A wave-acoustics theory has been developed to describe the propagation of zero sound parallel to vortex lines in rotating A3. We show that a diffraction shadow is formed in which the wave amplitude is suppressed by interference around vortices. This phenomenon contributes to the experimentally observed effect of rotation on the sound amplitude and exceeds the attenuation at large core radii. The dependence of the diffraction contribution on the angular velocity changes drastically at the transition from vortices with a finite core to coreless vortices when the magnetic field is decreased to zero. We derive conditions for the applicability of the effective-medium theory and the classical geometrical acoustic method in describing sound propagation along vortices.