Acoustic time reversal in granular media

Abstract

In a non-dissipative medium, the wave equation is symmetric in time. Therefore, for every wave diverging from a pulsed source, there exists a wave that retraces all its original paths in a reverse order and converges at the original source. In the early nineties, M. Fink proposed a method for generating such a time-reversed wave. This method was first tested with ultrasound and then successfully extended to other types of waves such as microwaves, water waves, and even in optics. Several studies have shown that time reversal wave focusing is very robust to disorder. Here, we investigate time reversal (TR) of elastic waves propagating in fragile granular media consisting of glass beads under static compression. Pulsed elastic waves transmitted from a compression or a shear wave source are measured, time reversed, and back-propagated. The ability of the time-reversed wave to focus at the initial source is checked as a function of the source amplitude. We find that TR of the ballistic coherent wave is very robust to perturbations but provides poor resolution. By contrast, the short-wavelength scattered waves offer a finer TR focusing but are sensitive to rearrangements induced by the forward propagation wave itself: at large source amplitudes, time reversal focusing is broken, due to sound-induced rearrangements but without visible grain motion. Experimental results are confronted with predictions from a numerical model in which the propagation medium is modelled by a percolating network of masses interacting via linear springs.