This study applies the Mode-Matching Method (MMM), a wave-based analytical technique widely used for waveguide analysis in electromagnetics and vocal tract acoustics, to predict the sound absorption characteristics of resonator-based sound absorbers. Helmholtz resonators and quarter-wave resonators (QWRs) are commonly used for low-to-mid frequency absorption in small rooms, and their resonant frequencies must be tuned to match the room’s frequency characteristics. Conventional one-dimensional methods such as the Transfer Matrix Method (TMM) are often used for this purpose, but their accuracy depends on empirical end corrections due to acoustic radiation at the resonator openings. MMM models three-dimensional wave behavior by accounting for higher-order transverse modes within waveguides, enabling accurate prediction without end corrections. This study outlines the MMM-based approach and validates it through numerical experiments using Finite Element Method (FEM) solutions as references. The numerical test cases include axisymmetric Helmholtz resonators, asymmetric Helmholtz resonators, and more complex cases, such as multi-layered resonators composed of series-connected resonators. In all cases, including those where applying end corrections is particularly challenging, MMM provides results comparable to FEM.
Iwanaga et al. (Wed,) studied this question.