# Difference between dispersive medium and non-dispersive medium.

by shayaan_musta
Tags: difference, dispersive, nondispersive
 P: 184 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? Thanks in advance.
P: 1,521
 Quote by 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? 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) = $\frac{ω(k)}{k}$

Group velocity (if of interest) is instead the derivative: νg(k) = $\frac{dω(k)}{dk}$.
 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?
P: 1,521
Difference between dispersive medium and non-dispersive medium.

 Quote by 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=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.
 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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