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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.
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. [ 1 ] [ 2 ] In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings .
While periodic travelling waves have been known as solutions of the wave equation since the 18th century, their study in nonlinear systems began in the 1970s. A key early research paper was that of Nancy Kopell and Lou Howard [1] which proved several fundamental results on periodic travelling waves in reaction–diffusion equations.
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
An illustration of a periodic function with period . A periodic function, also called a periodic waveform (or simply periodic wave), is a function that repeats its values at regular intervals or periods. The repeatable part of the function or waveform is called a cycle. [1]
The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile. Intuitively the wave envelope is the "global profile" of the wave, which "contains" changing "local profiles inside the global profile".
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.
Polarization (waves) Coherence (physics), the quality of a wave to display a well defined phase relationship in different regions of its domain of definition; Hilbert transform, a method of changing phase by 90° Reflection phase shift, a phase change that happens when a wave is reflected off of a boundary from fast medium to slow medium