Directivity of dodecahedral sound sources using a hybrid experimental-numerical approach

Standardized room acoustics measurements require a sound source as omnidirectional as possible with sound power large enough to excite the environment. ISO 3382 defines the maximum acceptable directivity deviations, and the most common geometry used is the dodecahedron to comply with these requirements. The deviation of the loudspeakers frequency response affects the directivity patterns of the sound source and manufacturers should be careful about it. In this work, the frequency response of the twelve loudspeakers attached to a dodecahedral sound source was measured using a laser vibrometer. Next, these results were applied to prescribe the velocities in a sound radiation model using Boundary Elements Method (BEM). Convergence analysis of the model showed the best match between acoustic field accuracy and computational cost using four elements per wavelength, with a divergence less than 0,05 dB. Directivity patterns showed an omnidirectional behavior up to the frequency in which the source circumscribed diameter times the wavenumber (ka) is 3. Up to this frequency, the sound source can be represented as a pulsating sphere. For frequencies above this limit, the directivity lobe of each speaker exerts a strong influence on the radiation pattern of the sound source. The frequency response deviation of the loudspeakers causes stronger effects within this frequency range. Perfectly coupled vibration between loudspeakers presents deviations up to 12 dB at 4 kHz, while the decoupling effect is prescribed in the BEM model, a deviation of 25 dB is obtained. This effect is much less prominent in lower frequencies. At 1 kHz a deviation of 1,2 dB was observed. The main conclusion about the coupling of loudspeakers resonance affects directivity patterns for shorter although the sound source can be considered omnidirectional for wave number times source diameter ka less than 3.