## Wave vector

Can anyone explain why the direction of a wave vector is the direction of wave propagation?
 Recognitions: Gold Member Science Advisor Staff Emeritus What definition of "wave vector" are you using?
 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.

## Wave vector

Just a classical 3D wave vector:

$$\psi \left(t , {\mathbf r} \right) = A \cos \left(\varphi + {\mathbf k} \cdot {\mathbf r} + \omega t\right)$$

 Quote by DaleSpam 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.
Thanks a lot!!!
 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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