Hydrodynamic theory of sound wave propagation

We formulate the limits of applicability of the hydrodynamic equations and prove the necessity of introducing a correction to the potential energy tra nsfer in the heat conductivity equation, which allows developing the hydrod ynamic theory of the propagation of sound waves with small amplitudes. We s how that this correction affects almost all predictions of the standard hyd rodynamic theory. In particular, this correction allows extending the appli cability domain of the hydrodynamic theory to the case of an arbitrarily vi scous liquid. Moreover, in total accordance with the experimental data, the theory predicts that the sound speed and the damping rate remain finite at all frequencies up to frequencies of the order of 10(-12) sec(-1), while t he hydrodynamic equations make no sense at higher frequencies and sound wav e propagation in the medium consequently becomes impossible. We show that t he dimensionless dispersion equation contains only one material parameter. We predict the existence of the highly damped second sound.