Abstract:

A geometric space-time approach to evaluate the on-axis response is developed for axisymmetric planar radiators with pulsed transient excitations. The approach is based on combining the Rayleigh time-dependent surface integral with a simple geometric focusing method. The acoustic field at the pulse center is simply related to the source signal or aperture distribution along a focusing line in the space-time domain. This space-time dynamic focusing approach is used to explain the behavior of localized wave solutions to the free-space scalar wave equation. As examples, two different types of localized wave fields are investigated. The characteristics of the space-time source distributions are connected to the on-axis acoustic field and energy distribution pattern, using the space-time dynamic focusing approach. Numerical results are presented to show both the source signals and the resulting acoustic fields for the localized waves. [Work supported by URI/Ocean Technology Center.]