Nonlinear reflection and transmission of plane acoustic waves

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.