# What is Dispersion: Definition and 284 Discussions

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.
Media having this common property may be termed dispersive media. Sometimes the term chromatic dispersion is used for specificity.
Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, in gravity waves (ocean waves), and for telecommunication signals along transmission lines (such as coaxial cable) or optical fiber. Physically, dispersion translates in a loss of kinetic energy through absorption.
In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light, as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses, in which chromatic aberration is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V, where lower Abbe numbers correspond to greater dispersion over the visible spectrum. In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion.

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10. ### A Dispersion of the wave packet over time

since, in order to view the shape changes in our wave packet we are presented with the taylor expansion of the frequency ω(k) = ω(k0) + (k − k0)dω/dk + 1/2*(k − k0)^2 (d^2ω/dk^2) we are told that only the third term that is the 1/2*(k − k0)^2 (d^2ω/dk^2) contributes to change in shape of the...
11. ### Assignment on the tight binding model

Summary:: Due tight-binding model I derived the energy spectrum of the particle, showing that it comprises three energy bands E+(k), E−(k) and E0(k)=0. Now, I have to find the dispersion laws. Why do I have a flat energy band? What is its physical significance?. Also, what happens to the...
12. ### Dispersion relation statistical mechanics

I know that this is the general case of the Einstein and Debye Model.
13. ### Infinite-Extent 2D Mass-Spring System vibration and dispersion relation

Hi, I am trying to find equation of motion and its solutions for a 2D infinite lumped mass spring system as depicted in figure. All the masses are identical, All the springs are identical, and even the horizontal and vertical periodicity is the same n=a. I need to try find dispersive relation...
14. ### Wave dispersion in 2D Unit cell subjected to a periodic boundary

How do I get the wave dispersion for a 2D continuum unit cell subjected to a periodic boundary which is excited longitudinally? I'll be applying forces in ABAQUS with varying frequencies. I have come across Blochs theorem but I can't find any application of it in continuous systems. Every...
15. ### B Ripple Tank Refraction: Frequency Effect on Angle & Speed?

Consider water waves refraction in a ripple tank. What happen if we increased the ripple frequency. I mean the refraction angle would change or not? Also, propagation speed will change or not? I had seen a photograph in PSSC Physics. According to that, the refraction angle was reducing if we...
16. ### Group velocity and the dispersion relation

After noting w=vk and differentiating with respect to k, and lots of simplifying, I get: Vg = c/n +(2*pi*0.6)/(k*n) This doesn't correspond to any numerical value though...
17. ### I Understanding the dispersion of waves

I am trying to learn about the dispersion of waves and used one of Walter Lewin's lectures (see below) as a source. I understand phase and group velocity and dispersion relations, but I don't understand when/what kinds of waves are prone to dispersion. For example, a simple wave in the form...
18. ### Index of refraction and wavelength

The problem is multiple choice. A) refraction b) diffraction c) reflection d) dispersion An explanation would also be greatly appreciated!
19. ### How to calculate this dispersion relation

I have no idea how this dispersion relation was deduced, and also what's the meaning of including plus and minus in the formula.
20. ### Solid State Physics: Draw the Dispersion Relation from the Fermi Surface

Homework Statement ln the figure below you (b, which is taken from Jenö Sólyom Fundamentals of the physics of solids. Volume 2 chapter 19) see the Fermi sphere of radius k_F inside one section in two dimensions of the Brillouin zone of Na. Draw the dispersion relation E(k) from the I point in...
21. ### Non-constant wave velocity in a ripple tank system

Hi. We tried to make some quantitative measurements with a Pasco ripple tank system, a video camera and software for video analysis. We generated circular waves and tracked the propagation of a crest, from which the software computed the phase velocity: We used 5 Hz, 10 Hz and 20 Hz...
22. ### Are superpositions of waves with different c still waves?

Hi. As far as I know, superpositions of waves are normally considered to be waves too, even in dispersive media. But how can they still be solutions of a wave equation of the form $$\left(\frac{1}{c^2}\frac{\partial^2}{\partial t^2}-\Delta\right)u=0$$ if ##c## isn't the same for all of them...
23. ### A Small & large argument expansion of plasma dispersion function

In plasma physics we have what is known as plasma dispersion function. There are two approximation under which this function can be expanded: when the argument is less than 1, we can use power series expansion and when the argument is greater than 1 we can have asymptotic expression. My...
24. ### Do metal atoms have dispersion force?

