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Can anyone explain why the direction of a wave vector is the direction of wave propagation?

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- Thread starter stevvvvv
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- #1

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Can anyone explain why the direction of a wave vector is the direction of wave propagation?

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HallsofIvy

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What **definition** of "wave vector" are you using?

- #3

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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.

- #4

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

- #5

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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!!!

- #6

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

Btw, welcome to PF!

Btw, welcome to PF!

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