Complex waves

Plotting the frequency versus the wave number provides a unifying way of permitting visualization of the linear dynamics of distributed systems. A series of simple examples is presented in order to illustrate the physical significance of ordinary and evanescent waves, absolute instability, waves on moving media, and convective instability or wave amplification. The examples give a rare opportunity to develop a complete physical and mathematical picture of the dynamics, since the presentation can serve as a guide to two films¿produced by the Education Development Center for the National Committee on Electrical Engineering Films¿in which the dispersion relation evolves by computer animation on the bottom half screen in synchronism with changes in the physical phenomenon in the top half screen.