Homework Statement Do metal atoms, such as Ti and Na, have London-dispersion force?2. The attempt at a solution In the textbook by Tro (6th ed), "Since all atoms and molecules have electrons, they all have dispersion forces." But metal atoms are held together by electrostatic forces. I think...
25. ### Dispersion equation for an LC Circuit

Need the dispersion equation for chain consisting of cell units ( LC unit scheme in attachments). I know I need to make complex Kirchhoff equations and after get the dispersion equation but absolutely don't know how to do it. All examples that I find in web very poor including books, articles...
26. ### A Incorrect Hybrid Polariton Dispersion Results

I am trying to verify the results of the hybrid polariton case with the following hamiltonian, but cannot seem to verify the results in various published papers. Can someone please explain what is wrong and how to get the a similar dispersion graph? I'm solving for the eigenenergies for the...
27. ### I Relativistic Energy Dispersion Relation: Explained

I'm in the process of learning special relativity (SR), and I'm a bit confused as to why the relativistic energy dispersion relation ##E^{2}=m^{2}c^{4}+p^{2}c^{2}## gives the energy for a free particle? I get that it is the sum of (relativistic) kinetic energy plus the rest mass term (a...
28. ### A Change in phonon dispersion with pressure

Hi, I'm looking into how phonon dispersion changes with pressure analytically and need to know how the atomic spacing in copper changes with pressure in order to model the crystal. I can't find any helpful papers online :( Any help would be appreciated thanks e
29. ### Dispersion relation for a surface wave of a pool of water

Homework Statement Homework EquationsThe Attempt at a Solution ## v = \frac { \omega } k ## ## \omega = \sqrt{ kg \tanh (k) } ##I have no idea to guess the graph. I put g = 9.8 and tried to calculate ## \omega ## for different values of k. ## \omega (0 ) = 0, \omega (30) =...
30. ### Why does ray a correspond to red and ray b to violet in this dispersion diagram?

Homework Statement Rays a and b are shown in the figure. Which corresponds to red and which to violet? The answer in mastering physics says that ray a corresponds to red. Why is this? I've read that colors with higher frequencies will bend more than those of lower frequencies. From what i can...
31. W

### Group Velocity of Non-Dispersive Wave Packet

Homework Statement I know that for a dispersive wave packet, the group velocity equals the phase velocity, which is given by v=w/k. But how do I calculate the group velocity of a non-dispersive wave packet? I'm supposed to be giving an example with any functional form. Homework Equations...
32. ### CFD Modeling of Flue Gas Pollution Dispersion

I've previously studied and used the k-epsilon turbulence model within Ansys to model water in a small stirred vessel. I am now interested in CFD models appropriate for modeling flue gas dispersion. I'd like to know: What additional considerations are required for modeling a gas as opposed to...
33. ### I Dispersive medium as a field

I am studying phase and group velocity in non-dispersive and dispersive media. My question is the following: Is there any reason why a dispersive medium simply cannot be modeled as a type of field?
34. S

### A Taylor expansion of dispersion relation - plasma physics

Hello, I may working through attached paper and really need help with deriving equation in appendix - A4 to give A10. http://iopscience.iop.org/article/10.1088/0004-637X/744/2/182/pdf Any help would be greatly appreciated. thanks, Sinéad
35. ### I Is the speed of gravitational waves non- dispersive?

Dear all, In a recent talk, I have heard that speed of gravitational waves is non-dispersive. How is it proved "observationally" in LIGO detections that all the frequencies travel with the same speed, so one can say the speed is non-dispersive?
36. T

### A Questions about Taylor dispersion in laminar pipeflow

In the equation characterizing the mass transfer in laminar flow, the radial variation of velocity and concentration can be lumped into the axial dispersion term as below: After reading the original paper about Taylor dispersion, I know how to derive this equation. But I am still not able to...
37. ### I Why use velocity dispersion in Faber Jackson relation

Hi all, Recently I am reading some online material about Tully-Fisher relation and Faber-Jackson relation which is describing the dynamical constrain on the mass of spiral/elliptical galaxies. In spiral galaxy, TF relation suggest Luminsoty ≈ (some const) (Vmax)^4 while in elliptical galaxy...
38. ### Nonlinear Schrodinger Equation Dispersion Relation

