Wavenumber in most physical sciences is a wave property inversely related to wavelength, having SI units of reciprocal meters (m−1). Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. Inverse --> Inverse is the opposite of something This word and its derivatives are used greatly In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International Wavenumber is the spatial analog of frequency, that is, it is the measurement of the number of repeating units of a propagating wave (the number of times a wave has the same phase) per unit of space. Space is the extent within which Matter is physically extended and objects and Events have positions relative to one another Frequency is a measure of the number of occurrences of a repeating event per unit Time. Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 Application of a Fourier transformation on data as a function of time yields a frequency spectrum; application on data as a function of position yields a wavenumber spectrum. This article specifically discusses Fourier transformation of functions on the Real line; for other kinds of Fourier transformation see Fourier analysis and Familiar concepts associated with a Frequency are colors musical notes radio/TV channels and even the regular rotation of the earth The exact definition varies depending on the field of study.

## In spectroscopy

In spectroscopy, the wavenumber $\tilde{\nu}$ of electromagnetic radiation is defined as

$\tilde{\nu} = 1/\lambda$

where λ is the wavelength of the radiation in a vacuum. Spectroscopy was originally the study of the interaction between Radiation and Matter as a function of Wavelength (λ Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. The wavenumber has dimensions of inverse length and SI units of reciprocal meters (m−1). Dimensional analysis is a conceptual tool often applied in Physics, Chemistry, Engineering, Mathematics and Statistics to understand Commonly, the quantity is expressed in the cgs unit cm−1, pronounced as reciprocal centimeter or inverse centimeter and historically synonymous with kayser. The centimetre-gram-second system ( CGS) is a system of physical units. The historical reason for using this quantity is that it proved to be convenient in the analysis of atomic spectra. Wavenumbers were first used in the calculations of Janne Rydberg in the 1880's. Johannes Robert Rydberg, (‘Janne’ to his friends ( November 8, 1854 &ndash December 28, 1919) was a Swedish Physicist The Rydberg-Ritz combination principle of 1908 was also formulated in terms of wavenumbers. The Rydberg-Ritz Combination Principle is the theory proposed by Walter Ritz in 1908 to explain relationship of the spectral lines for all atoms A few years later spectral lines could be understood in quantum theory as differences between energy levels, energy being proportional to wavenumber, or frequency. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons However, spectroscopic data kept being tabulated in terms of wavenumber rather than frequency or energy, since spectroscopic instruments are typically calibrated in terms of wavelength, independent on the value for the speed of light or Planck's constant. The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta.

A wavenumber can be converted into quantum-mechanical energy E in J or regular frequency ν in Hz according to

$E = hc\tilde{\nu} = 1.9865\times 10^{-23} \mathrm{J\,cm} \times \tilde{\nu} = 1.2287\times 10^{-4} \mathrm{eV\,cm} \times \tilde{\nu}$,
$\nu = c \tilde{\nu} = 29.978\times10^{9} \mathrm{Hz\,cm} \times \tilde{\nu}$.

Note that here wavenumber and the speed of light are in cgs units, so care must be taken when doing these calculations. The centimetre-gram-second system ( CGS) is a system of physical units.

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

$\tilde{\nu} = R\left(\frac{1}{{n_f}^2} - \frac{1}{{n_i}^2}\right)$

where R is the Rydberg constant and ni and nf are the principal quantum numbers of the initial and final levels, respectively (ni is greater than nf for emission). Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 The Rydberg Constant, named after the Swedish Physicist Johannes Rydberg, is a Physical constant relating to atomic spectra in the

In colloquial usage, the unit cm−1 is sometimes referred to as a "wavenumber", which confuses the role of a dimension with that of the name of a quantity. Dimensional analysis is a conceptual tool often applied in Physics, Chemistry, Engineering, Mathematics and Statistics to understand Furthermore, spectroscopists often express a quantity proportional to the wavenumber, such as frequency or energy, in cm−1 and leave the appropriate conversion factor as implied. Consequently, an incorrect phrase such as "The energy is 300 wavenumbers" should be interpreted or restated as "The energy corresponds to a wavenumber of 300 reciprocal centimeters (or inverse centimeters or per centimeter)" The analogous statements hold true for the unit m−1.

## In wave equations

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

$k \equiv \frac{2\pi}{\lambda}$

for a wave of wavelength λ (in cm).

For the special case of an electromagnetic wave,

$k \equiv \frac{2\pi}{\lambda} = \frac{2\pi\nu}{v_p}=\frac{\omega}{v_p}=\frac{E}{\hbar c}\;\;,$

where ν (Greek letter nu) is the frequency of the wave, vp is the phase velocity of the wave, ω is the angular frequency of the wave, E is the energy of the wave, ħ is the reduced Planck constant, and c is the speed of light in vacuum. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space Do not confuse with Angular velocity In Physics (specifically Mechanics and Electrical engineering) angular frequency In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. If the electromagnetic wave travels in vacuum, its phase velocity vp = c. The wavenumber is the magnitude of the wave vector. The magnitude of a mathematical object is its size a property by which it can be larger or smaller than other objects of the same kind in technical terms an Ordering A wave vector is a vector representation of a Wave. The wave vector has magnitude indicating Wavenumber (reciprocal of Wavelength) and the

For the special case of a matter wave, for example an electron wave, in the non-relativistic approximation:

$k \equiv \frac{2\pi}{\lambda} = \frac{p}{\hbar}= \frac{\sqrt{2 m E }}{\hbar}.$

Here p is the momentum of the particle, m is the mass of the particle, E is the kinetic energy of the particle, and $\hbar$ is the reduced Planck's constant. In Physics, the de Broglie hypothesis (pronounced /brœj/ as French breuil close to "broy" is the statement that all Matter (any object has a Wave In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object The kinetic energy of an object is the extra Energy which it possesses due to its motion The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta.

## 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. Atmospheric sciences is an umbrella term for the study of the atmosphere, its processes the effects other systems have on the atmosphere and the effects of the atmosphere In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 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. An atmospheric wave is a periodic disturbance in the fields of Atmospheric variables (like Surface pressure or Geopotential height, Temperature EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 Wavenumber-frequency diagrams are a common way of visualizing atmospheric waves. A wavenumber-frequency diagram is a plot of a field that has been subjected to a Fourier transform both in space and time An atmospheric wave is a periodic disturbance in the fields of Atmospheric variables (like Surface pressure or Geopotential height, Temperature