The timpani as a vibrating circular membrane : an analysis of several secondary effects
Mills, Ronald I.
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When the frequencies of the tiapani modes of vibration are compared with the frequencies predicted by the theory of an ideal circular membrane, the measured fequencies are spread out. Several factors that may cause this phenomenon are analyzed. Because on the low frequencies characteristic f the timpani vibrations, the stiffness of the membrane is ruled out as a contributing factor. The acoustic properties f the surrounding air are then considered. Resistive damping of the membrane is analysed as a possible cause of the frequency shift. When the decay constants for the timpani are measured, this resistive damping is determined. The measured decay constants indicate that this resistive damping causes negligible shifting of the timpani frequencies. Reactive impedance of the surrounding air is then considered. Assuming that the membrane behaves as a circular piston, an approximation f the reactive impedance can be. made and the effective mass loading of the surrounding air can be calculated. Theoretical wave velocities calculated by considering this effective mass loading are compared with the measured wave velocities. Agreement between these two wave velocities indicates that the effective mass loading is the doainant factor in shifting the frequencies of the timpani.