An improved King integral algorithm for finite amplitude sound beams

Abstract

This paper supercedes the previous analysis [J.H. Ginsberg, Acoust. Soc. Am. Suppl. 1 71, S30 (1982)] of the infinite baffle problem for an axisymmetric harmonic excitation, which derived a nonlinear King integral describing the distortion associated with finite acoustic Mach numbers. That analysis was shown [M. B. Moffett and J. H. Ginsberg, J. Acoust. Soc. Am. Suppl. 1 72, S40 (1982)] to exhibit excessive nearfield distortion in comparison to experiment. Using the linear King integral in its conventional complex function form, as opposed to the real function analysis employed previously, leads to formulation of the second order potential in terms of complex functions. Asymptotic integration of this potential function reveals that there may be significant contribution from the evanescent spectrum (small transverse wavenumbers), as well as from the propagating spectrum. A coordinate straining transformation describing the full spectrum is duduced. From it, the previous analysis is shown to be only asymptotically correct. The new analysis reveals that the distortion is governed by a transformation that involves Fresnel integrals for the propagating spectrum and the error function for the evanescent spectrum. Some comparisons of the analytical prediction and the results of Moffett and Ginsberg are presented [Work supported by ONR, Code 420.]