Question

A rockel is receding away from earth with velocity $=0.2\, c .$ The rocket emits signal or frequency $4 \times 10^{7} Hz$. The apparent frequency of the signal produced by the rocket observed by the observer on earth will be

• A. $3 \times 10^{6} Hz$
• B. $4 \times 10^{6} Hz$
• C. $2.4 \times 10^{7} Hz$
• D. $5 \times 10^{7} Hz$

Answer 1

Answer: (C)

As $v=\frac{1}{2} \frac{\Delta v}{v} c$
$\therefore 0.2 c =\frac{1}{2} \frac{\Delta v }{\left(4 \times 10^{7}\right)} c$
$\Delta v =1.6 \times 10^{7}\, Hz$
As the rocket is receding away
$\therefore v'=v-\Delta v=4 \times 10^{7}-1.6 \times 10^{7}$
$=2.4 \times 10^{7} Hz$