Plane Piston at Finite Amplitude: Second Harmonics

Abstract

The growth of harmonics in finite-amplitude acoustic beams is often measured with circular plane-piston sources, but then compared with plane-wave theory. The growth of second harmonics in the beam from a plane piston at finite amplitude is calculable after expanding the linear first-harmonic beam in plane waves. It can be shown that any two plane waves starting from the plane z=0 interact to produce a growing second-harmonic wave only if all three waves have identical directions. With this guidance, pairs of plane waves in the linear expansion for the piston are selected, combined, and added to give for the second-harmonic field a definite integral involving products of Bessel functions. Absorption can be included. Two special cases can be evaluated fairly easily and accurately: the field along the beam axis, and the signal on a centered receiver considerably larger than the source. The latter result agrees reasonably with measurements by Ryan, Lutsch, and Beyer [J. Acoust. Soc. Am. 34, 31 (1962]. (This work was supported by the Office of Naval Research and by the Wright Air Development Center.)