Breaking of time reversal invariance in nonlinear acoustics

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Abstract
Time-reversal invariance of nonlinear acoustic wave propagation is experimentally investigated. Reversibility is studied for propagation shorter or longer than shock formation distance. In the first case, time-reversal invariance holds and a sinusoid distorted by nonlinearities during forward propagation progressively recovers its initial shape after the time-reversal operation. In the second case, reversibility is broken locally at the shock front as a time-reversal operation transforms a stable compression shock into an unstable expansion shock. Achieving experimentally the time-reversal process with a time-reversal mirror made of reversible piezoelectric transducers for very broadband signals, would require transducers with huge bandwidths. To date, such transducers remain unavailable. In order to overcome this technical limitation, we restricted ourselves in this study to one-dimensional (1D) propagation, for which an experimental ersatz of a time-reversal mirror can be used. Indeed, in a 1D case, the time-reversal operation applied on a plane wave can be mimicked for an antisymmetric wave form by a reflection of the plane wave onto a pressure-release interface.

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