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Difference between dispersive medium and non-dispersive medium.

by shayaan_musta
Tags: difference, dispersive, nondispersive
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shayaan_musta
#1
Nov29-11, 12:34 PM
P: 184
Hello experts!

I have 2 questions.

1)Difference between dispersive and non-dispersive medium.

2)ω=[itex]\sqrt{\frac{4β}{m}}[/itex]sin[itex]\frac{Ka}{2}[/itex] 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([itex]\frac{Ka}{2}[/itex])→[itex]\frac{Ka}{2}[/itex]
so the equation becomes,
ω=[itex]\frac{2}{a}[/itex]νs[itex]\frac{Ka}{2}[/itex]
or,
ω=νsK
where, νs is phase velocity.

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

Thanks in advance.
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lightarrow
#2
Dec11-11, 12:46 PM
P: 1,521
Quote Quote by shayaan_musta View Post
Hello experts!

I have 2 questions.

1)Difference between dispersive and non-dispersive medium.

2)ω=[itex]\sqrt{\frac{4β}{m}}[/itex]sin[itex]\frac{Ka}{2}[/itex] 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([itex]\frac{Ka}{2}[/itex])→[itex]\frac{Ka}{2}[/itex]
so the equation becomes,
ω=[itex]\frac{2}{a}[/itex]νs[itex]\frac{Ka}{2}[/itex]
or,
ω=νsK
where, νs is phase velocity.

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

Thanks in advance.
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) = [itex]\frac{ω(k)}{k}[/itex]

Group velocity (if of interest) is instead the derivative: νg(k) = [itex]\frac{dω(k)}{dk}[/itex].
shayaan_musta
#3
Dec11-11, 01:15 PM
P: 184
Late reply.

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?

lightarrow
#4
Dec11-11, 06:14 PM
P: 1,521
Difference between dispersive medium and non-dispersive medium.

Quote Quote by shayaan_musta View Post
Late reply.

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?
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.
shayaan_musta
#5
Dec13-11, 01:52 PM
P: 184
Oh great
Thanks a lot.

Best answer.
Thanks.

And one thing I want to say you that kindly, visit this solid state portion at least once a week but try it every week. Because only you are here to answer the post. No one else.

Thanks once again.


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