SATHEE: Optics Question 149

Optics Question 149

Question: A rocket is going towards moon with a speed v. The astronaut in the rocket sends signals of frequency $ν$ 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)

[RPMT 1996; DPMT 2000]

Options:

A) $\frac{c}{c - v} ν$

B) $\frac{c}{c - 2 v} ν$

C) $\frac{2 v}{c} ν$

D) $\frac{2 c}{v} ν$

Show Answer

Answer:

Correct Answer: B

Solution:

In this case, we can assume as if both the source and the observer are moving towards each other with speed v.

Hence $ν ‘ = \frac{c - u_{o}}{c - u_{s}} ν = \frac{c - (- v)}{c - v} ν = \frac{c + v}{c - v} ν$

$= \frac{(c + v) (c - v)}{{(c - v)}^{2}} ν = \frac{c^{2} - v^{2}}{c^{2} + v^{2} - 2 v c} ν$ Since v«c, therefore $ν ‘ = \frac{c^{2}}{c^{2} - 2 v c} = \frac{c}{c - 2 v} ν$

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Optics Question 149

Question: A rocket is going towards moon with a speed v. The astronaut in the rocket sends signals of frequency ν 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)

Options:

Answer:

Solution:

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Question: A rocket is going towards moon with a speed v. The astronaut in the rocket sends signals of frequency $ν$ 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)