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Wavenumber

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Wave Number

The exact definition is dependent on the field.

CIRCULAR WAVENUMBER

The circular wavenumber, ''k'', often misleadingly abbreviated as "wavenumber", is defined as
:

k \equiv rac{2\pi}{\lambda} = rac{2\pi
u}{v_p}=rac{\omega}{v_p}=rac{E}{\hbar c},

where ''λ'' is the wavelength in the medium,

u

(Greek letter nu) is the frequency, ''v_p'' is the Phase Velocity of wave, ''ω'' is the Angular Frequency , ''E'' is the Energy , ''ħ'' is the Reduced Planck Constant , and ''c'' is the Speed Of Light in vacuum. The wavenumber is the Scalar of the Wave Vector .

WAVENUMBER

In Spectroscopy , the wavenumber

ilde{
u}

of Electromagnetic Radiation is defined as
:

ilde{
u} = 1/\lambda,

where

\lambda

as a length in the SI-system is measured in ''meters'' (m) and commonly quantified in centimetres (cm = 10⁻² m) refers to the wavelength ''in Vacuum ''. The unit of this quantity is cm⁻¹, pronounced as ''reciprocal centimeter'', or "inverse centimeter". The historical reason for using this quantity is that it is proportional to energy, but not dependent on the Speed Of Light or Planck's Constant , which were not known with sufficient accuracy (or rather not at all known).

For example, the wavenumbers of the emissions lines of Hydrogen atoms are given by
:

ilde{
u} = R\left({1\over - {1\over
ight)

where λ is the wavelength, ''R'' is Rydberg Constant ,

n_1

and

n_2

are the orbit numbers, and

n_2

is greater than

n_1

.

Spectroscopists often express various quantities, such as frequency and energy in cm⁻¹. In colloquial usage, the unit cm⁻¹ is sometimes referred to as a "wavenumber", which confuses the role of a unit with that of a quantity. An incorrect phrase such as "The energy is 300 wavenumbers" should be read as "The energy corresponds to a wavenumber of 300 reciprocal centimeters", or as "The energy corresponds to a wavenumber of 300 inverse centimeters".

ATMOSPHERIC SCIENCE

Wavenumber in atmospheric science is defined as length of the spatial domain divided by the Wavelength , or equivalently the number of times a wave has the same Phase over the spatial domain. The domain might be 2π for the non-dimensional case, or

:

2\pi R \cos\left(\phi
ight)

for an Atmospheric Wave , where ''R'' is Earth 's radius and φ is latitude. Wavenumber-frequency Diagrams are a common way of visualizing Atmospheric Wave s.