Q. A rocket is going towards moon with a speed $v$. The astronaut in the rocket sends signals of frequency $v$ towards the moon and receives them back on reflection from the moon. What will be the frequency of the signal received by the astronaut (Take $v \ll c$)
A) $\frac{c}{c - v}v$
B) $\frac{c}{c - 2v}v$
C) $\frac{2v}{c}v$
D) $\frac{2c}{v}v$
Explanation
(b) In this case, we can assume that both the source and the observer are moving towards each other with speed
$v$. Hence $v^{'} = \frac{c - u_{o}}{c - u_{s}} = \frac{c - ( - v)}{c - v}v = \frac{c + v}{c - v}v$
$= \frac{(c + v)(c - v)}{(c - v)^{2}}v = \frac{c^{2} - v^{2}}{c^{2} + v^{2} - 2vc}v$
Since $v < \ < c$, therefore $v^{'} = \frac{c^{2}}{c^{2} - 2vc} = \frac{c}{c - 2v}v$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.