Coupling Helmholtz resonators for sound manipulation

In this work, we discuss the interaction between Helmholtz resonators, using the finite element method. We show that the coupling between two spheres gives rise to two resonant modes at low frequencies. One is symmetric and corresponds to a mono-polar breathing mode, as currently observed. The second one is anti-symmetric and behaves as a dipole. We show that the first one generates an isotropic wave in the far pressure field while the second one gives rise to a directional propagative wave. The two modes are discussed as a function of the geometrical and physical parameters. When considering the thermo-viscous properties of air for a specific set of parameters, one finds that the behavior of the dipolar mode can be changed from a diffuser to an absorber. By managing double Helmholtz resonators, we aim to create a multifunctional meta-surface operating at two different frequencies.