A comparative study of platonic solid loudspeakers as directivity controlled sound sources

Compact spherical loudspeaker arrays in the shape of Platon ic solids have been used as directivity controlled sound sourc es. Such devices are commonly used to synthesize spherical harmonic (SH) radiation patterns, which might be later combine d to produce different directivities. The SH synthesis prese nt two main difficulties whose extent depends on the Platonic so l d used: large synthesis error at high frequencies due to spati al aliasing and huge membrane velocities at low frequencies du to low radiation efficiency. This work presents a comparativ e theoretical study of the five Platonic loudspeakers. Their a bility to reproduce SHs and the radiation efficiencies of their acou stic radiation modes are evaluated. It is shown that the dodecahe dron presents the best compromise between complexity of the controllable patterns, number of channels and sound power.