What is Dispersion relation: Definition and 65 Discussions
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the phase velocity and group velocity of waves in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency dependence of wave propagation and attenuation.
Dispersion may be caused either by geometric boundary conditions (waveguides, shallow water) or by interaction of the waves with the transmitting medium. Elementary particles, considered as matter waves, have a nontrivial dispersion relation even in the absence of geometric constraints and other media.
In the presence of dispersion, wave velocity is no longer uniquely defined, giving rise to the distinction of phase velocity and group velocity.
Homework Statement
Show that c^2 = g/k*(rho1 - rho2)/ (rho1 + rho2)
where rho1 and rho 2 are the different densities, k is the constant from solving the PDE (separation of variables).
Homework Equations
Use the fact that phi(1) --> 0 as y --> neg. infinity and phi(2) --> 0 as y -->...
Ok so here's another problem that i just completely don't understand at all. Thanks for your help.
A linear chain consists of 2N equally spaced identical particles with mass m and speration a, coupled by springs with alternating constands k1 and k2. Use the periodicity of the system to find...
Hi guys,
I don't understand how one would exactly determine a dispersion relation
of phonons experimentally.
There are two equations, one for momentum and one for energy conservation:
\vec{k} - \vec{k^{'}} = \vec{G} + \vec{K}
\omega - \omega ^{'} = \omega(K)
where...
Homework Statement
Use the dispersion relation to find the group velocity v_group and phase velocity v_phase.
Homework Equations
omega(k) = [(hbar)k^2]/2m
The Attempt at a Solution
v_group = domega(k)/dk = [hbar]k/m = h/m lambda = p/m = v
This isn't right.
v_phase = omega...
Homework Statement
Consider the linearized, quasi-geostrophic vorticity equation on the beta-plane,
with a mean background flow umean , which allows for vertical structure and propagation of Rossby waves:
(d/dt+umean*d/dx)=(nabla2 ψ+(f02/N2)*(d2 ψ/dz2)+bv
where ψ is the horizontal...
I've been working on problems trying to find the dispersion relation of monatomic and diatomic chains. I'm able to find the dispersion relation, but I don't really understand what it is. I'm pretty sure that it's the relation of the frequency to the wave vector.
I'm working through Kittel's...
I'm doing an experiment, in which I have a one dimensional lattice held up by strings. That is I have a series of n masses each of mass M each connected to each other by springs with spring constant C and unstretched length a. Each mass is suspended from the ceiling by a string of length L. I'm...
The group velocity of traveling wave is defined as v_g =\partial \omega/\partial k. I am confused about how to actually calculate this. For instance, in the Schrodinger equation, we find that plane waves solve the equation provided that
\omega = k^2 \hbar/2m
Does this mean that the group...
Hi all.
I have some questions about the dispersion relation in the study of waves.
First of all, why do we always assume a plane wave solution when we want to obtain a dispersion relation?
Second, is "assuming a plane wave solution" a general way to obtian all dispersion relations? for both...
In dispersion relation diagrams, where omega is plotted against k, omega is sometimes nonzero at k=0. How is this possible? I thought a wave had to have a nonzero wavenumber :confused:
I'm studying the phenemenon of band gaps in a experiment, however the stop bands are proving hard to define using just a transmission spectrum dervived from the fft alogrithm.
I've heard that it may be possible to define the band region by plotting the dispersion relation of sound waves the...
Hello, I was wondering if someone more knowledgeable in loop-quantum gravity or string theory could discuss a bit about the following topic for me:
If there is a lower size limit (or length itself is quantized), does this (or can this) mean that there would be a dispersion relation for light...
Dispersion relations have the tendency to confuse me.
In general, I know what dispersion is, but trying to apply it to crystals, I just "can't see the forest among all those trees". :rolleyes:
In phonon dispersion, acoustical and optical phonons have quite a different dispersion behaviour...