A basic problem in theoretical solid-state physics is to solve the Schrödinger equation for an electron in the scattering field of some very large number of ions, which is certainly a formidable problem. Fortunately, for a crystal the scattering field is periodic, and one may use Bloch's theorem and obtain a manageable calculation. Unfortunately, real crystals have defects, or one may have an alloy, an amorphous material, or a quasicrystal, for which there is no known “quasi-Bloch theorem;” solving the Schrödinger in these cases is difficult, if not impossible. However, the Schrödinger equation is a wave equation, the same as for sound waves, and it is possible to construct acoustic systems that have scattering fields analogous to those in a solid-state system, and whose governing equations may be mathematically identical to a complicated solid-state model system. For the acoustic system, one may measure eigenvalues and eigenfunctions directly, as well as study inelastic and nonlinear effects. Research has been undertaken for a random field (involving Anderson localization) and for a quasicrystallization system. [Work supported by NSF Grant DMR 9000549 and ONR.]