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...