Determining direction of wave propagation from the phase?

[AxiomOfChoice]

Suppose you know the phase of a wave is given by

$$\phi_1 = \vec k \cdot \vec r - \omega t.$$

How can you determine in which direction this wave is propagating? I guess, more specifically, how does a wave described by this phase differ from a wave described by the phase

$$\phi_2 = \vec k \cdot \vec r + \omega t$$

I may not have provided enough detail...please tell me if I haven't! Thanks.

 

[AxiomOfChoice]

(I was always under the impression that it was the wave vector $$\vec k$$ that carried the information about which way the wave was propagating, but recent discussions in my E&M class have caused me to question this belief.)

 

[Born2bwire]

You first need to define your time progression. If your standard is good ole e^{-i\omega t}, then the phase dependence is given by:

$$\mathbf{k}\cdot\mathbf{r}-\omega t$$

The wave propogates in the \hat{k} direction. If you have

$$\mathbf{k}\cdot\mathbf{r}-\omega t$$

as your phase progression then you must have changed your time convention to e^{i\omega t} or you are missing a minus sign here where the actual dependence is e^{-\phi_2} in which case we are progressing in the -\hat{k} direction, but this information is not given in what you have.

 

[rahulk]

Take r vector to be in the direction of k vector.
Now, take kx-wt=A (some constant phase) and differentiate it with respect to t . you get dx/dt=w/k which is the velocity of the point whose A(phase) is constant, and hence velocity of wave . It is called phase velocity. Direction of the propagation is the direction of k vector.

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