The idea proposed and implemented by Landau and Khalatnikov to describe the dispersion and absorption of sound in superfluid helium is applied to smectic liquid crystals. The order parameter Φ that describes the phase transition between an orthogonal smectic SmA and a tilted smectic SmC is a two-component complex scalar and in this sense resembles the order parameter of superfluid helium. The interaction of the sound waves propagating in a system with the order parameter Φ leads to a periodic modulation of the system’s physical characteristics and parameters (in particular, its temperature). However, the order parameter cannot follow the temperature oscillations induced by a sound wave due to the presence of spatial order parameter correlations (long-range ones near the phase transition). It is this delay that leads to a sound-frequency-dependent dynamic specific heat. In this paper, we calculate this dynamic specific heat for the SmA–SmC phase transition for the so-called de Vries smectics (SmdV), with a highly developed short-range order. In turn, we analyze the dependence of the dynamic specific heat on frequency and temperature and find the dispersion and absorption of sound near the SmdV–SmC phase transition.