Wavenumber

Encyclopedia : W : WA : WAV : Wavenumber

Wavenumber in most physical sciences is a wave property inversely related to wavelength, having units of inverse length (radians per meter). Wavenumber is the spatial analogue of angular frequency. Application of a Fourier transformation on data in the time domain yields a frequency spectrum; applied on data in the spatial domain (data as a function of position) yields a spectrum as a function of wavenumber. The exact definition is dependent on the field.

In wave equations

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

[k \equiv \frac = \frac=\frac=\frac,]

where λ is the wavelength in the medium, [\nu] (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.

In spectroscopy

In spectroscopy, the wavenumber [\tilde] of electromagnetic radiation is defined as

[\tilde = 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

[\tilde = R\left({1\over - {1\over\right)]

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".

In 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\right)]

for an atmospheric wave, where R is Earth's radius and φ is latitude. Wavenumber-frequency diagrams are a common way of visualizing atmospheric waves.

From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.