Acoustic and quantum chaos

We study wave mechanics of a system very different from quantum systems, namely ultrasonic resonances of solid objects. We measure the frequency spectra - the eigenvalues - and the standing wave patterns - the eigenfunctions. We are mostly looking at freely vibrating plates. The plates can have regular or chaotic shapes, where regular and chaotic are defined in terms of classical billiards. By going to the acoustic system are be testing the predictions of RMT on systems governed by a much more complex wave equation than the Schrödinger equation. In plates the acoustic waves can be either flexural, in-plane compressional or in-plane shear. These will be mixed through mode conversion at the boundaries and other perturbations so there will in general be complex mixtures in the standing waves. We show different experimental techniques for separating the different modes. We measure transitions from regularity to chaos and show the effects of specific symmetry breaking, some of these unique to the acoustic system.