In a suspension, the hydrodynamic interactions between particles can propagate by two mechanisms: relatively slowly, by the diffusion of transverse momentum, or relatively rapidly, by the propagation of sound waves. Here we describe computer simulation results for the collective and single particle dynamics of colloidal particles with the aim of clarifying the role of sound. We find that for single particle motion the effect is rather trivial. As for an isolated particle, compressibility modifies the decay of velocity fluctuations only at very short times. For collective correlations this is not true. Our results show that the multiple scattering of sound waves between particles can induce correlated collective motions on time scales comparable with the diffusion of transverse momentum. The effects of compressibility are no longer restricted to very short times and manifest themselves as rapid oscillations in the time dependence of the collective diffusion coefficient. We suggest that these oscillations can largely be explained in terms of "effective" incompressible hydrodynamic theory, the suspension bulk viscosity, kinematic viscosity, and speed of sound becoming the relevant parameters. The oscillations are furthermore centered on the (hypothetical) incompressible result. Thus, while the effects of sound propagation may extend to surprisingly long times, the net effect remains limited to very short times. We discuss where these sound-induced oscillations will be relevant experimentally.