On the Eigen Frequencies of Rectangular Resonator with a Hole in the Wall

The rectangular waveguide is attached to a hole in a wall of rectangular resonator and the corresponding to the hole part of the waveguide boundary is cross-section of the waveguide. The problem of excitation of the resonator by an eigen wave of the waveguide is investigated. The condition on a hole is obtained from the condition defining the wave in the waveguide, outgoing from cross-section. The initial diffraction problem is reduced to some infinite set of linear algebraic equations. Numerical experiment shows that the dependence of expansion coefficients of the field in the resonator on frequency of exciting wave has resonant nature. We propose to use the real values of the resonance frequencies of the running on the hole wave as the initial approximations for eigen frequencies of the resonator with a hole in the wall.