Far-field multimodal acoustic radiation directivity

A comparison is made between approximate equations for far-field acoustic radiation patterns and exact equations for single and multimodal excitations in order to determine the validity range for the approximate approach. It is found that for single-mode cases: (1) the gross behavior of the primary lobes is adequately described by the approximate equations, (2) some error is found for lower and zero radial order modes, and (3) some agreement is yielded between exact and approximate sidelobes, although the approximate equation was not intended to simulate sidelobes. Multimodal approximate equations are compared to exact equations for various distributions of modal power; for all cases excellent agreement is found. For multimodal patterns it is noted that many modes influence the final level and shape of the directivity curve, although the major contributions are from the higher radial order modes.