Multimode radiation from an unflanged, semi-infinite circular duct

Abstract

Theoretical expressions for sound radiation from a single incident duct mode, arriving at the open end of a semi-infinite circular unflanged duct with rigid walls, are used to obtain numerical results for (1) the single-mode sound power transmission coefficient, and (2) the multimode far-field directivity factor. For the multimode calculations the modes are assumed incoherent, and a weighting model is adopted which includes, as special cases, equal power per mode (above cutoff), and excitation by incoherent monopoles or axial dipoles uniformly distributed over a duct cross section. High-frequency asymptotic features of the results are explored in detail and analytical approximations are given. The findings have practical application to sound power measurement from tall exhaust stacks.