<title>Time development of acoustic bullets, wave-zone form of focus wave modes, and other solutions of the acoustic equations</title>

Abstract

1407_40It has previously been shown that all causal finite energy solutions of the time-dependent acoustic and Maxwell's equations have forms which, except for a factor (1/r), behave like one-dimensional solutions propagating outward along each radial direction (or ray) when the time and distances are large. The region where the one-dimensional form dominates is called the wave zone. The authors have previously given exact solutions of the acoustic and Maxwell's equations in which the solutions in the wave zone differ from zero only for rays in a right circular cone and for a given finite radial interval within the cone. The exact solutions are called 'bullets' because asymptotically they represent packets of energy which are 'shot' through the cone which is a kind of 'rifle.' In the present paper it is shown graphically how the exact solution in the acoustic case develops into its wave zone form with increasing time. Also considered are solutions of the acoustic equations such as the focus wave mode solutions, and the wave zone forms are given. These solutions are compared with each other and with the bullets in the wave zone region.