The sound field of a Gaussian transducer

Abstract

The advantages of a Gaussian amplitude distribution at the surface of a transducer are similar to the advantages of a Gaussian amplitude distribution in a light beam: the diffraction pattern is both simpler to measure and simpler to calculate. Further, the simplification remains when one considers nonlinear terms in the wave equation. If one can achieve a truly Gaussian amplitude distribution, then comparison of experimental data with theoretical calculation also is facilitated. Previously we used electrical fringing to produce a one‐dimensional Gaussian amplitude distribution for schlieren photography. Now, we have used an electrical fringing to produce a two‐dimensional Gaussian distribution in an ultrasonic beam. The sidelobes are undetectable, and the maxima and minima in the Fresnel region have disappeared. Design and testing of the transducer are discussed. Both advantages and limitations are delineated. The mathematical description of the sound field is discussed. Analytical expressions are given for the amplitude in the nearfield (Fresnel?) as well as in the farfield (Fraunhofer?). In both cases the distribution is described by a Gaussian function. [Research supported in part by ONR.]