Momentum, radiation pressure, and other second-order quantities in ideal gas (liquid) in some boundary-value problems

Problems related to such properties of sound waves as momentum, radiation pressure, and sound energy density and flux are investigated on the basis of the solutions of particular problems in the first-and second-order approximations using the Eulerian representation. Specifically, it is shown that a disturbance propagating in a continuous medium may have a nonzero momentum when the average density of the medium in the volume occupied by the wave coincides with the density of the undisturbed medium. In this case, the momentum and the related mass transfer and radiation pressure are caused by variations in the wave profile (envelope). Andreev’s expression for the energy density that differs from the commonly used one is verified, and some other paradoxical consequences of the theory of sound are considered. The correctness of using the quantities averaged over time and space is discussed.