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Relationship between wavelength, angular wavelength, and other wave properties. A quantity related to the wavelength is the angular wavelength (also known as reduced wavelength), usually symbolized by ƛ ("lambda-bar" or barred lambda). It is equal to the ordinary wavelength reduced by a factor of 2π (ƛ = λ/2π), with SI units of meter per ...
Diagram illustrating the relationship between the wavenumber and the other properties of harmonic waves. In the physical sciences, the wavenumber (or wave number), also known as repetency, [1] is the spatial frequency of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber).
For de Broglie matter waves the frequency dispersion relation is non-linear: +. The equation says the matter wave frequency ω {\displaystyle \omega } in vacuum varies with wavenumber ( k = 2 π / λ {\displaystyle k=2\pi /\lambda } ) in the non-relativistic approximation.
These quanta would have an energy given by the Planck–Einstein relation: = and a momentum vector | | = = =, where ν (lowercase Greek letter nu) and λ (lowercase Greek letter lambda) denote the frequency and wavelength of the light, c the speed of light, and h the Planck constant. [3]
A wavenumber–frequency diagram is a plot displaying the relationship between the wavenumber (spatial frequency) and the frequency (temporal frequency) of certain phenomena. Usually frequencies are placed on the vertical axis, while wavenumbers are placed on the horizontal axis. [1] [2]
It is also occasionally referred to as temporal frequency for clarity and to distinguish it from spatial frequency. Ordinary frequency is related to angular frequency (symbol ω, with SI unit radian per second) by a factor of 2 π. The period (symbol T) is the interval of time between events, so the period is the reciprocal of the frequency: T ...
ω is the (temporal) angular frequency of the wave, describing how many radians it traverses per unit of time, and related to the period T by the equation =, k is the angular wave vector of the wave, describing how many radians it traverses per unit of distance, and related to the wavelength by the equation | k | = 2 π λ . {\displaystyle ...
Inherent in these equations is a relationship between the angular frequency ω and the wave number k. Numerical methods are used to find the phase velocity c p = fλ = ω/k , and the group velocity c g = dω / dk , as functions of d / λ or fd .