Specific Propagation Directions of Acoustic Waves in Media of Various Acoustic Symmetries

We consider propagation of acoustic waves in media of lowest elastic symmetries. We showed that the number of acoustical axes for media with triclinic symmetry cannot be larger than 132. We proposed analytical method of determining components of longitudinal normals. By extending the Khatkevich approach and using the Bezout theorem we proved that the number of longitudinal normals for mechanically stable triclinic media can be larger than 16 and not, as claimed by some authors, 13. We also proved that the number of longitudinal normals for monoclinic media cannot be larger than 13, whereas, according to Khatkevich, this number cannot be larger than 17. Using our method we numerically established directions of longitudinal normals for several monoclinic elastic media. For media of higher symmetries (rhombic, trigonal, tetragonal, hexagonal and cubic) our method of determining components of longitudinal normals yields well-known results obtained by Borgnis and Khatkevich.