Wave propagation is the transport of energy in space and time. That is, the essence of wave propagation is the space–time localization of energy that moves with definite speed and amplitude characteristics. This contrasts with vibrations that set each point in the structure in motion simultaneously. Figure 4.1 illustrates some characteristic wave behaviors. It shows the velocity response of a semi-infinite two-material rod free at one end and impacted at the junction. The pulse in the lower semi-infinite part travels at a constant speed, conducting energy away from the joint. Observe how the pulse is initially trapped in the upper material (resulting in multiple reflections) but eventually leaks away after the multiple reflections.

The general wave in a structure is dispersive; that is, it changes its shape as it propagates, and so identifying the appropriate propagating entities is quite difficult. For example, Figure 4.2 shows an example of the deflected shapes of a plate transversely impacted; observe that, although “something” is propagating out from the impacted region, it is not obvious how to characterize it.

The collection of explorations in this chapter considers waves in extended media as well as in particular types of waveguides with an emphasis on understanding dispersive behavior. The first exploration uses a pretensioned cable to introduce the fundamental ideas in wave propagation; namely, the speed with which entities propagate in space and time and their amplitude variation.