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.