Effects of air loading on timpani membrane vibrations

Abstract

Measurements and theoretical calculations of timpani modal frequencies and decay times are made for the cases of no kettle enclosure and kettle enclosures of varying volume. For the calculations, the timpani membrane is assumed to be ideal and the kettle is assumed to be a rigid cylinder which is volume equivalent to the actual kettle. A Green function method is used for calculating the effects of air loading. The calculated modal frequencies and decay times are generally in good agreement with the experimental measurements. In particular, for typical kettle enclosures, the frequency ratios f11 : f21 : f31 ; f41 are found to be close to the harmonic ratios 2 : 3 : 4 : 5 over the normal playing range 100 Hz≲f11≲175 Hz.