Analysis of the broadband parametric array with Gaussian primary directivity patterns

Abstract

The three-dimensional integral solution for the secondary sound produced by a parametric array is formulated in a manner useful for the consideration of broadband or transient primary signals. It is shown that when the primary pressure field can be modeled as spherically spreading from the origin, the low-frequency secondary sound can be expressed as the convolution of the "input" to the parametric array with the "impulse response" of the parametric array. By modeling the primary directivity functions as Gaussian, the impulse response is reduced to a single integral. The "frequency response" of the parametric array is derived and /shown to be the Fourier transform of the impulse response. For the special case of an observer on the axis of symmetry, an exact analytic result for the frequency response is obtained and is compared with previous theories and with experiment. A Fourier transform of secondary pressure field a primary pressure field directivity parameter for Gaussian directivity C = •SR•õ exp(2aRo)•/(2poCo 4) Co small signal sound speed D•, 2 primary pressure field directivity functions

Comparative Experimental Investigation on Optimal Parametric Array Types

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Parametric speaker consisting of small number of transducers with sonic crystal waveguide

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