Dispersion refers to the frequency dependence of the properties of a wave.

learn more… | top users | synonyms

26
votes
4answers
7k views

Why do prisms work (why is refraction frequency dependent)?

It is well known that a prism can "split light" by separating different frequencies of light: Many sources state that the reason this happens is that the index of refraction is different for ...
3
votes
1answer
150 views

More extensions of the wave equation for dispersion

The Phys.SE question Minimal Extension of Wave Equation to Include Dispersion extended the wave equation for only a very simple form of dispersion. However, what about more complex dispersion ...
2
votes
2answers
110 views

Why is rainbow always circular?

From the article that I read on physics classroom website on rainbow, rainbow is formed with red on the top and violet on the bottom because violet refracts more, and has a smaller angle of deviation ...
3
votes
1answer
218 views

Why don't the De Broglie dispersion relation contain a constant term?

Wikipedia says that the dispersion relation for a non-relativistic particle is: $$ \omega = \frac{\hbar k^2}{2m}. $$ But when I tried to calculate it myself, I seem to get a constant term in that ...
1
vote
1answer
41 views

Is difference in wave number always small?

Over the last few days I have been looking at a derivation of group velocity. The derivation is the one shown in this question Deriving group velocity. I have seen this derivation in many places, and ...
5
votes
3answers
2k views

Is speed of sound really constant?

Does not speed of sound actually depend on the frequency and/or amplitude of the waves? If so, why it is constant?
7
votes
1answer
264 views

PDE from dispersion relation?

Suppose I have knowledge of a system's dispersion relation $f(\omega,k)$. Is it possible to recover the underlying PDE describing the system? Can I simply use the replacement $k=-i\nabla$, ...
7
votes
1answer
137 views

Minimal Extension of Wave Equation to Include Dispersion

Let's say you are modeling some process with the wave equation $\frac{1}{c^{2}}\frac{\partial^{2}\psi}{\partial t^{2}} = \nabla^{2}\psi$. You wish to improve your model by including dispersive ...
1
vote
1answer
94 views

Density of States in NOT Free Electron Gas

I think that I understand how the density of states works for a free electron gas. It is effectively just a conversion factor between summing over values of k and integrating over values of E. If you ...