Relativistic Doppler Effect - Arbitrary Velocity

[unscientific]

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)

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

Is this too easy to be true?

 

[vela]

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.

 

[unscientific]

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)?

 

[unscientific]

bumpp