Effects of low-frequency evanescent acoustic waves in cavities with a small opening

Abstract

Evanescent acoustic waves are usually neglected in plane-wave approximation, but they may have remarkable effects on acoustic fields on occasions where the approximation is not strictly valid. Here, we investigate effects of low-frequency evanescent acoustic waves excited in a cavity of transverse dimensions not much smaller than, or even comparable to, the relevant wavelength. We find that the evanescent acoustic waves excited around a small opening of the cavity collectively behave as an acoustic inertia whose interaction with the acoustic compliance inherent to the cavity gives rise to a L-C-like series resonance at a frequency considerably lower than the cutoff frequency, resulting in vanishing sound pressure on average over the opening interface as if the interface acts as an absolutely soft boundary. Unlike a traditional Helmholtz resonator, the acoustic mass necessary for the resonance is totally provided, without the need for a physical neck, by the transverse evanescent acoustic waves inside the cavity, and thus, the proposed resonance is internal to the cavity. We also find that the interference of evanescent acoustic waves with a propagating sound wave can lead to the formation of a unique nodal curve of the sound field inside the cavity. The theoretically predicted effects of evanescent acoustic waves are well demonstrated both by our experiments and numerical simulations.