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A radar transmitter (T) is fixed to a system $S_{2}$ which is moving to the right with speed v relative to system $S_{1}$. A timer in $S_{2}$, having a period $\tau_{0}$ (measured in $S_{2}$) causes transmitter T to emit radar pulses, which travel at the speed of light, and are received by R, a receiver fixed to $S_{1}$. If I want to calculate the signal period in different points in $S_{1}$ (point A or B) will those be different and why?

I thought the signal periods at both points are just be the dilated time with respect to the moving frame i.e $$\tau_ {A}=\tau_{B}=\tau_{0}/(1-v^{2}/c^{2})$$ (Assuming $\tau >> \tau_{0}$). But then It doesn't consider the distance in between them.

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What have you tried? The site rules forbid us from just answering your question but can provide hints if you tells us where you're stuck. – John Rennie Mar 19 '13 at 7:55
I wanted to calculate the periods in different points but I got same answer for both the points.As if the Distance between them does not matter – WInterfell Mar 19 '13 at 7:58
Can you show your working as part of the question. – John Rennie Mar 19 '13 at 8:01

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