On the directionality of membrane coupled Helmholtz resonators under open air conditions.

Controlling the absorption and diffusion of sound in the audible range constitutes an exciting field of research. Acoustic absorbers and diffusers perform extraordinarily well at high frequencies with sizes comparable to the wavelength of the working frequency. Conversely, efficient low-frequency attenuators demand large volumes leading to unpractical sizes, and there is now interest in determining whether the size of the resonator can be reduced while not compromising - or perhaps even decreasing - the working frequency. One viable approach is through the use of metamaterials to enable the control of device dynamics such that heavy sub-wavelength attenuation can be efficiently realised. To achieve this goal, the theoretical (including a mathematical model and the use of finite element analysis) and experimental characterisation of 3D-printed membrane-coupled Helmholtz resonator (HR) acoustic metamaterials (AMMs) is explored. The results reveal good agreement between theory and experiments, and show that membrane-coupled HR AMMs feature heavy sub-wavelength acoustic attenuation (λ/55) while also showcasing directional responses under open air conditions. These features are explained by the interplay between resonator size, membrane characteristics, and the presence of two acoustic ports. It is anticipated that, together with recent advances on smart AMMs, these systems will foster new progress in the development of dynamic AMMs for wideband attenuation.