Focusing Radiators

Abstract

An approximate theory has been derived describing part of the sound field due to a concave spherical radiator, vibrating with uniform normal velocity. The diameter of the circular boundary is assumed to be large relative to the wave-length and large relative to the depth of the concave surface. The theory describes the distribution of sound pressure, particle velocity, and intensity along the axis of symmetry and in the vicinity of the focal plane. It is shown that the ratio of the intensity at the center of curvature to the average intensity at the radiating surface is nearly equal to (2πh/λ)2, where h is the depth of the concave surface and λ is the wave-length. This ratio can be made very large by suitable choice of dimensions. The diffraction pattern in the focal plane is nearly the same as the diffraction pattern of a flat circular piston at large distance from the piston, if the piston and concave radiator have boundaries of equal radius. The theory has been compared with experimental data for a 5-mc concave quartz crystal, described previously by G. W. Willard and J. F. Muller. The calculated and experimental data are in reasonable agreement when allowance is made for the non-uniform distribution of normal velocity of the crystal.