In this paper, we consider the effect of the emergence of transparency of a resonantly absorbing medium for electromagnetic radiation due to the excitation of piston-like acoustic oscillations of the medium along the direction of radiation propagation – acoustically induced transparency. The physical mechanism and basic conditions for the implementation of the effect are discussed, as well as its application to reduce the propagation velocity of gamma-ray photons and on-demand recovery of an arbitrary part of a single-photon wave packet resonantly absorbed in the medium.