We study the coupled macroscopic and lattice wave propagation in anisotropic crystals seen as continua with affine microstructure (or micromorphic). In the general case, we obtain qualitative information on the frequencies and the dispersion relations. These results are then specialized to crystals of the tetragonal point group for various propagation directions: exact representation for the acoustic and optic frequencies and for the coupled vibrations modes are obtained for propagation directions along the tetragonal c-axis.
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