Extrapolation of 3D directivity balloon of dodecahedron loudspeaker from measurements near its equatorial plane

This paper presents a method to calculate the full 3D directivity balloon of dodecahedron sound sources based on simple laboratory measurements and spatial rotations. Dodecahedron-shaped loudspeakers are used extensively in acoustic measurements. Knowledge of the 3D directivity pattern of this kind of sound sources is necessary in many applications. For example, this directivity feature may be required to predict facade coverage according to the ISO 16283-3 standard regarding sound insulation. The proposed method consists in extrapolating the complete 3D directivity balloon of these dodecahedron loudspeakers by exploiting the invariant rotations that dodecahedral geometry offers in conventional directivity measurements carried out an anechoic chamber by means of a turntable. To validate the proposed procedure, it is initially used on a computationally generated 3D model with dodecahedral geometry. Then, the extrapolation is applied to actual directivity measurements on a commercial model of a dodecahedron loudspeaker. The model generated from the laboratory measurements is used to predict the acoustic coverage in a facade according to the procedure outlined in the ISO 16283-3 standard, and it is compared with the coverage measured in a facade of the same dimensions and under free-field conditions in an anechoic chamber.