Determination of complex resonant frequencies in rectangular and circular cylindrical rooms

A numerically efficient procedure for the determination of complex resonant frequencies in rectangular and cylindrical rooms having absorbing floor and ceiling is presented in this paper. The procedure is based on the analogies between the electromagnetic and acoustic problems. As the first step, the exact sound field solutions in the convenient form of double infinitive sum are derived for both types of rooms. Using these solutions, a transcendental equation for the calculation of sound field complex resonant frequencies is obtained. This equation is transformed to a convenient form and numerically solved. Resonant frequencies and damping factors are obtained as real and imaginary parts of the complex resonant frequencies, respectively. The influence of the real acoustic admittances of absorbing walls on the resonant frequencies, compared to an idealised room, is illustrated and discussed.