Abstract:
Using the method of successive approximation, the reflection and refraction (transmission) of a large amplitude plane sound wave are treated, as the sound wave impinges normally on the plane interface of two acoustically different media. It is shown that, when second order of approximation is taken into account, there are second order reflected waves and second order transmitted waves, whose amplitudes are proportional to the square of the first order reflection coefficient and first order transmission coefficient respectively, and waves, defined by second order reflection coefficient and second order transmission coefficient respectively. The phase shifts of the later to the second order incident wave are found and are determined by acoustic parameters and nonlinear parameters of these two different media. It is interesting to point out that amplitudes of the in-phase components are linearly dependent upon first order reflection coefficient and first order transmission coefficient respectively and the mutipliers are independent upon acoustic parameters of the second medium. An improvement on transfer efficiency of parametric array, obtained by Ryder et al., can be explained theoretically.