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Relativistic Doppler Effect - Arbitrary Velocity

  1. May 30, 2015 #1
    1. The problem statement, all variables and given/known data

    Find the observed frequency ##\nu## in terms of proper frequency ##\nu_0##, speed ##v## and radial velocity component ##v_r## for a source moving at velocity ##\vec v## with respect to the observer.

    Now consider an observer in frame S where the source is seen moving at speed ##\vec v## along x-axis and at ##y=y_0##. At ##t=0##, the source is seen to emit frequency in ##-\hat y## direction. Find energy detected by the observer in terms of ##E_0## and ##|v|##.

    2. Relevant equations


    3. The attempt at a solution

    Part(a)
    Not sure how to approach this part. We've always done problems in standard configuration..


    Part (b)

    2010_B2_Q6.png

    [tex]\nu = \gamma \nu_0[/tex]
    [tex]E = \gamma E_0 = \frac{E_0}{\sqrt{1 - \frac{v^2}{c^2}}} [/tex]

    Is this too easy to be true?
     
  2. jcsd
  3. May 30, 2015 #2

    vela

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    That's right. If you think about it, this differs from the non-relativistic Doppler shift because at t=0, the source isn't moving toward or away from the observer, yet you still see a change in frequency.
     
  4. May 30, 2015 #3
    Yeah I thought so too, it's just a manifestation of time dilation (which is independent of how far you are away in the non-general relativity context).

    Any tips on part (a)?
     
  5. Jun 1, 2015 #4
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