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大振幅平面声波的反射和折射(Ⅱ)——二维情况

THE REFLECTION AND REFRACTION OF A LARGE AMPLITUDE PLANE SOUND WAVE (Ⅱ) TWO DIMENSIONAL CASE

  • 摘要: 在Lagrange坐标系中,根据流体力学的基本方程式,利用逐级近似法推导了计及二级近似的二维空间内平面波传播的波动方程式。以这组方程式为出发点分析了二层液态介质模型下,大振幅平面声波在平面分界面上的反射和折射。二级近似下的反射系数和透射系数不仅与介质的参数(包括非线性参数)有关,而且依赖于声源的位置。在斜投射时,一般而言,遵循线性声学反射和折射定律的二级近似反射波和折射波的波前上,波的幅度不再保持恒等。因之,除遵循线性声学反射和折射定律的二级近似反射波和折射波外,在其他方向上也有二级近似反射波和折射波。这个现象表明解释Muir等人的实验结果必须计及非线性效应。

     

    Abstract: Using the successive approximation method, a wave equation, in which the second order of approximation was taken into account, ras been derived from the basic equations of hydrodynamics in Lagrangian coordinates. The reflection and refraction of an obliquely incident large amplitude plane sound wave on the plane interface of two non-mixing liquids were studied. It is interesting to point out that the reflection and refraction coefficients of second order approximation not only depend upon parameters of media, but also relate to the position of sound source. It is found that the amplitude of second order reflected wave and refracted wave doer not keep constant at the wave front, as these waves obey laws of reflection and refraction in linear acoustics. Therefore there are reflected wave and refracted wave which propagate in the direction other than, that of waves travelling along the directions according to laws of reflection and refraction in linear acoustics. The nonlinear effects have to be taken into account for understanding the physical basis of results reported by Muir et al.

     

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