Synthesis of Line Source Directivity Patterns

Abstract

The distribution of sound intensity in space (pattern function) from a line source of finite length is given by an integral involving the distribution of source strength along the line of the source (excitation function). Synthesizing a desired pattern function with a given length of source requires the solution of an integral equation for the excitation function. Practical solutions may be obtained by expressing the pattern function as a finite sum of “characteristic functions” and obtaining the excitation function as a similar sum of complementary functions. One such scheme relates the zeroes of the pattern function to the coefficients of the Fourier expansion of the excitation function. Equal-minor-lobe patterns may be approximated, but the solution is not obtained in closed form as with linear point-source arrays.