Oscillatory Phenomena

Abstract

The nature of wave propagation involves the oscillations or vibrations of a dependent variable such as gas pressure or lateral displacement of a string with respect to space and time. At a fixed point in the material the particle oscillates sinusoidally performing simple harmonic motion, if we neglect damping. On the other hand, a snapshot of the wave form at a fixed time shows a sinusoidal picture (again, for the case of no damping). These two types of vibrations, both in time and space, make the subject appear to be quite complicated for the beginner. Therefore, for pedagogical reasons we feel it is best to introduce the subject of wave propagation by an investigation of the harmonic motion of masses about their equilibrium points. Concerning this approach, we have an excellent example in the approach taken by Lord Rayleigh [32, Vol. I, p. 19]. He said, “The vibrations expressed by a circular function (sinusoidal function) of the time... are so important in Acoustics that we cannot do better than devote a chapter to their consideration, before entering on the dynamical part of our subject (wave propagation).”