Energy and momentum of sound pulses

The energy and momentum of three-dimensionally localized sound pulses are shown to be constant in time for propagation in fluids of negligible viscosity. Further, the energy always exceeds the product of the momentum and the speed of sound. This property follows from the fact that three-dimensionally localized pulses are necessarily converging or spreading (they have a focal region). A consequence of this convergence/divergence is that the associated pressure gradient, density gradient and particle velocity are not purely longitudinal, as they are for pulses localized in only one dimension. The velocity remains curl-free up to second order, however. Analytic values of energy and momentum are obtained from a particular localized solution of the wave equation.