Acoustic seminar | 06 November 2026

The seminar is devoted to the T-matrix theory of acoustic scattering by Helmholtz resonators, with particular emphasis on a cylindrical cavity coupled to the surrounding medium through a slit. The central idea is to use an aperture projection operator to obtain a compact T-matrix expression with explicit coefficients describing coupling and decoupling between external fields and cavity resonances. The T-matrix formulation provides a framework for describing the scattered field and relating its frequency dependence to the resonant properties of the structure. The discussion addresses the relationship between the resonance poles and observable scattering features, including the role of modal symmetry and the direction of incidence in determining which resonances are excited. Particular attention is given to asymptotic behavior as the slit width tends to zero. This limit reveals the distinct behavior of the fundamental Helmholtz resonance and higher resonance families, and clarifies their connection to the corresponding closed-cavity and exterior scattering problems.

Main paper/arXiv, related to the seminar, and other references:

1) P. C. Waterman, New formulation of acoustic scattering, Journal of the Acoustical Society of America 45, 1417 (1969).
2) G. R. Bigg and E. O. Tuck, Two-dimensional resonators with small openings, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics 24, 2–27 (1982).
3) A. N. Norris and G. Wickham, Elastic Helmholtz resonators, The Journal of the Acoustical Society of America 93, 617 (1993).
4) R. W. Scharstein, M. L. Waller, and T. H. Shumpert, Near-field and plane-wave electromagnetic coupling into a slotted circular cylinder: Hard or TE polarization, IEEE Transactions on Electromagnetic Compatibility 48, 760 (2006).