An analytical model for a dodecahedron loudspeaker applied to the design of omni-directional loudspeaker arrays

The dodecahedron (12 sided) loudspeaker is used extensively for acoustic measurements as an approximation to an omni-directional sound source, for example in building acoustics and automotive applications. In many instances its use is favoured above other omni-directional source approximations e.g. open pipe because of its greater power. However, analysis by other authors has shown that the radiation deviates from omni-directional above a certain frequency. In this paper an analytical model of the sound pressure field generated by a dodecahedron loudspeaker is constructed. The sound pressure field generated by the model is then compared with measured data and good agreement is demonstrated. Having established and validated the model, it is adapted to form alternative spherical loudspeaker arrays based on Platonic and Archimedean solid geometry and also a number of spherical packing routines. The aim of the analysis is to determine the optimal geometry for an omni-directional source using pistonic loudspeakers. The analysis shows that constructive interference of the pressure field across the spherical baffle surface and not individual loudspeaker pistonic radiation characteristics is the most significant factor with respect to deviations from omni-directional radiation for a complete spherical array. Consequently, loudspeaker elements which physically occupy the spherical baffle surface to their maximum extent provide the most extended frequency range of omni-directional operation. The most optimal spherical array distribution is shown to be the dodecahedron. (C) 2014 Elsevier Ltd. All rights reserved.