Low-frequency radiation from a vibrating cap on a rigid spherical shell with a circular aperture

Theoretical models based on spherical geometries have long provided essential insights into the directional behavior of sound sources such as loudspeakers and human speech. Because commonly applied models predict omnidirectional radiation at low frequencies and increasing directionality at higher frequencies, they fail to predict the directional characteristics of certain sources with different source geometries. These sources include violins and open-back guitar amplifiers that have openings or ports connecting a cavity or enclosure to the exterior domain. This work presents the low-frequency radiation from a vibrating cap on a rigid spherical shell with a circular aperture to study the directional characteristics of such sources. The proposed model predicts dipolar radiation at very low frequencies, monopolar radiation near the Helmholtz resonance, and increasing directionality at higher frequencies. Experimental results based on measuring the sound field of an open-back spherical loudspeaker validate the theoretical model and highlight its utility in predicting directional behavior.