Electromagnetic waves have, as light and radio waves, been recurring examples for many of the phenomena that we have met throughout this book, from reflection and refraction to diffraction and interference, and for many of the technological applications, from antireflection coatings to Doppler radar. Using Maxwell's equations of electromagnetism, we can describe in exquisite detail how each of these processes occurs; and, since in characterizing the wave by the electric field strength E we refer directly to the force that the wave will exert on a static point-like test charge, we can see quite directly the processes by which electromagnetic waves are detected. The accompanying magnetic field, and its effects and detection, require only small steps further; and even the extension of our classical treatment into a quantum-mechanical description proves to be straightforward. The detailed processes by which moving charges give rise to electromagnetic waves, however, prove to hold many subtleties, and to yield some elegant but somewhat startling results.

Our general approach throughout this book has been to determine the characteristics of wave propagation in each case from the physical mechanisms by which a disturbance at one point affects that at its neighbours. This allows us to write and solve a wave equation for the system, and to determine amongst other properties the phase velocity Up of the propagating wave. We showed in Section 1.3, however, that wave propagation can be approached in a different order, and that the propagation of a disturbance from an emitter to an observer or receiver may be regarded as a version of the static interaction between the source and detector when the finite propagation speed is taken into account.

When we revised our Southampton undergraduate programme to draw into a single course the wave phenomena hitherto distributed among optics, electromagnetism, thermal physics, quantum mechanics and solid-state physics, there seemed to be no single text to recommend. This book is an expanded version of the lecture notes that resulted, and its aim, beyond covering wave physics in its own right, is to introduce the common phenomena and analytical methods that are encountered in these individual fields as well as in the disciplines such as oceanography from which we have always drawn a further audience.

There were nonetheless some excellent textbooks for individual aspects. Coulson's classic [15] provides a concise and elegant mathematical introduction; French's once ubiquitous volume [29] is admirable for its clarity and brevity; and Crawford's brilliant and popularly acclaimed approach through everyday examples [16] suffers only from being long out-of-print. Many other texts are highly satisfactory in the areas they cover, and references to their recent editions are included throughout the following chapters.

One privilege for the author of any new volume is to have a new range of scientific and technological examples upon which to draw. Oscillations in the circulations of the oceans have been quite recently recognized; the extraction of power from ocean waves and tides is only now emerging as practical and necessary; the electronic control of holographic arrays has been possible for just a few years; and the quantum mechanics of coherent systems now underpins major research fields and devices that not long ago appeared impossible.

In Chapter 2 we saw how the motion of a guitar string could be established by considering the physical mechanisms that governed it and using them to determine the wave equation for the system. In this chapter we shall see that the same approach can be applied to a wide range of physical systems. We begin with detailed derivations of the wave equations for electromagnetic waves along a coaxial cable and in free space, and then examine ocean waves and ripples on a fluid surface, showing how they may be extended to describe a variety of atmospheric and oceanic phenomena.

In each case, we begin by determining how the disturbance or displacement at any point is affected by that at adjacent points, and how the physical properties of the system determine how quickly it can respond. This allows us to derive a partial differential equation that describes the wave propagation and embodies all the relevant physics. What remains, as before, is the purely mathematical solution of this wave equation.

Although this chapter provides many useful illustrations of the principles outlined in Chapter 2, the reader may safely skip these examples without missing any fundamental principles upon which we shall build later.

Waves along a coaxial cable

Coaxial cables are used for the distribution of electrical signals, and include microphone cables, television aerial leads and, indeed, most of the connections between audio and video apparatus.

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.