Starting with a complete set of coupled Langevin equations for the hydrodynamic variables including the order parameter and the acoustic phonons, the critical sound dispersion relation is derived for models C and F. The final expression for the sound dispersion relation contains a quantity which can be interpreted as a frequency-dependent specific heat depending only on the critical degrees of freedom. The elimination of the phonons from the self-energy is justified in detail. Our microscopic result agrees with the phenomenological formula of Ferrell and Bhattarcharjee only in limiting cases. In general, as for instance for model F, it is more complicated than one could have anticipated on a phenomenological basis. For model C, the scaling function of the critical sound attenuation coefficient is calculated to two-loop order. Finally, it is shown that for model C with more than one order parameter component and model F the sound dispersion relation obtained at the critical point is also valid in the crossover region between the critical point and the coexistence region which is in a critical state due to the Goldstone modes.