Experimental study of the Doppler shift generated by a vibrating scatterer.

We report an experimental study of the backscattering of a sound wave of frequency f by a surface vibrating harmonically at frequency F (F << f) and amplitude A in the regime where the Doppler effect overcomes bulk nonlinear effects. When the duration to of the analyzed time series of the scattered wave is small compared to the vibration period, the power spectrum of the backscattered wave is proportional to the probability density function of the scatterer velocity, which presents two peaks shifted from f by roughly 2fAomega/c (omega = 2piF). On the contrary, when t0 >> F(-1), sidebands at frequencies f +/- nF (n integer) appear in the power spectrum, which are due to the phase modulation of the backscattered wave induced by its reflection on a moving boundary. We use the backscattered power spectrum to validate the phase modulation theory of the Doppler effect in the latter case for 2kA << 1 and 2kA approximately > 1 (k = 2pif/c, where c is the wave velocity) and we test the validity of an acoustic nonintrusive estimator of A as a function of power spectrum bandwidth and of A itself.