Question

An astronaut is approaching the moon. He sends out a radio signal of frequency 5000 MHz and the frequency of echo is different from that of the original frequency by 100 kHz. His velocity of approach wrt, to the moon, is ______.

Options

• 2 kms^-1

• 3 kms^-1

• 4 kms^-1

• 5 kms^-1

Answer 1

An astronaut is approaching the moon. He sends out a radio signal of frequency 5000 MHz and the frequency of echo is different from that of the original frequency by 100 kHz. His velocity of approach wrt, to the moon, is 3 kms^-1.

Explanation:

Let the shift in apparent frequency be Δn,

then Δn = `100 xx 10^3` Hz = 10⁵ Hz

n = 500 MHz = `5000 xx 10^6` Hz = `5 xx 10^9` Hz

and v = relative speed

Then, `(Deltan)/n = (2ν)/c`

⇒ v = `(Deltan)/(2n)c = 10^5/(2 xx 5 xx 10^9) xx 3 xx 10^8`

= 3000 ms^-1

= 3 kms^-1