# A rocket is receding away from earth with velocity = 0.2 c. The rocket emits signal of frequency 4×10^7 Hz .

Q:A rocket is receding away from earth with velocity = 0.2 c. The rocket emits signal of frequency 4 × 107 Hz . The apparent frequency of the signal produced by the rocket observed by the observer on earth will be

(a) 3 × 106 Hz

(b) 4 × 106 Hz

(c) 2.4 × 107 Hz

(d) 5 × 107 Hz

Ans:(c)

Sol: As , $\displaystyle v = \frac{1}{2} \times \frac{\Delta \nu}{\nu} c$

$\displaystyle 0.2 c = \frac{1}{2} \times \frac{\Delta \nu}{4 \times 10^7} c$

$\displaystyle \Delta \nu = 1.6 \times 10^7 Hz$

As the rocket is receding away

$\displaystyle \Delta \nu = \nu – \nu’$

$\displaystyle \nu’ = \nu – \Delta \nu$

$\displaystyle = 4 \times 10^7 – 1.6 \times 10^7$

= 2.4 × 107 Hz