Acoustic Field of Circular Plane Piston in Limits of Short Wavelength or Large Radius

Abstract

The acoustic beam of a circular plane piston (radius a) is analyzed as it approaches either the short-wavelength limit (SWL) or the large-radius limit (LRL). Using a new expression for the beam, we show that with no absorption the SWL would be a cylindrically collimated beam, with radius a, of plane waves. If absorptive effects are minor, the chief deviations during approach to the SWL occur in two decreasing volumes, a horn-shaped paraxial region and a cylindrical shell of mean radius a. One consequence is that any second harmonic, self-generated in the beam, approaches its own SWL more rapidly than does the first harmonic. Approach to the LRL yields a known paradox: Even the piston's nearfield need not approach a uniform plane wave. We show that the presence of absorption does make the LRL a plane wave and that in the absence of absorption there is a valid reason for the paradox: The piston beam must have a unique axis of cylindrical symmetry; an unbounded plane wave cannot.