The τ(t) solution for fast-maneuvering acoustical point source emitters

A solution of the inhomogeneous wave equation which describes the far field of an acoustical point source in arbitrary motion is developed. The solution is analogous to but more general than the Lienart-Weichart solution of electromagnetics. For stationary listeners and motion which is expandable in a vector Taylor series, a computational routine has been found, using matrix calculus, to solve for all retardation effects including time-varying delay τ(t), wideband Doppler, and amplitude spotlighting. This routine is straightforward on a computer, giving exact results to any desired accuracy, the most complicated subroutine being the extraction of a root of a polynomial with real coefficients.