Introduction

The physics of waves is too often presented only in a few rather straightforward and sometimes uninspiring contexts: the motion of strings, sound, light and so on. Students may be led to regard the topic with disdain; and they may be left with some crucial misconceptions, such as that all waves are sinusoidal. Wave physics may hence be considered an old-fashioned field with little relevance to the more modern, exciting areas of quantum physics, nanotechnology and cosmology. Yet there is plenty to find interesting just in classical and modern optics and the physics of musical instruments; and wave phenomena prove to be central to most of the fascinating and newly emerging branches of both fundamental and applied physics.

Most aspects of physics may be viewed from two perspectives: one, named after Lagrange, addresses particles, while the other, due to Euler, considers fields. We may, for example, establish the electromagnetic properties of matter by considering the Coulomb forces among all the constituent charged particles; or we may describe the material's bulk response to a field and tackle the problem that way. This duality pervades most areas of physics and, while one of the alternatives often proves vastly more convenient than the other, the two are ultimately quite consistent, equivalent viewpoints.

When we extend our analysis to dynamic systems, the particle approach becomes a form of ‘kinetics’ or ballistics, and changes in the field description are manifest as waves.