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Encyclopedia > Wavenumber

Wavenumber in most physical sciences is a wave property inversely related to wavelength, having SI units of reciprocal meters (m−1). Wavenumber is the spatial analogue 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. 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. The exact definition varies depending on the field of study. A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... Surface waves in water This article is about waves in the most general scientific sense. ... Inverse is the opposite of something. ... For other uses, see Wavelength (disambiguation). ... The International System of Units (symbol: SI) (for the French phrase Système International dUnités) is the most widely used system of units. ... This article is about the unit of length. ... Space has been an interest for philosophers and scientists for much of human history. ... For other uses, see Frequency (disambiguation). ... Various meters Measurement is an observation that reduces an uncertainty expressed as a quantity. ... This article is about a portion of a periodic process. ... In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ... Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. ...

## Contents

In spectroscopy, the wavenumber $tilde{nu}$ of electromagnetic radiation is defined as Extremely high resolution spectrogram of the Sun showing thousands of elemental absorption lines (fraunhofer lines) Spectroscopy is the study of the interaction between radiation (electromagnetic radiation, or light, as well as particle radiation) and matter. ... Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. ...

$tilde{nu} = 1/lambda$

where λ is the wavelength of the radiation in vacuo. The wavenumber has dimensions of inverse length and SI units of reciprocal meters (m−1). Commonly, the quantity is expressed in the cgs unit cm−1, pronounced as reciprocal centimeter or inverse centimeter and historically synonymous with kayser. 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. The Rydberg-Ritz combination principle of 1908 was also formulated in terms of wavenumbers. A few years later spectral lines could be understood in quantum theory as differences between energy levels, energy being proportional to wavenumber, or frequency. 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. For other uses, see Wavelength (disambiguation). ... Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ... The International System of Units (symbol: SI) (for the French phrase Système International dUnités) is the most widely used system of units. ... CGS is an acronym for centimetre-gram-second. ... Kayser is a surname, and may refer to Allan Kayser, American actor Alois Kayser, German missionary Emanuel Kayser, German geologist Heinrich Kayser, German physicist See also Kayser-Fleischer ring This human name article is a disambiguation page â€” a list of pages that might otherwise share the same title, which is... Johannes Rydberg, commonly known as Janne Rydberg, (November 8, 1854 - December 28, 1919), was a Swedish physicist mainly known for devising the Rydberg formula, which is used to predict the wavelengths of photons (of light and other electromagnetic radiation) emitted by changes in the energy level of an electron in... It has been suggested that this article or section be merged with Ritz method. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... The speed of light in vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ...

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

$E = 100 hctilde{nu} = 1.9865times 10^{-23} mathrm{J,cm} times tilde{nu}$,
$nu = 100 c tilde{nu} = 29.978times10^9 mathrm{Hz,cm} times tilde{nu}$

For example, the wavenumbers of the emissions lines of hydrogen atoms are given by General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ...

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

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). The Rydberg constant, named after physicist Janne Rydberg, is a physical constant discovered when measuring the spectrum of hydrogen, and building upon results from Anders Jonas Ã…ngstrÃ¶m and Johann Balmer. ...

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. 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. Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ...

## In wave equations

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

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

for a wave of wavelength λ.

For the special case of an electromagnetic wave, Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ...

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

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. The wavenumber is the magnitude of the wave vector. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ... It has been suggested that this article or section be merged into Angular velocity. ... Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ... The speed of light in vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ... 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 of the class of objects to which it belongs. ... A wave vector is a vector that represents two properties of a wave: the magnitude of the vector represents wavenumber (inversely related to wavelength), and the vector points in the direction of wave propagation. ...

For the special case of a matter wave, for example an electron wave, in the non-relativistic approximation: In physics, the de Broglie hypothesis (pronounced /brÅ“j/, as French breuil, close to broy) is the statement that all matter (any object) has a wave-like nature (wave-particle duality). ...

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

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. This article is about momentum in physics. ... This article or section is in need of attention from an expert on the subject. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ...

## 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 Meteorology is the scientific study of the atmosphere that focuses on weather processes and forecasting. ... For other uses, see Wavelength (disambiguation). ... This article is about a portion of a periodic process. ...

$2pi R cosleft(phiright)$

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. An atmospheric wave is a periodic disturbance in the fields of atmospheric variables (like surface pressure or geopotential height, temperature, or wind velocity) which may either propagate (traveling wave) or not (stationary wave). ... This article is about Earth as a planet. ... A Wavenumber-frequency diagram is a plot in 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, or wind velocity) which may either propagate (traveling wave) or not (stationary wave). ...

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