A comparative study of platonic solid loudspeakers as directivity controlled sound sources
Alexander Mattioli Pasqual, José Roberto de França Arruda, and Philippe Herzog
Compact spherical loudspeaker arrays in the shape of Platonic solids have been used as directivity controlled sound sources. Such devices are commonly used to synthesize spherical harmonic (SH) radiation patterns, which might be later combined to produce different directivities. The SH synthesis presents two main difficulties whose extent depends on the Platonic solid used: large synthesis error at high frequencies due to spatial aliasing and huge membrane velocities at low frequencies due to low radiation efficiency. This work presents a comparative theoretical study of the five Platonic loudspeakers. Their ability to reproduce SHs and the radiation efficiencies of their acoustic radiation modes are evaluated. It is shown that the dodecahedron presents the best compromise between complexity of the controllable patterns, number of channels and sound power.