Difference between dispersive medium and non-dispersive medium.

  1. 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.
     
  2. jcsd
  3. 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].
     
  4. 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?
     
  5. 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.
     
  6. 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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