The basic equation for plane elastic waves in crystals remains invariant under a reversal of the propagation direction. If the direction of the wave normal is rotated in a crystallographic plane containing an acoustic axis, a situation may arise under certain conditions which leads to an apparent violation of this inversion symmetry, namely, to a period of 360° for the angular dependence of phase velocity and displacement eigenvectors of both quasitransverse modes. A specific example for this is given and the general conditions for the occurrence of this situation are discussed.