Sound field reconstruction using multipole equivalent source model with un-fixed source locations

The equivalent source methods (ESM) that have been developed to this point can generally be classified into two categories: one in which a relatively large number of lower order sources are fixed at various locations, and one in which a series of higher order sources are fixed at one location. The present work started with a model in the latter category, but the individual sources were then allowed to move separately to locations which were determined by using a nonlinear optimization procedure based on the measured sound field data. To test this approach, experiments were conducted using a small loudspeaker cabinet; measurements were made using an array of microphones on all sides of the loudspeaker. It was found that by allowing the source components to move, the sound field representation in both the near and far fields was improved, particularly at high frequencies, compared to the model with fixed source locations. By comparison with results obtained from boundary element calculations based on laser vibrometer measurements of the loudspeaker's diaphragm and tweeter velocities, it was found that the proposed ESM can also be used to accurately predict the sound pressure distribution on the source surface.