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Group/Phase velocity - amplitude, frequency, velocity

  1. Apr 14, 2013 #1
    1. The problem statement, all variables and given/known data

    I've been working on a python simulation program that is based on phase velocity and group velocity. It looks like the following screenshot, where three parameters (E02, f2, and v2) can be adjusted. These three parameters are adjusted in terms of E01, f1, and v1.

    attachment.php?attachmentid=57864&stc=1&d=1365968654.png

    I adjusted the parameters for E_02, f2, and v2 to get the following cases:

    attachment.php?attachmentid=57865&stc=1&d=1365969062.png

    As a result of obtaining these arbitrary parameteres, I need to develop a theory that tells how to adjust these parameters E02, f2, v2 to get the group velocity designated in the cases above.

    2. Relevant equations

    I know that:
    Vp = ω/β = (2πf)/β
    VG = dω/dβ

    For the python simulation:
    Group velocity is the velocity of the envelopes, phase velocity is the velocity of the resultant wave (white curve)
    Positive velocity: Wave is moving from left to right
    Negative velocity: Wave is moving from right to left

    3. The attempt at a solution

    Observing the cases in the above table:
    For VG = 0, it appears that the value for E02 and f2 does not matter as long as v2 = 0*v1 = 0.

    For VG = VP, it is also knows the E02 = E01, f2=f1, and v2 = v1. So the parameters of one wave are equivalent to the parameters of the other wave.

    At this point, I'm a little lost. My TA says that there is an equation to be derived so that I can obtain the above cases by inputting certain values to it. I don't know where to go from here to obtain that equation. Will someone please help me? I'd highly appreciate it.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
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