同济大学：《大学物理》课程教学资源（电子教案，英文版）第九章 机械波（中）

Mechanical waves II)

Mechanical waves (II)

agenda today 1.Energy of harmonic waves 2.Interference of mechanical waves 3.Standing waves

Agenda today 1. Energy of harmonic waves 2. Interference of mechanical waves 3. Standing waves

Energy of harmonic waves Energy travels when waves travel Average energy of medium When transverse waves travel in some elastic medium:

Energy of harmonic waves Energy travels when waves travel When transverse waves travel in some elastic medium： Average energy of medium

Choose a segment infinite small dy Sdx dm pSdx Its kinetic energy: dw=dmv "V= y=-Aosin o(1- dw=(pdv)Ao'sin'o(t-

Choose a segment infinite small dV  Sdx dm  Sdx Its kinetic energy： 2 2 1 dW dmv k  sin ( ) u x A t t y v          ( ) sin ( ) 2 1 2 2 2 u x dW dV A t  k     

Its potential energy: dw,-Gdv dx ->G=u"p dW, pu .d-pdsin U

Its potential energy： 2 2 1        dx dy dWp GdV  2 G  u 2 2 2 1        dx dy dW u p  sin ( ) u x t u A dx dy      sin ( ) 2 1 2 2 2 u x dW dVA t  p     

dw.dw, Total energy: dwdW +dW,pdVAo'sin2 w(t-X) U the kinetic energy and potential energy of the infinitely small mass in the medium is the same. dw W= dy =PA0'sin2@(t-*) 7pfw'sm'og三d

k p dW  dW Total energy： sin ( ) 2 2 2 u x dW dW dW dVA t  k  p      the kinetic energy and potential energy of the infinitely small mass in the medium is the same. sin ( ) 2 2 2 u x A t dV dW w       dt u x A t T w T sin ( ) 1 2 2 2 0      

Average energy density 20 Energy flux:the energy pass certain cross section of medium in unit time

Average energy density： 2 2 2 1 w   A  Energy flux：the energy pass certain cross section of medium in unit time. u S u

Average energy flux: P=WuS Energy flux density(Intensity)(波的强度)： The average energy pass through a certain unit area along the direction that waves travel =wu= puA"@

Average energy flux： P  wuS Energy flux density(Intensity)（波的强度）： The average energy pass through a certain unit area along the direction that waves travel 2 2 2 1 I  wu   uA 

Interference of harmonic waves Interference(干涉) the various pattern caused by the superposition of harmonic waves. Coherence(相干 性)：the sources S are coherence when they have same frequency and fixed phase difference

Interference of harmonic waves Interference（干涉） : the various pattern caused by the superposition of harmonic waves. Coherence （相干 性）: the sources are coherence when they have same frequency and fixed phase difference S1 S2

同一直线上同频率振动的合成 说明：绿色相位为0，振幅是25 红色为合振动 0 π 12.5 蓝色相位 蓝色振幅 ■C■么△ Superposition of oscillations with same frequency

Superposition of oscillations with same frequency