機械波 Mechanical Waves Mechanical 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 medium Longitudinal wave is 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τ 繩波的速度 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τ ←單位因次 唯一可能 其中C為一無單位之常數。
力學分析
Wave Equation
sinusoidal wave moving in +x-direction Mathematical Description of a Wave sinusoidal wave moving in +x-direction Phase
Energy in Wave Motion The instantaneous rate of doing work at the point x and time t is For sinusoidal wave with wave function given as
sinusoidal wave on a string Maximum Power average power, sinusoidal wave on a string
inverse-square law for intensity Average intensity inverse-square law for intensity
Wave Interference Boundary Conditions and Superposition
Overlap of two wave pulses
standing wave on a string, 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 稱為基頻(fundamental frequency) T為f(t)之週期。 注意事項： 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 Waves Sound is a longitudinal wave in a medium Audible range of human ear is 20 to 20000Hz
Gauge pressure
Gauge pressure
In a sinusoidal sound wave the max pressure variations are 3 In 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*105Pa
The Anatomy of Human Ear A eardrum = 43mm2 A stirrup = 3.2 mm2 V fluid =1500m/s
Sound Velocity and Gauge Pressure intensity of a sinusoidal sound wave definition of sound intensity level
http://www.sfu.ca/sca/Manuals/ZAAPf/e/equal_loud_cont.html
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 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 求在0℃的聲速
Basic Principle of Doppler Flowmeter
16.8 The Doppler effect Moving listener and stationary source
Moving source and moving listener
Beats 拍音 2smcosw't 拍音可利用來做樂器的調音。人類可感覺之拍音約<7Hz
People used Doppler flow meter to measure the blood flow rates 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 5μm. Please estimate 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/s
Shack Wave (Sonic Boom) http://en.wikipedia.org/wiki/Sound_barrier
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7.83×103 kg/m3，G=8.3×1010 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3.51×103 kg/m3，他的shear modulus為 =5.75×1011 Pa