Wave Interactions with Moving Boundaries

Abstract

The general theory of the double Doppler effect is reviewed for both vacuum and material media. Frequency and amplitude changes in the reflected and transmitted waves at a partially reflecting moving interface are calculated for cases in which the medium behind the interface: (a) moves at a different velocity than the interface; (b) moves at the interface velocity; (c) is stationary. The advantages of case (c) for practical frequency conversion are discussed. Multiple moving interfaces in a stationary medium are also considered. On the basis of this theory, Doppler shifts at moving, tapered transition regions are analyzed as a series of discrete, closely spaced steps. This shows that the frequency conversion of the transmitted wave is independent of the slope of the taper. By use of a transmission line model, a simple physical explanation is given for the double Doppler effect in a moving taper.