A radar transmitter T is fixed to a reference frame S 1 that is moving to the ri

Question

A radar transmitter T is fixed to a reference frame S1 that is moving to the right with speed v relative to reference frame S (the figure below). A mechanical timer (essentially a clock) in frame S1, having a period T0 (measured in S1), causes transmitter T to emit timed radar pulses, which travel at the speed of light and are received by R, a receiver fixed in frame S. (a) What is the period of the timer as detected by observer A, who is fixed in frame S? (b) What is the time interval between pulses arriving at R? State your answers in terms of the given variables, using c when needed.

There are two answers that will be derived from the above data with no numbers

A radar transmitter T is fixed to a reference frame S1 that is moving to the right with speed v relative to reference frame S (the figure below). A mechanical timer (essentially a clock) in frame S1, having a period T0 (measured in S1), causes transmitter T to emit timed radar pulses, which travel at the speed of light and are received by R, a receiver fixed in frame S. (a) What is the period of the timer as detected by observer A, who is fixed in frame S? (b) What is the time interval between pulses arriving at R? State your answers in terms of the given variables, using c when needed. There are two answers that will be derived from the above data with no numbers

Explanation / Answer

If s is fixed.

frequency = 1/period = 1/T0

By doppler effect, frequency = frequency*(v+v_receiver)/(v+v_source) = 1/T0*(c/(c-v))

b) Time interval = 1/frequency = T0*(1-v/c)

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