The Nonlinear Schrodinger Equation (NSE) is presented as: $$i\frac{∂A}{∂z} = \frac{1}{2}β_2\frac{∂^2A}{∂t^2}-\gamma|A^2|A$$ The steady state solution $$A(z)$$ Can be derived as an Ansatz given by: $$A(z) = \rho(z)e^{i\phi(z)}$$ By substituting and solving the ODE, the steady state...
39. ### Dispersion Relations in Cold Plasma waves

Homework Statement Im stuck on a old exam in plasma physics. It is about how to determine dispersion relations for high frequency waves in cold plasma's. I'm not sure how they do in the solution manual. Homework Equations B = B_0z^ E = E_0exp(i(kx-wt))z^ The Attempt at a Solution The...
40. ### How to calculate heat dispersion through a solid copper rod?

I'm trying to build a fanless computer case for a small electronic device. I'm trying to figure out what type of heat-sink material I should use. I have a solid copper rod about 3cm in length with a radius of .05cm. I've determined and calculated the density, specific heat, thermal...
41. ### A Classical gas with general dispersion relation

i'm trying to understand the solution to this problem: http://physweb.bgu.ac.il/COURSES/StatMechCohen/ExercisesPool/EXERCISES/ex_2065_sol_Y13.pdf (link to the problem and the solution of it) All my questions come from the partition function: 1) From where the term (2*pi)^d comes from?, I...
42. ### 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...
43. ### I A question on dispersion of Prism

As the Figure shown, a white light beam is dispersed by the prism. The refracted beams will have different directions. My question is, will their reverse extension lines intersect into one point, or not? If it will, where is the point? And the proof? Thanks a lot.
44. ### A Change in the EM field energy due to dispersion of a wave packet

Let’s suppose we have an electron with a Gaussian eigenstate, as the time runs, the wave spreads in space without changing its energy, however, the induced EM field caused by the particle decreases its energy. I assert this from the classical electromagnetism result in which the more...
45. ### Group delay with Gaussian pulse

Hello! Starting from a gaussian waveform propagating in a dispersive medium, is it possible to obtain an expression for the waveform at a generic time t, when the dispersion is not negligible? I know that a generic gaussian pulse (considered as an envelope of a carrier at frequency k_c) can be...
46. ### I How does the London dispersion force really work?

I wonder about this. The explanation that I keep finding is that "dipoles" occur "randomly" when "electrons move" to different sides of the atom. Yet I find this difficult to reconcile with what I understand about quantum mechanics -- so I must be missing something, on either side or both. In...
47. ### B Black hole mass and sigma (velocity dispersion)

It seemed to have been asked before, but I am still a bit confused. How is the velocity dispersion formed? Doesn't the evidence of dark matter tells us that the orbital speed is uniform in a galaxy? Is there a direction of dispersion? (e. g velocity gets larger to the core) And why does...
48. ### I Attractive Kronig-Penney Potential Dispersion Relation Confirmation

Hi all! Can anyone confirm (or point me to literature) that the dispersion relation for the attractive Kronig-Penney potential is correctly given on Wikipedia (https://en.wikipedia.org/wiki/Particle_in_a_one-dimensional_lattice): cos(ka) = cos(\beta b)cos(\alpha (a-b))-\frac{\alpha ^2 +...
49. ### Diffraction Grating Question, Dispersion and Resolving

Homework Statement One diffraction grating has 9600 lines uniformly spaced over a width of 3cm, it is illuminated by light from a mercury vapour discharge. The other has 5000 lines/cm and is a 3.5cm grating, this one is used in the second order to resolve spectral lines close to 587.8002 nm...
50. ### I Dispersion relation in tight binding model

Hamiltonian of tight binding model in second quantization is given as H = -t \sum_{<i,j>} a_i^{\dagger} a_j After changing basis it is H = \sum_{\vec{k}} E_{\vec{k}} a_{\vec{k}}^{\dagger} a_{\vec{k}} where E_{\vec{k}} = -t \sum_{\vec{b}} e^{i \vec{k} \cdot \vec{b}} where \vec{b} is a nearest...