Modeling the sound radiation of gamelan gongs using closed-form rigid spherical models

The structural modes of gamelan gongs have clear connections with the gongs' far-field radiated patterns. However, the instruments' unique geometry and modal characteristics limit the applicability of simple theoretical closed-form models, such as a radially vibrating cap on a sphere, for understanding their radiation. This work develops and applies two different models, a vibrating cap on a spherical shell with a circular aperture and a vibrating cap with imposed mode shapes, to better understand the gongs' directional characteristics. The models agree with acoustical measurements, predicting dipole and cardioid-like patterns and lobes formed from constructive and destructive interference.