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A rocket is going towards moon with a speed v. The astronaut in the rocket sends signals of frequency n 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 < <c)

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a

$\frac{cn}{c â 2 v}$

b

$\frac{2 c n}{V}$

c

$\frac{cn}{c â v}$

d

$\frac{2 Vn}{c}$

answer is B.

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Detailed Solution

In this case, we can assume that both the source and observer are moving towards each other with velocity v' If c be the velocity of signal, then
${Î·}^{â²} = (\frac{c + v}{c â v}) n or n^{â²} = [\frac{(C + V) (C â V)}{(C â V)^{2}}] n n = [\frac{c^{2} â v^{2}}{c^{2} + v^{2} â 2 cv}] n = (\frac{c^{2}}{c^{2} â 2 cv}) n (âµ c >> v) (\frac{c}{c â 2 v}) n$

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