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In an anisotropic medium there are only certain directions along which elastic waves can propagate in pure longitudinal and transverse modes. For the determination of third-order elastic coefficients from sound speed measurements in stressed crystals it is desirable to know these modes. Using a method due to Borgnis the pure mode directions are determined for all crystal point groups belonging to the orthorhombic, tetragonal, cubic, rhombohedral, and hexagonal systems. The eigenvalue problem is solved for each of these directions, and the polarization vectors and the wave speeds are tabulated.

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Third-order elastic coefficients can be derived from sound speed measurements in statically stressed crystals. The necessary relations between experimental data and elastic coefficients are here presented for orthorhombic, tetragonal, cubic, rhombohedral, and hexagonal crystal classes. For each symmetry a sufficient number of wave modes and stress systems is selected to determine all third-order coefficients and to allow experimental cross checks. All the modes considered are pure longitudinal or transverse. They are selected so as to minimize the number of specimen orientations required, and following experimental procedures for uniaxial static stress, only wave modes propagating at right angles to the stress direction are considered.