Bounds and approximations for elastic wave speeds in cubic crystals

Unlike an isotropic elastic medium, the wave speeds in an anisotropic medium depend on the direction of wave propagation. In this paper, bounds are developed on the speeds of waves propagating along an arbitrary direction in a cubic crystal through an additive split of the acoustic tensor into two parts, the eigenproperties of which are trivial to determine. The bounds are obtained by applying the minimax property of eigenvalues. Linear estimates of the wave speeds are obtained from a first-order expansion of the eigenvalues of the acoustic tensor, with respect to an anisotropy index, about the value of that index for which anisotropy vanishes.