Energy, momentum, and angular momentum of sound pulses

Pulse solutions of the wave equation can be expressed as superpositions of scalar monochromatic beam wavefunctions (solutions of the Helmholtz equation). This formulation leads to causal (unidirectional) propagation, in contrast to all currently known closed-form solutions of the wave equation. Application is made to the evaluation of the energy, momentum, and angular momentum of acoustic pulses, as integrals over the beam and pulse weight functions. Equivalence is established between integration over space of the energy, momentum, and angular momentum densities, and integration over the wavevector weight function. The inequality linking the total energy and the total momentum is made explicit in terms of the weight function formulation. It is shown that a general pulse can be viewed as a superposition of phonons, each with energy (h) over bar ck, z component of momentum (h) over barq, and z component of angular momentum hm. A closed-form solution of the wave equation is found, which is localized and causal, and its energy and momentum are evaluated explicitly. (C) 2017 Acoustical Society of America.