The simple resonators that have been the principal theme up to this point possessed one resonant mode only and were, moreover, excited by external influences whose reaction to the effect they produced could be ignored. We turn now to extensions of these ideas in two directions. First, the resonator may consist of a string, a tube, a transmission line, a waveguide – all media for the propagation of waves, whether mechanical, acoustic or electromagnetic – and may therefore be capable of excitation in a number of different modes (see the discussion of the vibrations of a string in chapter 2). Secondly, the resonator, which may be one of the above or something simpler, may be embedded in a medium for wave-propagation, being excited by the incidence of a wave and re-radiating a wave as it responds to the excitation. For the most part we shall confine the discussion to onedimensional systems, with only occasional excursions into the considerably more versatile and complicated realm of three dimensions, such as the response of a small resonant system to a plane wave.

Preliminary remarks about one-dimensional waves; characteristic impedance and admittance

A well-developed calculus exists for treating the reflection and transmission of waves on one-dimensional transmission lines, and this is unquestionably the right approach to adopt in engineering design and in the analysis of all but the most elementary problems.