ABSTRACT
For bulk waves in isotropic media, there is one longitudinal mode and two transverse modes. It turns out that for crystalline media, the corresponding general treatment that one can make is that for a given direction of propagation, three independent waves may be propagated, each at a particular phase velocity and whose displacements are mutually orthogonal. The elastic constants for different crystal lattices are determined by the corresponding symmetry properties of those systems. The crystal structure does more than impose severe restrictions on the allowed directions for the propagation of pure modes. The physics of the piezoelectric effect can be understood by referring to the case of quartz. The piezoelectric crystal is placed between two metallic plates, which can support a stress and also serve as electrodes.
