Difference between dispersive medium and non-dispersive medium.

[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}ν_s\frac{Ka}{2}
or,
ω=ν_sK
where, ν_s is phase velocity.

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

Thanks in advance.

 

[lightarrow]

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}ν_s\frac{Ka}{2}
or,
ω=ν_sK
where, ν_s is phase velocity.

So ω=ν_sK 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):

ν_s(k) = \frac{ω(k)}{k}

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

 

[shayaan_musta]

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=v_sk is not for the non-dispersive medium?

 

[lightarrow]

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=v_sk is not for the non-dispersive medium?

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

 

[shayaan_musta]

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.