Acoustically-excited vibrations in pipes

Abstract

This project represents an attempt to investigate and analyse the excitation of a thin-walled cylindrical pipe by means of sound waves. A theoretical treatise is developed with reference to the behaviour of sound waves in a cylindrical pipe, including such complications as reflection and terminal effects, but effecting considerable mitigation by omitting the effects of attenuation and distortion. Such phenomena have, in general, only a minor role to play in the subject matter and their omission does not invalidate or in any way adversely affect the validity of the theory. Various modes of vibration in thin-walled pipes are described and analysed mathematically, the result of this mental exertion being the conversion of customarily abstruse differential equations into somewhat more intelligible expressions for frequency, amplitude and other parameters habitual to the field of vibrations. Integration of the aforementioned analytical exercises results in the extraction of a relationship between the characteristics of a sound wave entering a pipe and the vibrations produced by virtue of its sound energy. Finally, experimental work is carried out to test the validity of the theory. Special emphasis is placed on the length and diameter parameters describing the pipe since these are the ones which can be most conveniently varied.