A NOTE ON PURE-LONGITUDINAL AND PURE-SHEAR WAVES IN CUBIC-CRYSTALS

The acoustic tensor of a general anisotropic material is derived using the spectral representation of the elasticity tensor, an approach that makes the contribution from each projection operator more visible than the customary approach of using matrix components of the elasticity tensor. As an application of the approach, the acoustic tensor for a cubic crystal is explicitly formulated, and the directions for which purely longitudinal or shear waves can propagate are found rigorously. The result proves that the directions stated by Thurston are indeed the only ones along which pure waves can exist. © 1995, Acoustical Society of America. All rights reserved.