A theoretical analysis is given of the acoustic wave propagation in periodically nonhomogeneous media made of a solid material whose stiffness tensor is uniformly rotating along a given axis. In the last years, such media have been studied theoretically as well as experimentally, in particular for what concerns sample preparation and possible applications. A detailed analysis of their acoustical properties is given here, based on fully analytic and simple propagation equations. For axial propagation: (i) the dispersion curves of media where the transversal field components and the longitudinal ones are not coupled show only one forbidden band, that gives selective Bragg diffraction; in the opposite case they show at least a second forbidden band, that involves the quasilongitudinal and one of the quasitransversal eigenmodes; (ii) in the first case (absence of coupling), the medium gives pure acoustical rotation for p<<lambda, where p is the helical pitch and lambda the acoustical wavelength, a nonperfectly uniform but very large rotatory power for p of the order of lambda, and a guided rotation for p>>lambda; (iii) in the presence of the coupling, regions of mode exchange between the longitudinal component and a transversal one are generally present. The cases of lossy media and of quasiaxial propagation are also considered, and the analogies between optical and acoustical properties discussed.