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181. Problem 2.44 (R) A, on the Earth, is sending signals with a flashlight every six minutes. B is on a space station that is stationary with respect to the Earth. C is on a rocket travelling from A to B with a constant velocity of 0.6c relative to A. (a) We have to find the time interval between the signals received by B from A; (b) the time interval between the signals received by C from A; and (c) if C flashes a light using intervals equal to those he received from A then the interval between the signals received by B from C.
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Solution: Click For PDF Version For solving this problem we have to use the longitudinal Doppler effect in relativity. Let the source frequency be
then the observed frequency
As period
If the source and the observer move toward one another with velocity V,
the Doppler shifted frequency and period are related to the transmitting
frequency,
(a) It is given that the space station B is stationary with respect to the
Earth, A. Therefore, there will not be any Doppler shift between the
signals transmitted from A and received by B. If the signals are
transmitted by A every six minutes,
(b) As the source A and the receiver C are moving away from one
another with velocity 0.6 c, the period of signals received by C
transmitted from A with period
(c) As the source C and the observer B are moving toward one
another with velocity V = 0.6 c the period of signals transmitted
by C,
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. If the
source and the observer move away from one another with velocity V, 
is
related to
is the
reciprocal of the frequency,
, we have
, as 
. The
period of signals received by B will also be 6 min.
, and
received by B will be Doppler shifted. We have