  Acoustic axes are spatial directions in media (often crystals) where at least
two of the three acoustic waves have the same phase velocity. Identification of
such directions for materials with specific elasticity parameters is both
theoretically fascinating and practical in acoustic applications. In this
paper, we introduce the notion of the reduced acoustic tensor. In contrast to
the ordinary Cristoffel's tensor, this tensor is traceless. Then it has only
five independent components and fulfills the depressed cubic characteristic
equation. We show that the conditions for the existence of an acoustic axes in
a given propagation direction are determined solely by the reduced acoustic
tensor. The necessary and sufficient conditions takes a simple compact
invariant form. We also present the expression for the wave velocities along
the acoustic axis. The conditions for the oblate/prolate types of the axis are
derived in terms of reduced acoustic tensor.
