# Wavenumber

Physical size
Surname Wavenumber
Formula symbol ${\ displaystyle {\ tilde {\ nu}}}$, ${\ displaystyle k}$
Size and
unit system
unit dimension
SI m −1 , rad m −1 L −1
cgs cm −1 , rad cm −1 L −1

The term wave number (also called repetition) is used in the physical literature for various physical quantities in connection with the frequency and the phase velocity of waves or the wavelength . ${\ displaystyle \ nu}$ ${\ displaystyle c}$ ${\ displaystyle \ lambda}$

Depending on the subject, two different definitions are used:

${\ displaystyle {\ tilde {\ nu}} = {\ frac {\ nu} {c}} \ quad}$ or. ${\ displaystyle \ quad k = {\ frac {\ omega} {c}}}$

Here is the angular frequency . The two forms differ only by the constant factor . To avoid confusion, it is also called circular wave number . ${\ displaystyle \ omega}$${\ displaystyle 2 \ pi}$${\ displaystyle k}$

## Spectroscopy

A wave that swings twice in one meter. Therefore it has a wavelength of 0.5 m and a wave number of 2 m −1 .

In spectroscopy , the wave number is the reciprocal of the wavelength : ${\ displaystyle {\ tilde {\ nu}}}$${\ displaystyle \ lambda}$

${\ displaystyle {\ tilde {\ nu}} = {\ frac {\ nu} {c}} = {\ frac {1} {\ lambda}} = {\ frac {N} {l}}}$,

where c stands for the speed of light in a vacuum and for the frequency. ${\ displaystyle \ nu}$

The wave number is thus also the quotient of the number N of the wavelengths allotted to the length l .

It is clear the number of oscillations that it performs in a unit length (in the case of the circular wave number in a length of ). ${\ displaystyle 2 \ pi}$

Its SI unit is m −1 , especially in spectroscopy the CGS unit is cm −1 , i.e. H. Number of oscillations of a wave per centimeter , given. This unit is also called Kayser , after Heinrich Kayser . For example, rotational spectra are in the range of 1–100 cm −1 , while vibrational spectra are in the range of 100–10,000 cm −1 . In parlance, the unit cm −1 is usually called the wave number, so instead of “the band is 120 inverse centimeters” it is said “the band is 120 wave numbers”.

Since 1 cm corresponds to about 1 / 30,000,000,000 light second , there is a proportionality factor of 30 billion between wave number and frequency (1 cm −1 corresponds to 30 GHz)

Table for rough calculations
Wave number in cm −1 Wavelength in µm Frequency in THz application
10,000 1 300 Infrared spectroscopy
1,000 10 30th Infrared / Terahertz Spectroscopy
100 100 3 Terahertz Spectroscopy
10 1000 0.3 Microwave spectroscopy

## Amount of the wave vector

In the multi-dimensional case, the circular wave number is the magnitude of the wave vector . She calculates too ${\ displaystyle k = | {\ vec {k}} |}$

${\ displaystyle k = | {\ vec {k}} | = {\ frac {\ omega} {c}} = {\ frac {2 \ pi} {\ lambda}} = 2 \ pi \ cdot {\ tilde { \ nu}}.}$

The wave number is sometimes also referred to as the spatial frequency .

## Individual evidence

1. German Institute for Standardization (Ed.): DIN 1304-1 formula symbols - general formula symbols . Beuth Verlag GmbH, Berlin, p. 3 .
2. Otto-Albrecht Neumüller (Ed.): Römpps Chemie-Lexikon. Volume 6: T-Z. 8th revised and expanded edition. Franckh'sche Verlagshandlung, Stuttgart 1988, ISBN 3-440-04516-1 , p. 4614.