What is wavenumber: Definition and 30 Discussions

In the physical sciences, the wavenumber (also wave number or repetency) is the spatial frequency of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time (ordinary frequency) or radians per unit time (angular frequency).
In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck's constant is the canonical momentum.
Wavenumber can be used to specify quantities other than spatial frequency. For example, in optical spectroscopy, it is often used as a unit of temporal frequency assuming a certain speed of light.

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  1. Lotto

    B What do these wavenumbers correspond to in Raman spectroscopy?

    I don't know whether it is an energy of a photon emitted by a deexciting molecule, or if it is an energy of laser's photons. Here is an example of such spectrum: For example, that value of wavenumber ##3000\, \mathrm {cm^{-1}}## is an energy of an emitted photon or a photon from laser? And that...
  2. shankk

    I Issue with wavenumber in the free particle wavefunction

    To me, the ##K## obtained by solving the Schrodinger equation and the de broglie wavelength seem two completely unrelated quantities. Can someone explain why have we equated ##K## and ##\frac{2\pi}{\lambda}##. Also, isn't writing ##p = \hbar K## implying that eigenstate of energy is also an...
  3. D

    I Planck's law in wavenumber vs. wavelength

    I have asked this question elsewhere. I have gotten no clear answer. What I already know: The interval (differential) sizes (areas) are different in terms of wavelength and wavenumber. The total energy is the same when the curves are integrated over all wavelengths or wavenumbers So please...
  4. A

    Converting between wavenumber and wavelength

    By dimensional analysis, we have that the wavenumber: $$k = \frac{\text{radians}}{\text{distance}}$$ And the wavelength: $$\lambda = \frac{\text{distance}}{1 \text{wave}}$$ Then: $$\lambda k = \frac{\text{radians}}{\text{distance}}\frac{\text{distance}}{1 \text{wave}} = \frac{\text{radians}}{1...
  5. C

    I What does the wavenumber in a group velocity represent?

    I'm trying to wrap my head around the dispersion relation ##\omega(k)##. I understand how you can construct a wavepacket by combining multiple traveling waves of different wavelengths. I can then calculate the phase and group velocities of this wavepacket: \begin{align*} v_p &=...
  6. A

    A Complex wavenumber of Lamb waves in lossy materials

    Dear all, I have a question related to acoustic propagation in isotropic lossy media, more specifically generation of Lamb waves at fluid-solid interfaces. There goes the question: I am trying to obtain the Lamb wave velocity and attenuation dispersion curves of viscoelastic materials...
  7. E

    I Dispersion: expansion of wavenumber as function of omega

    Hi! Dealing about wave propagation in a medium and dispersion, wavenumber k can be considered as a function of \omega (as done in Optics) or vice-versa (as maybe done more often in Quantum Mechanics). In the first case, k (\omega) \simeq k(\omega_0) + (\omega - \omega_0) \displaystyle \left...
  8. adamaero

    Given wavenumber find spring constant harmonic oscillator

    Homework Statement The separation between energies of an oxygen molecule is 2061 cm-1 (wavenumber). Treating the molecule as a simple harmonic oscillator whose fundamental frequency is related to its spring constant and reduced mass, calculate the spring constant for an O2 molecule. meff =...
  9. S

    I Physical Meaning of complex wavenumber?

    Hey, This is my first post so I am hoping to do everything right :-) I do not understand the physical meaning of a complex wavenumber. I understand that, with a general approach u(x,t) = Re(A*[e][(i(kx-omega*t)]) and a complex wavenuber that the wave is decaying exponentially with x. What...
  10. M

    Wavenumber of corresponding isotope peak in IR?

    Homework Statement The infrared spectrum of CO shows a vibrational absorption peak at 2170 cm-1 (a) What is the force constant of the CO bond? (b) At what wavenumber would the corresponding peak for 14CO occur? Homework Equations k=ω2μ = (2πcv)2μThe Attempt at a Solution So I solved part a...
  11. E

    Another question about dispersion (and wavenumber)

    Hello! I still would like to thank those who participated to my previous thread about group velocity and dispersion. Now there is a (maybe) simpler question. A sinusoidal, electro-magnetic plane wave in the vacuum propagates in a certain direction with the following wavenumber, which is supposed...
  12. M

    Why do I plot certain Raman against the wavenumber

    I am currently writing my Bachelorthesis about Raman spectroscopy. For measurement with a 785 nm Laser I plot the Intensity against the Raman shift. But for measurements involving a 532 nm, I had so select the program (Spectrasuite) so display them against the "normal" wavenumber. Why is that...
  13. evinda

    MHB Why can we only change the wavenumber?

    Hello! (Wave) Wave equation: $u_{tt}=au_{xx}, a>0$ We are looking for solutions of the wave equation of the form of a wave function. We suppose that $u(x,t)=A \cos(kx- \omega t)$ is a solution of $u_{tt}=au_{xx}, a>0$. We have: $$u_x(x,t)=-Ak \sin(kx- \omega t)\\u_{xx}(x,t)=-Ak^2...
  14. A

    Exploring Wavenumber & Position Eigenstates

    If the wavenumber eigenstates are |k> and the position eigenstates are |x>, then my notes say we can write |k>=∫-∞∞ek(x)|x>dx i.e express a wavenumber eigenstate in terms of a superposition of position eigenstates. Now they state that ek(x)=eikx/√(2π). I don't understand how we can say that the...
  15. J

    Wavenumber Units: Standard or Free-for-All?

