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Wave vector direction

  1. Apr 6, 2010 #1
    Can anyone explain why the direction of a wave vector is the direction of wave propagation?
     
  2. jcsd
  3. Apr 6, 2010 #2

    HallsofIvy

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    Staff Emeritus
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    What definition of "wave vector" are you using?
     
  4. Apr 6, 2010 #3

    Dale

    Staff: Mentor

    The direction of propagation of a wave is given by the change in the location of different points with the same phase, for convenience let's say a phase of 0º. So we have:
    cos(wt-k.r) and at t=0 the location of all points with phase of 0º is given by:

    k.r=0 (all r locations perpendicular to k)

    Then at some time t later we have the position of 0º phase given by:

    k.r=wt (all r locations whose normalized projected distance along k is wt)

    So the set of points with 0º has moved a certain distance in the k direction.
     
  5. Apr 6, 2010 #4
    Just a classical 3D wave vector:

    [tex]\psi \left(t , {\mathbf r} \right) = A \cos \left(\varphi + {\mathbf k} \cdot {\mathbf r} + \omega t\right)[/tex]
     
  6. Apr 6, 2010 #5
    Thanks a lot!!!
     
  7. Apr 6, 2010 #6

    Dale

    Staff: Mentor

    You are very welcome. It is a nice little convention once you get used to it.

    Btw, welcome to PF!
     
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