical wave is a disturbance that travels through some material or substance called the medium for wave.Transverse wave is the wave that the displacement of the medium are perpendicular or transverse to the direction of travel of the wave along the mediumLongitudinal wave is
2、the wave that the motions of particles is the same as the direction of wave.機械波的種類單位因次分析（Dimensional Analysis）和波速有關的物理量有繩子單位長度的質量m及繩上之張力單位因次唯一可能其中C為一無單位之常數。繩波的速度力學分析Wave Equation Mathematical Description of a Wavesinusoidal wave moving in +x-direction PhaseEnergy in Wave MotionThe instantaneous rate
3、 of doing work at the point x and time t isFor sinusoidal wave with wave function given asMaximum Poweraverage power, sinusoidal wave on a string inverse-square law for intensity Average intensityWave Interference Boundary Conditions and SuperpositionOverlap of two wave pulsesstanding wave on a stri
4、ng, fixed end at x = 0 Normal Modes of a String傅立葉分析(Fourier Analysis)f(t)是週期性函數注意事項：稱為基頻(fundamental frequency)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：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(sawtooth wave)利用電腦繪出(1)n=3 (2)n=7之圖形Sound WavesSound is a longitudinal wave in a mediumAudible range of hu
5、man ear is 20 to 20000HzGauge pressureGauge pressureIn a sinusoidal sound wave the max pressure variations are 3.0*10-2Pa above the atmospheric pressure. Find the max displacement if frequency is 1000Hz. Given speed of sound is 344m/s and bulk modulus is 1.42*105PaThe Anatomy of Human EarA eardrum =
6、 43mm2 A stirrup = 3.2 mm2 V fluid =1500m/sintensity of a sinusoidal sound wave definition of sound intensity level Sound Velocity and Gauge Pressure空氣的bulk modulus 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。He在STP，M0=4.00 kg/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2smcoswt拍音可利用
7、來做樂器的調音。人類可感覺之拍音約7Hz Beats 拍音16.8 The Doppler effectMoving listener and stationary sourceMoving source and moving listener People used Doppler flow meter to measure the blood flow rates. The speed of sound in blood is known to be 1570 m/s and a typical red blood cell has a radius of 5m. Please estim
8、ate what would be the frequency for the flow meter?If the frequency shift measured by the Doppler flow meter is 100Hz (the meter was operated at 107Hz), please find the average velocity of blood flow. 1.5cm/sShack Wave (Sonic Boom)橫波(transverse wave)彈性體所產生之形變為剪應變(shear strain)縱波(longitudinal wave)彈性體所產生之形變為拉伸應變(tensile strain)恢復力為拉伸應力(tensile stress)(a)鋼之密度為7.83103 kg/m3，G=8.31010 Pa，橫波在鋼中傳遞之速率為 (b)鑽石的橫波聲速高達12800 m/s，密度為3.51103 kg/m3，他的shear modulus為=5.751011 Pa
