ABSTRACT
Plane waves are the best-known solutions describing linear wave processes. They have already been known to D'Alembert and Euler. In considering plane waves, important notions of the theory of wave phenomena naturally appear; in particular, the notions of phase and group velocities, slowness, wavenumber, etc. Generalization of these notions marks out the solutions of the elastodynamics equations that are called waves. A plane wave is the simplest solution of the elastodynamics equations in the absence of external forces. The velocity of a wave can be defined in different ways, and its values and directions will, generally speaking, be different. The theory of waves in homogeneous anisotropic media is important first of all for investigating elastic properties of crystals but is also applicable to geophysics and other fields of science and technology. This chapter shows that the velocity of propagation of perturbation is bounded above by the maximal velocity of plane waves, which is true in the case of arbitrary anisotropy.
