Nonlinear reflection and transmission of plane acoustic waves

Abstract

In the present, paper the classical problem of reflection and transmission of a plane acoustic wave is analyzed and solved for nonlinear propagation. Two adjacent media with a plane boundary between them are assumed. The parameters characterizing the properties of the media can be changed stepwise on the boundary. The wave incident on the boundary surface is plane. It was assumed that the disturbance in the first medium is a superposition of the incident and reflected waves, and in the second medium there is only the transmitted wave. On the base of nonlinear acoustic equations, assuming continuity of the velocity and pressure fields, the reflection and transmission operators of velocities and pressures were determined. The operators are nonlinear in relation to the incident wave field. It was found that near the boundary there occurs "a reflecting-transmitting" layer which is decisive for the description of the nonlinear phenomenon of the reflection and transmission. There arises a nonlinear feedback between the reflecting and incident waves. This is the fundamental difference between the nonlinear and the linear reflection. Equations of the incident reflected and transmitted waves are given. In the case of classical viscous media, they are the Burger's equations in asymptotic areas. The operators and the experimental significance of the results obtained were additionally discussed. An example of the effective application of the analysis performed is given in Sec. 6. Key words: reflection, transmission, nonlinearity.