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.

Presentation on theme: "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."— Presentation transcript:

1 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.

2 機械波的種類

3 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。

4 力學分析

5

6 Wave Equation

7 sinusoidal wave moving in +x-direction
Mathematical Description of a Wave sinusoidal wave moving in +x-direction Phase

8 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

9 sinusoidal wave on a string
Maximum Power average power, sinusoidal wave on a string

10 inverse-square law for intensity
Average intensity inverse-square law for intensity

11 Wave Interference Boundary Conditions and Superposition

12 Overlap of two wave pulses

13 standing wave on a string, fixed end at x = 0

14 Normal Modes of a String

15 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：

16 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

17 Sound Waves Sound is a longitudinal wave in a medium
Audible range of human ear is 20 to 20000Hz

18 Gauge pressure

19 Gauge pressure

20

21 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

22 The Anatomy of Human Ear
A eardrum = 43mm2 A stirrup = 3.2 mm2 V fluid =1500m/s

23 Sound Velocity and Gauge Pressure
intensity of a sinusoidal sound wave definition of sound intensity level

24

25 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 。

26

27 He在STP，M0=4.00 kg/kmole, g=5/3
求在0℃的聲速

28 Basic Principle of Doppler Flowmeter

29 16.8 The Doppler effect Moving listener and stationary source

30 Moving source and moving listener

31 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

32 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

33 Shack Wave (Sonic Boom)

34 橫波(transverse wave)彈性體所產生之形變為剪應變(shear strain)

35 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)

36 (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