Acoustic axes in orthorhombic media

The directions in an anisotropic medium along which there occur multiple points on the slowness (or velocity) surface for elastic waves are termed acoustic axes. The degeneracies, in general, may be characterized as tangential or conical and may be essential, dictated by symmetry,' or inessential, dependent on relative magnitudes of stiffnesses within a given symmetry. The existence of such axes for all possible elastodynamic classifications of orthorhombic media has been investigated. In general, the essential degeneracies are of conical type and occur in all but two of the 120 classifications. Observed stiffnesses show that all known media exhibit at least two essential acoustic axes, a few exhibit four. The maximum number of acoustic axes, hitherto reported as 14, is shown to be 16 and the observed stiffnesses of iodine and boron fibre are used to investigate this possibility in real materials. The geometry of a typical conical degeneracy is discussed and equations to the cone of tangency and corresponding ray cone are explicitly derived.