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Determining direction of wave propagation from the phase?

  1. Dec 16, 2009 #1
    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.
  2. jcsd
  3. Dec 16, 2009 #2
    (I was always under the impression that it was the wave vector [tex]\vec k[/tex] 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.)
  4. Dec 16, 2009 #3


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    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:

    [tex]\mathbf{k}\cdot\mathbf{r}-\omega t[/tex]

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

    [tex]\mathbf{k}\cdot\mathbf{r}-\omega t[/tex]

    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.
  5. Dec 18, 2009 #4
    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.

    http://www.actionurl.com/jpxp [Broken]
    Last edited by a moderator: May 4, 2017
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