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English: This shows several waveforms: sine wave, square wave, triangle wave, and rising sawtooth wave. The fundamental frequencies of each waveform have the same frequency and phase, for comparison. Uses the data files and the gnuplot code in #Source code below.
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The wave vector and angular wave vector are related by a fixed constant of proportionality, 2 π radians per cycle. It is common in several fields of physics to refer to the angular wave vector simply as the wave vector, in contrast to, for example, crystallography. [1] [2] It is also common to use the symbol k for whichever is in use.
In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics.
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
The Airy wave train is the only dispersionless wave in one dimensional free space. [20] In higher dimensions, other dispersionless waves are possible. [21] The Airy wave train in phase space. Its shape is a series of parabolas with the same axis, but oscillating according to the Airy function.