An astronaut is approaching the moon. He sends out a radio signal of frequency 5000 MHz and the frequency of…
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. Find his velocity of approach with respect to the moon.
Solution
Sol. Let the shift in frequency be $\Delta n$.
$\Delta n = 100 \times 10^3$ Hz, $v =$ relative speed
Then, $\dfrac{\Delta n}{n}=\dfrac{2v}{c}\Rightarrow v=\dfrac{\Delta n}{2n}c=\dfrac{100\times10^3\times3\times10^8}{2\times5000\times10^6}$
$=3000\,\mathrm{ms^{-1}}=3\,\mathrm{km\ s^{-1}}$
Answer: $3000\,\mathrm{ms^{-1}}=3\,\mathrm{km\ s^{-1}}$