Helmholtz resonators are often applied for the sound equalisation of control rooms in recording studios, through adequate levelling of the low frequency acoustic modal room responses. The number of controlled acoustic modes depends on the central frequency and damping of resonators, as well as on the modal density of the controlled system within the resonators frequency range. In a recent paper we proposed to improve the efficiency of such devices by, instead of using basic Helmholtz resonators develop shape optimized multi-modal resonators in order to cope with a larger number of intrusive room modes. In spite of the promising results thus obtained, further work is needed to demonstrate the feasibility of such approach. The present paper is a further step in that direction by analysing the acoustics of the fully coupled room/resonators system. More specifically, using a substructure computational approach we theoretically derive the coupled acoustical modes of control rooms fitted with several optimized multi-mode resonators.
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