1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor

    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!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook