If a wave propagates in an infinite and non-dispersive medium, its phase velocity v(p) and its group velocity v(g) are equal to the speed of propagation v, which appears in the wave equation for any frequency of the wave. All physical quantities associated with the wave are transferred with the group velocity. A wave is guided if it is canalized between surfaces, which limit the propagation medium in one transverse direction or in both of them. Guided waves propagate in specific modes. Each mode is characterized by a cut-off frequency, a phase velocity and a group velocity, which depend on the frequency of the wave and on the geometry of the waveguide. The propagation properties in the infinite medium are recovered if the transverse dimensions of the waveguide are much larger than the wavelength. We may analyze their propagation by studying the successive reflections on the guide walls. However, a more practical and general method consists of directly finding the solutions of the wave equation that satisfy the boundary conditions.
If the medium is bounded in the direction of propagation, it can support only standing (or stationary) waves in normal modes of discrete frequencies (called normal frequencies). The modes are determined from the wave equation and the boundary conditions of the medium. In each mode, the propagation medium is a juxtaposition of wave zones with points called antinodes, where the amplitude of the wave is large, and points called ...