Continuous waves generated by focused radiators

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Abstract
A single integration technique for calculating the pressure distribution in the field of a focused sinusoidally oscillating radiator is described. This technique involves the direct closed form integration of one of the integrals in the Rayleigh formula; the latter formula itself contains a double integral corresponding to integration over the area of the source transducer face. Precise experimental measurements of a hydrophone’s response to the pressure field generated by a focused medical diagnostic transducer are also reported, and comparison between experiment and theory is made. Very good agreement between theory and experiment is demonstrated with respect to both amplitude and phase for lateral beam profiles at six different distances from the source transducer. At a seventh distance (about 1 cm from the source transducer) much more violent fluctuations in the response are observed than result from the theory.

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