Relativistic Doppler Effect - Arbitrary Velocity

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Homework Statement



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|##.

Homework Equations

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


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

Is this too easy to be true?
 
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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.
 
vela said:
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.

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)?
 
bumpp
 
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