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Dopper Effect in Special Relativity

  1. Sep 27, 2005 #1
    Suppose there is a planet, the traffic law there is~
    car should stop if the traffic light in infrared region,i.e wavelenght ~10^-5m, otherwise the driver will be fined.
    There is a driver claimed that he saw the traffic light still in the X-ray region i.e wavelenght ~10^-10m when passing the traffic light so he hadn't violated the law
    If possible, what will be the speed of the car~

    However, I found it is impossible for the driver to have this dopper shift, as the speed of the car will be about 600c ~

    I did in following step:
    by the formula of dopper effect for SR
    [(1-v/c)/(1+v/c)]^1/2 = L0/L = 10^-5/10^-10where L is the wavelenght
    L0/L = 10^5
    the RHS value is so large~
    so I expand the LHS as:

    (0.5 - 0.5V/c) (0.5+ 0.5v/c) than I get the value as v~600c!!

    What's going wrong, can anyone help me!!!!

  2. jcsd
  3. Sep 27, 2005 #2

    Doc Al

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    Staff: Mentor

    For one thing, the doppler formula is:
    [tex]f = f' \sqrt{\frac{1 + v/c}{1 - v/c}}[/tex]

    As far as your expansion, I don't understand what you are doing. (Realize that v/c is not necessarily small compared to 1.)
    Last edited: Sep 27, 2005
  4. Sep 27, 2005 #3
    f is stand for frequency here I use wavelenght instead~
  5. Sep 27, 2005 #4

    Doc Al

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    Staff: Mentor

    You can convert from one to the other: [itex]f = c/\lambda[/itex].
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