A source and receiver of EM waves move relative to one another at velocity v. Let v be positive if the receiver and source are moving apart from one another. The source emits an EM wave at frequency fs (in the source frame). The time between wave fronts as measured by the source is Ts = 1/fs.
(a) In the receiver's frame, how much time elapses between the emissions of wave fronts by the source? Call this Tr€².
(b) Tr€² is not the time that the receiver measures between the arrivals of successive wave fronts because the wave fronts travel different distances. Say that, according to the receiver, one wave front is emitted at t = 0 and the next at t = To€². When the first wave front is emitted, the distance between source and receiver is dr. When the second wave front is emitted, the distance between source and receiver is dr + v Tr€². Each wave front travels at speed c. Calculate the time Tr between the arrival of these two wave fronts as measured by the receiver.
(c) The frequency detected by the receiver is fr = 1/Tr. Show that fr is given by

1- v/c