Influence of the position of the opening and its shape on the properties of a Helmholtz resonator

The method of matched asymptotic expansions is used to influence the choice of the position of the opening and its shape on the properties of a Helmholtz acoustic resonator. It is shown that these parameters influence the imaginary part of the pole of the analytic continuation of the Green's function of the Helmholtz resonator, which, in its turn, has a strong influence on the behavior of the solutions of the corresponding scattering and radiation problems.