    Hi there, quick question about units. I know wavenumber can be defined as 1/λ or 2π/λ, the latter sometimes being termed 'angular' wavenumber. Is there an agreed upon way of distinguishing between these two definitions when displaying units on, for example, a graph or paper? I've seen...
  16. S

    Difference between wavenumber and wave mode?

    Are these two, wave number and wave mode, same thing? If not, what is the difference? Thanks...
  17. J

    Propagation of uncertainty from wavenumber to wavelength

    Hi, This is just a quick question. If wavenumber is a variable with some standard deviation Δk, how do I propagate this spread when converting from wavenumber to wavelength? Is it just 2π/Δk or is it more complex than that? Thanks
  18. B

    Kramers-Kronig relations for the wavenumber

    Hi all, I am wandering if I can apply the Kramers-Kronig (KK) relations to the complex wavenumber k(ω) = k'(ω) + i k"(ω). I have a measurement that easily gives me k'(ω) for a certain range of frequencies, but where k"(ω) is unreliable. I would like to use KK to find k" from k'. According...
  19. C

    Can I have different wavenumber and frequency in E and B for a plane e

    Homework Statement To solve the wave equations in vacuum for ##\vec{E}## and ##\vec{B}## we made the ansatz: \begin{array}{cc} \vec{E}\left(\vec{r},t\right)=\vec{E}_{0}\cos\left(\vec{k}\cdot\vec{r}-\omega t+\delta\right)...
  20. A

    Finding band origin of electronic transition and wavenumber of vibrational mode

    Homework Statement The first vibrational band in the absorption spectrum of H2CO is at 28871 cm-1. The first two bands in the emission spectrum (from v'=0 level) lie at 27021 cm-1 and 24687 cm-1. Explain these observations. Determine the band origin of the electronic transition and the...
  21. B

    Show that the real and imaginary parts of the wavenumber, k, are given by

    Homework Statement Show that the real and imaginary parts of the wavenumber, k, are given by k(real)=[sqrt(epsilon(real))]omega/c and k(imaginary)=[epsilon(imaginary) *omega/(2c sqrt(espilon(real))) The Attempt at a Solution k^2= mu epsilon omega^2 (1+(i g/epsilon*omega)) k^2...
  22. R

    What is the Wavenumber and Transition for an H-Atom with n=732 to n=731?

    Homework Statement Calculate a diameter of an H-atom with n=732. Calculate also the value of the wavenumber corresponding to the transition from n=732 to n=731 Homework Equations E_{trans}= \frac{-E_{h}}{(732)^2}-\frac{-E_{h}}{(731)^2}} The Attempt at a Solution...
  23. P

    Physical significance of wavenumber

    i do not understand what is the physical significance of wavenumber. i have a plot with wavenumber on x-axis and count on the y axis. what does the plot mean, how can i relate to a practical example. please help
  24. M

    How to Insert Wavenumber Symbol and Draw Triple Bonds in Word?

    Hi Does anyone know how to get the symbol for wavenumber, nu bar, in Word? Also if anyone has any tips on how to draw a triple bond quickly in Word. I'm happy to use the equal sign for a double bond thanks
  25. I

    Lenard Jones Potential & wavenumber

    I was just wondering, given that you have the dispersion relation omega = omega(k) for a Lenard-Jones potential in say a monatomic crystalline solid of lattice spacing a, which is proportional to sin(ka/2) where k is the wavenumber. The group velocity is the derivative of the dispersion relation...
  26. N

    Planck function expressed in Wavenumber?

    Homework Statement I am checking some equations for my simulation and are looking at the Planck function. My question involves the constant used for the Planck function expressed in Wavenumbers. I have found this expression for the function...
  27. T

    Explanation of Wavenumber wrt Turbulence and Energy dissipation

    Hi there Can anyone provide me with an explanation of what a wavenumber is, and how it can be used in determining the extent to which energy is dissipated during turbulence (ideally in the context of the ocean)? I am aware of the basic definition of a wavenumber (i.e. the reciprocal of wave...
  28. R

    How Is Wavenumber Calculated for Large Topography Disturbances in Steady Waves?

    This is an ultra vague question, but I'm hoping to bump into an expert who might know. Consider the steady flow of water over a polygonal surface (like a step, for instance -- something that can be easily conformally mapped). The wavenumber of the far field (large x) gravity waves can be found...
  29. D

    Sign of Wavenumber: Electromagnetic Material

    Hi. In electromagnetics, a material(linear,isotropic,homogenous) with constitutive parameters \epsilon and \mu has the wavenumber k^2=\omega^2\epsilon\mu. Consequently k=\pm\omega\sqrt{\epsilon\mu}. Does this mean that \omega can actually be negative, and if so, when is it the case? It seems...
  30. maverick280857

    Difference in Physics and Chemistry Text regarding Wavenumber

    Hi Those of you who have read Bohr's Theory in Chemistry may have encountered the relation, \frac{1}{\lambda} = RhcZ^{2}(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}) for the wavelength of radiation emitted when an electron goes from a higher energy level n_{2} to a lower energy level...