An analytical expression for the impulse response of a focused transducer with an axisymmetric nonuniform surface velocity distribution is derived using a finite polynomial expansion of the velocity distribution function. A computing scheme is presented for the numerical calculation of the transient pressure at an observation point in front of the transducer. The effect of various nonuniform velocity distributions on the characteristics of the pressure field of a medium focused transducer is shown with grey-scale pictures of calculated continuous-wave and pulsed pressure distributions.
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Verhoef et al. (1984) studied this question.
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