A study of the acoustic Helmholtz resonator and of its electromagnetic analog (a cylinder with a narrow slit) is performed. For the associated Green functions, power series asymptotics with respect to a small parameter ε (‘‘radius’’ of the resonator hole or the width of the slit), and ln ε of poles τε with small imaginary parts are obtained by using the method of matching asymptotic expansions. The principal terms of solution asymptotics for corresponding boundary value problems are given.

Topics
Acoustics, Helmholtz resonator, Asymptotic analysis, Power series
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