Energy Invariant for Geometric Acoustics in a Moving Medium

Volume integrals of the quantity $\mathrm{E/\Omega }$ , where E is the classical acoustic energy density of Rayleigh and Ω is a frequency variable as measured by an observer moving with the medium, are conserved within the assumptions of geometric acoustics in a moving medium whose undisturbed motion is not necessarily steady. With $A_n$ the area of a ray tube cut by a wave front, the quantity ${\mathrm{EaA}}_n{\mathrm{/\Omega }}^2$ is constant along a ray. These results generalize classical results of Blokhintsev.