Refined acoustic modeling and analysis of shotgun microphones

A shotgun microphone is a highly directional pickup device widely used in noisy environments. The key element that leads to its superior directivity is a tube with multiple slot openings along its length. One traditional way to model the directional response of a shotgun is to assume plane waves traveling in the tube as if it is in the free field. However, the frequency response and directivity predicted by this traveling wave model can differ drastically from practical measurements. In this paper, an in-depth electroacoustic analysis was conducted to examine the problem by considering the standing waves inside the tube with an analogous circuit containing phased pressure sources and T-networks of tube segments. A further refinement is to model the housing diffraction effect with the aid of the equivalent source method (ESM). The on-axis frequency response and directivity pattern predicted by the proposed model are in close agreement with the measurements. From the results, a peculiar bifurcation phenomenon of directivity pattern at the Helmholtz frequency was also noted. While the shotgun behaves like an endfire array above the Helmholtz frequency, it becomes a broadside array below the Helmholtz frequency. The standing wave effect can be mitigated by covering the slot openings with mesh screen, which was found to alter the shotgun response to be closer to that of the traveling wave model above a critical frequency predicted by the half-wavelength rule. A mode-switching model was developed to predict the directional responses of mesh-treated shotguns.