Question

A rocket is going towards moon with a speed $v$. The astronaut in the rocket sends a signal of frequency $f$ towards moon and receives it back on reflection from moon. What will be the frequency of the signal received by the astronaut? $(\text{Take}v<<<c)$

• A. $\left(\frac{c}{c-v}\right)f$
• B. $\left(\frac{c}{c-2v}\right)f$
• C. $\left(\frac{2v}{c}\right)f$
• D. $\left(\frac{2c}{v}\right)f$

Answer 1

The correct option is B $\left(\frac{c}{c-2v}\right)f$

When rocket is moving towards the moon, rocket is the source and moon is the observer. When the man in the rocket receives the reflected signal, the observer is moving towards the source.

So, the apparent frequency of the signal is given by, $f^{\prime }=\left(\frac{c+v}{c-v}\right)f$

$=\left(\frac{(c+v)(c-v)}{(c-v{)}^2}\right)f$

$=\left(\frac{(c^2-v^2)}{(c^2-2cv+v^2)}\right)f$

$\because v<<<c$, we can write,

$f^{\prime }=\left(\frac{c^2}{c^2-2cv}\right)f=\left(\frac{c}{c-2v}\right)f$

Hence, $\left(D\right)$ is the correct answer.