Design of duct cross sectional areas in bass-trapping resonators for control rooms

Small rooms, such as the ones specifically designed for listening to amplified music, like control rooms in recording studios, face the problem of low-frequency over-enhancement by acoustic resonances. Several devices have been developed to tackle this problem, such as Helmoltz resonators. The number of controlled acoustic modes depends on several factors among which are the central frequency chosen, the modal density in that frequency range, and the coupling between the resonator and the room. In this paper we suggest that the efficiency of such resonators may be significantly improved if, instead of using basic Helmholtz or devices with uniform cross-section, more complex shape-optimized resonators are used, in order to cope with a larger number of undesirable acoustic modes. We apply optimization techniques to the uncoupled resonator, developed in our previous work, in order to obtain the optimal shapes for devices that resonate at a design set of acoustic eigenvalues, within imposed physical and/or geometrical constraints. One-dimensional and three-dimensional finite element models were implemented. The one-dimensional model was coupled to optimization techniques in order to achieve the design goal. We illustrate the proposed approach with two examples of resonator shapes and different design sets of absorption frequencies.