Interaction of counterpropagating acoustic waves in media with nonlinear dissipation and in hysteretic media

Abstract

The interaction of sound waves travelling in the opposite directions in media with quadratic nonlinearity is analyzed theoretically. It is well-known that quadratic elastic nonlinearity does not provide an effective interaction of counterpropagating acoustic waves. One of the research results presented here is rather expected. It consists of the prediction that in media with quadratic nonlinear dissipation a wave travelling in one direction induces additional attenuation of a wave travelling in the opposite direction. A more interesting result is the prediction that in media with hysteretic quadratic nonlinearity a strong sound wave travelling in one direction induces amplification of a weak sound wave travelling in the opposite direction. The threshold of the stimulated backscattering of acoustic waves in the hysteretic media is evaluated. Possible applications include thermoacoustics and acoustic diagnostics of micro-inhomogeneous materials.