A Paper on the Theory of Sound

Abstract

It has been known for some time that sound is produced by a sound-generating body causing the air to vibrate; Lagrange was the first to subject this motion to mathematical analysis and deduce the principal elements comprising the theory of sound. Geometricians are so familiar with his elegant research on this subject that there is little need to repeat his findings here. However, at the time of their publication, very little was known about the use of partial differential equations on which the solution for these types of problems depend. There was disagreement on the use of discontinuous functions which are nevertheless fundamental for representing the status of the air at the origin of the motion: thankfully, these difficulties have been removed with the progress made in the analysis, whilst those which persist relate to the nature of the problem. Much work still needs to be undertaken before all these can be overcome, thus the principal aim of this paper is to prove several general theorems which would appear to be of interest to both physicists and geometricians.