# Homework Help: Relativistic Doppler Effect - Arbitrary Velocity

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1. May 30, 2015

### unscientific

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)

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

Is this too easy to be true?

2. May 30, 2015

### vela

Staff Emeritus
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.

3. May 30, 2015

### unscientific

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)?

4. Jun 1, 2015

bumpp