# Difference between dispersive medium and non-dispersive medium.

1. Nov 29, 2011

### shayaan_musta

Hello experts!

I have 2 questions.

1)Difference between dispersive and non-dispersive medium.

2)ω=$\sqrt{\frac{4β}{m}}$sin$\frac{Ka}{2}$ is a relation for dispersive medium. How to reduce it to non-dispersive relation? Here is some math work I have performed to reduce it to non-dispersive relation i.e.

At low frequency K→0
so,
sin($\frac{Ka}{2}$)→$\frac{Ka}{2}$
so the equation becomes,
ω=$\frac{2}{a}$νs$\frac{Ka}{2}$
or,
ω=νsK
where, νs is phase velocity.

So ω=νsK is the relation for non-dispersive medium? Is it?

2. Dec 11, 2011

### lightarrow

Don't know what are β and m in your equations, however, for every frequency ω you can write that ω is equal to phase velocity multiplied wave vector modulus k, only that in a dispersive medium the phase velocity is not constant but depends on k (or ω, depending on which is your independent variable):

νs(k) = $\frac{ω(k)}{k}$

Group velocity (if of interest) is instead the derivative: νg(k) = $\frac{dω(k)}{dk}$.

3. Dec 11, 2011

### shayaan_musta

But you are the only one up till now who replied me. So thanks for reply.

β is spring constant. It is come from the derivation of 1D mono-atomic.

m is the mass of the atoms.

You mean ω=vsk is not for the non-dispersive medium?

4. Dec 11, 2011

### lightarrow

ω=vsk is valid in both cases. If the medium is non-dispersive, vs is a constant, independent of k; if it's dispersive, vs depends on k.

5. Dec 13, 2011

### shayaan_musta

Oh great
Thanks a lot.