Acoustics of the orchestral kettledrum

Abstract

A complete theoretical overview of the acoustics of the kettledrum is taken. Starting with the well understood vibrations of a stretched circular membrane in a vacuum, the thesis goes on to investigate the deformation produced when the drum is struck and the subsequent behaviour of the system with time. The vibration of the membrane is modified by mass loading, by the hemispherical kettle, by the membrane's stiffness and by the air loading present; the latter is accounted for using a Green function technique. These effects produce significant changes to the frequencies of a freely vibrating system. The results are compared with those obtained experimentally, with good agreement. The most significant conclusions are that the air loading modifies the frequencies of vibration of those modes having only radial nodes to match the harmonic series, thereby creating a distinct sensation of musical pitch, and that the fundamental mode of vibration is damped completely.