Propagation of sound waves through a spatially homogeneous but smoothly time-dependent medium

• Analytically exact study of sound propagation through a non-stationary medium.
• Energy exchange between the non-stationary medium and the sound wave.
• Transformation of hypersonic and ultrasound frequencies in non-stationary media.
• Propagation of sound backward in time in close analogy to anti-particles.
• Prediction of tsunamis both in spatially and temporally inhomogeneous oceans.

The propagation of sound through a spatially homogeneous but non-stationary medium is investigated within the framework of fluid dynamics. For a non-vortical fluid, especially, a generalized wave equation is derived for the (scalar) potential of the fluid velocity distribution in dependence of the equilibrium mass density of the fluid and the sound wave velocity. A solution of this equation for a finite   transition period ττ is determined in terms of the hypergeometric function for a phenomenologically realistic, sigmoidal change of the mass density and sound wave velocity. Using this solution, it is shown that the energy flux of the sound wave is not conserved but increases always   for the propagation through a non-stationary medium, independent of whether the equilibrium mass density is increased or decreased. It is found, moreover, that this amplification of the transmitted wave arises from an energy exchange with the medium and that its flux is equal to the (total) flux of the incident and the reflected wave. An interpretation of the reflected wave as a propagation of sound backward in time is given in close analogy to Feynman and Stueckelberg for the propagation of anti-particles. The reflection and transmission coefficients of sound propagating through a non-stationary medium is analyzed in more detail for hypersonic waves with transition periods ττ between 15 and 200 ps as well as the transformation of infrasound waves in non-stationary oceans.