1、第四章-聲波在平面界面的反射、折射和透射4.1聲波垂直入射到平面界面一垛普通的磚墻既可以隔掉部分聲音，但又不能把全部的聲音都隔掉；一垛木板墻將有更多的聲音被透射進去。聲波的這種反射、透射現(xiàn)象也是聲傳播的一個重要特征。 聲學(xué)邊界條件質(zhì)量元M的運動方程2靜壓強在分界面處連續(xù) 1、分界面處聲壓連續(xù)2、分界面處法向速度連續(xù)平面聲波垂直入射時的反射和透射3媒質(zhì)I中入射波和反射波媒質(zhì)II中只有透射波媒質(zhì)I和II中的速度場4利用邊界條件與媒質(zhì)的特性阻抗c有關(guān)！反射和透射系數(shù)5討論1、沒有反射！2、3、硬邊界，聲壓同位相，速度反相！絕對硬邊界，聲壓全反射！邊界上壓強的靜態(tài)傳遞，而不是疏密交替的聲壓！聲波從空氣

2、入射到空氣水的分界面上！64、5、軟邊界，聲壓反相，速度同相！絕對軟邊界，聲壓全反射！邊界上速度的波腹，聲壓的波節(jié)。能量反射和透射系數(shù)7Reflection from a HARD boundary8Reflection from a SOFT boundary9From high acoustic impedance to low acoustic impedance Reflection from an impedance discontinuity10From low acoustic impedance to high acoustic impedance114.2 聲波斜入射到平面界

3、面x-y平面入射折射波12在媒質(zhì)I中在媒質(zhì)II中:只有透射波13邊界條件注意：法向在x-方向所有y恒成立條件Snell定律14折射和透射系數(shù)15Notice that as the wavefronts cross the boundary the wavelength changes, but the frequency remains constant. 16法向聲阻抗率法向速度！全透射17全透射條件全反射18全反射條件 Water Air如果注意：角度變化90意味著不存在真正的透射波！全反射臨界角！19垂直透射聲波入射到多孔材料情況！能量關(guān)系聲強折射和透射系數(shù)20能量不守恒？聲強是單位面

4、積通過的聲能量流！斜入射使聲束變化了！平均聲能量流的透射系數(shù) 能量守恒！ 21This 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 u

5、pwards. 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. 22A spherical wave

6、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 direc

7、tion as it propagates. 23the 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. 24the propagation of a sp

8、herical 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. 254.3 聲波垂直入射到多層平面界面媒質(zhì)I: 入射波+反射波連續(xù)波I和III相同26媒質(zhì)II: 透射波+反射波媒質(zhì)III: 透射波為了方便2

9、7邊界條件x=0處界面x=D處界面28聲壓透射系數(shù)聲強透射系數(shù)聲強反射系數(shù)29分析1、頻率；2、厚度；3、特性阻抗低頻注意：是媒質(zhì)II中的波長中間層好象不存在！聲波完全透過！30半波長的整數(shù)倍注意：是媒質(zhì)II中的波長中間層好象不存在！聲波完全透過！1/4波長的奇數(shù)倍注意：是媒質(zhì)II中的波長如果：中間層完全隔離聲波！31十分重要的結(jié)論：低頻聲波的隔離是十分困難的！水-鋁水-有機玻璃低頻全透射32脈沖波情況連續(xù)波：在中間層形成駐波，透射系數(shù)為脈沖波：如果中間層足夠?qū)?，或脈沖寬度足夠窄，中間層不形成駐波，那么相當(dāng)于兩個無限大平面的透射1233匹配技術(shù)I和III不同媒質(zhì)I和媒質(zhì)III相同隔聲作用！媒質(zhì)

10、I和媒質(zhì)III不同阻抗匹配作用！如果選擇中間層厚度和特性阻抗：中間層起匹配作用匹配技術(shù)！34斜入射情況垂直入射推廣：(1) 法向聲阻抗率代替特性阻抗率; (2)波矢k2是x方向的分量。35斜入射2t中間層的折射角！IIIIi2t364.4 隔聲的基本規(guī)律中間層一般固體固體中的聲波彈性波！垂直入射或者中間層比較薄只有縱波流體模型！單層墻的隔聲本領(lǐng)一般建筑材料37低頻條件M2=2D單位面積墻的質(zhì)量 重墻條件隔聲的質(zhì)量作用定律！38斜入射情況IIIIi2t低頻條件 重墻條件39雙層墻的隔聲本領(lǐng)單層墻的隔聲：墻厚一倍，隔聲量僅僅增加6dB，代價太大了！雙層墻的隔聲：4面，8個方程，復(fù)雜！長波近似：墻厚波長可近似看做整體振動。三個區(qū)域的聲壓1c11c11c1IIIIIIabI區(qū)域40II區(qū)域III區(qū)域墻a的運動方程41墻b的運動方程42墻a處速度