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

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.