Longitudinal wave and seismic P-waves (created by earthquakes and explosions). In longitudinal waves, the displacement of the medium is parallel to the propagation of the wave, and waves can be either straight or round. A wave along the length of a stretched Slinky toy, where the distance between coils increases and decreases, is a good visualization. In the case of longitudinal harmonic sound waves, the frequency and wavelength can be described by the formula where: The quantity "x"/"c" is the time that the wave takes to travel the distance "x". The ordinary frequency ("f") of the wave is given by The wavelength
Propagation constant of transmission lines, the term transmission coefficient has a different meaning despite the similarity of name: it is the companion of the reflection coefficient. The propagation constant, symbol formula_1, for a given system is defined by the ratio of the complex amplitude at the source of the wave to the complex amplitude at some distance "x", such that, Since the propagation constant is a complex quantity we can write: where That "β" does indeed represent phase can be seen from Euler's formula: which is a sinusoid which varies in phase as "θ" varies but does not vary in amplitude because