Reflection of focused sound beams from curved surfaces.

Abstract

The reflection of focused sound beams from surfaces with spherical curvature is investigated theoretically and experimentally. Theoretical predictions for the incident and reflected beams are based on the parabolic wave equation. A circular source with a uniform amplitude and quadratic phase distribution is assumed. Solutions for the reflected beam are derived for both pulsed and continuous sources. The experiments were performed in water with a 3.5-MHz source that has a nominal radius of 2.5 cm and focal length of 15 cm. Accurate measurements of the incident beam, particularly very near the source, were used to characterize the effective radius and focal length. Reflection from both convex and concave surfaces was investigated. The targets were made of nickel with radii of curvature that vary from 5 cm up to infinity (planar targets). Measurements of the reflected beam were obtained with a needle hydrophone that passed through a small hole in the center of the source. Agreement between theory and experiment is excellent, and the results suggest novel ways to measure surface curvature. [Work supported by the David and Lucile Packard Foundation, ONR, and NSF.]