Scattering of Acoustic Waves from a Moving Elastic Nonlinearity

Abstract

A Doppler-like phenomenon for acoustic waves is investigated by studying the scattering of a plane acoustic wave from a moving elastic nonlinearity in a nonlinear acoustic medium. By using the Green's-function technique, the first-order waves scattered in both forward and backward directions are calculated in terms of radiations arising from secondary sources induced in the region of the moving elastic nonlinearity. Three typical profiles of the moving elastic nonlinearity (rectangular, sawtooth, and trapezoidal) are considered. A Doppler-frequency shift similar to that in the electromagnetic-wave case is found in the backward-scattered wave but not in the forward-scattered wave. This frequency shift depends on the phase velocity of the acoustic wave in the unperturbed medium and the velocity of the moving elastic nonlinearity but not on the detail profile of the elastic nonlinearity. The intensity of the frequency-shifted scattered wave depends very strongly on the wavenumber of the incident wave, width and detail profile of the elastic nonlinearity, and less strongly on the velocity of the elastic nonlinearity. A possible experimental structure for investigating the Doppler-like phenomenon is suggested. The application of the Doppler-like phenomenon as a tool for investigating dynamical properties of a moving elastic nonlinearity or an elastic shock wave in liquids or solids is also indicated.