Modeling and analysis of secondary sources coupling for active sound field reduction in confined spaces

This article addresses the coupling of acoustic secondary sources in a confined space in a sound field reduction framework. By considering the coupling of sources in a rectangular enclosure, the set of coupled equations governing its acoustical behavior are solved. The model obtained in this way is used to analyze the behavior of multi-input multi-output (MIMO) active sound field control (ASC) systems, where the coupling of sources cannot be neglected. In particular, the article develops the analytical results to analyze the effect of coupling of an array of secondary sources on the sound pressure levels inside an enclosure, when an array of microphones is used to capture the acoustic characteristics of the enclosure. The results are supported by extensive numerical simulations showing how coupling of loudspeakers through acoustic modes of the enclosure will change the strength and hence the driving voltage signal applied to the secondary loudspeakers. The practical significance of this model is to provide a better insight on the performance of the sound reproduction/reduction systems in confined spaces when an array of loudspeakers and microphones are placed in a fraction of wavelength of the excitation signal to reduce/reproduce the sound field. This is of particular importance because the interaction of different sources affects their radiation impedance depending on the electromechanical properties of the loudspeakers.