Volume integrals of the quantityE/&OHgr;, whereEis the classical acoustic energy density of Rayleigh and &OHgr; 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. WithAnthe area of a ray tube cut by a wave front, the quantityEaAn/&OHgr;2is constant along a ray. These results generalize classical results of Blokhintsev.