The study of the resonances of theHelmholtz resonator has been broadly described in previous works (see  and references therein). Here, for a simple 2-dimensional resonator in the shape of a tube, we analyze the transition zone where oscillations start to appear. Following a careful analysis, we obtain an optimal lower bound of the width of the resonances.
Cite this article
André Martinez, Laurence Nédélec, Optimal lower bound of the resonance widths for a Helmholtz tube-shaped resonator. J. Spectr. Theory 2 (2012), no. 2, pp. 203–223DOI 10.4171/JST/27