声波在平面界面的反射、折射和透射.ppt

1,第4章 声波在平面界面的反射、折射和透射,4.1 声波垂直入射到平面界面 4.2 声波斜入射到平面界面 4.3 声波垂直入射到多层平面界面 4.4 隔声的基本规律,2,4.1声波垂直入射到平面界面,一垛普通的砖墙既可以隔掉部分声音，但又不能把全部的声音都隔掉；一垛木板墙将有更多的声音被透射进去。声波的这种反射、透射现象也是声传播的一个重要特征。,声学边界条件,质量元M的运动方程,3,静压强在分界面处连续,1、分界面处声压连续,2、分界面处法向速度连续,平面声波垂直入射时的反射和透射,4,媒质I中入射波和反射波,媒质II中只有透射波,媒质I和II中的速度场,5,利用边界条件,与媒质的特性阻抗c有关！,反射和透射系数,6,讨论,1、,没有反射！,2、,3、,硬边界，声压同位相，速度反相！,绝对硬边界，声压全反射！,边界上压强的静态传递，而不是疏密交替的声压！,声波从空气入射到空气水的分界面上！,7,4、,5、,软边界，声压反相，速度同相！,绝对软边界，声压全反射！,边界上速度的波腹，声压的波节。,能量反射和透射系数,8,Reflection from a HARD boundary,9,Reflection from a SOFT boundary,10,From high acoustic impedance to low acoustic impedance,Reflection from an impedance discontinuity,11,From low acoustic impedance to high acoustic impedance,12,4.2 声波斜入射到平面界面,x-y平面入射,折射波,13,在媒质I中,在媒质II中:只有透射波,14,边界条件,注意：法向在x-方向,所有y恒成立条件,Snell定律,15,折射和透射系数,16,Notice that as the wavefronts cross the boundary the wavelength changes, but the frequency remains constant.,17,法向声阻抗率法向速度！,全透射,18,全透射条件,全反射,19,全反射条件,Water,Air,如果,注意：角度变化90,意味着不存在真正的透射波！,全反射临界角！,20,垂直透射,声波入射到多孔材料情况！,能量关系声强折射和透射系数,21,能量不守恒？,声强是单位面积通过的声能量流！斜入射使声束变化了！,平均声能量流的透射系数, 能量守恒！,22,This means that for a sound wave traveling close to the ground, the part of the wave closest to the ground is traveling the fastest, and the part of the wave farthest above the ground is traveling the slowest. As a result, the wave changes direction and bends upwards. This can create a “shadow zone“ region into which the sound wave cannot penetrate. A person standing in the shadow zone will not hear the sound even though he/she might be able to see the source. The sound waves are being refracted upwards and will never reach the observer.,23,A spherical wave pulse propagates in a medium where the wave speed is constant in all directions. The wave expands outwards as an ever expanding circle, with the wave traveling at the same speed in all directions. Since the wave speed is the same everywhere, there is no refraction, and the wave does not change direction as it propagates.,24,the propagation of a spherical wave pulse in a medium where the wave speed in the x-direction is constant, but where the speed in the vertical y-direction decreases with height (c = 1 - 0.05y) As a result the wave changes direction and bends upwards.,25,the propagation of a spherical wave pulse in a medium where the wave speed in the x-direction is constant, but where the speed in the vertical y-direction increases with height (c = 1 + 0.05y) As a result the wave changes direction and bends downwards.,26,4.3 声波垂直入射到多层平面界面,媒质I: 入射波+反射波,连续波I和III相同,27,媒质II: 透射波+反射波,媒质III: 透射波,为了方便,28,边界条件,x=0处界面,x=D处界面,29,声压透射系数,声强透射系数,声强反射系数,30,分析,1、频率；2、厚度；3、特性阻抗,低频注意：是媒质II中的波长,中间层好象不存在！声波完全透过！,31,半波长的整数倍注意：是媒质II中的波长,中间层好象不存在！声波完全透过！,1/4波长的奇数倍注意：是媒质II中的波长,如果：,中间层完全隔离声波！,32,十分重要的结论：低频声波的隔离是十分困难的！,水-铝,水-有机玻璃,低频全透射,33,脉冲波情况,连续波：在中间层形成驻波，透射系数为,脉冲波：如果中间层足够宽，或脉冲宽度足够窄，中间层不形成驻波，那么相当于两个无限大平面的透射,34,匹配技术I和III不同,媒质I和媒质III相同隔声作用！,媒质I和媒质III不同阻抗匹配作用！,如果选择中间层厚度和特性阻抗：,中间层起匹配作用匹配技术！,35,斜入射情况,垂直入射,推广：(1) 法向声阻抗率代替特性阻抗率; (2)波矢k2是x方向的分量。,36,斜入射,2t中间层的折射角！,37,4.4 隔声的基本规律,中间层一般固体固体中的声波弹性波！垂直入射或者中间层比较薄只有纵波流体模型！,单层墙的隔声本领,一般建筑材料,38,低频条件,M2=2D单位面积墙的质量,重墙条件,隔声的质量作用定律！,39,斜入射情况,低频条件,重墙条件,40,双层墙的隔声本领,单层墙的隔声：墙厚一倍，隔声量仅仅增加6dB，代价太大了！,双层墙的隔声：4面，8个方程，复杂！,长波近似：墙厚波长可近似看做整体振动。,三个区域的声压,I区域,41,II区域,III区域,墙a的运动方程,42,墙b的运动方程,43,墙a处速度连续性方程