We investigate the acoustics of saturated porous media with a double porosity constituted by pores and fractures. This work is the direct extension of earlier papers by Auriault and Boutin, where the quasi-static behaviour was studied. The different macroscopic descriptions of the acoustics are shown to be the quasi-static ones, completed by classical inertial terms and with a generalized seepage law for the fractures. Therefore, when the three scales, i.e. the pore, the fracture and the macroscopic scales are equally separated, the medium exhibits memory effects. Finally, we investigate the interpretation of laboratory experiments on single porosity medium under an acoustic excitation. It is shown that the viscoelastic effects which are observed when the frequency is about a few kHz have their origins in the same phenomenon. But the macroscopic description now depends on the size and the shape of the sample, and therefore it is nonspecific for the porous medium.