Question

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

• A. 4 $\times$ 10${}^6$ Hz
• B. 3.2 $\times$ 10${}^7$ Hz
• C. 3 $\times$ 10${}^6$ Hz
• D. 5 $\times$ 10${}^7$ Hz

Answer 1

The correct option is B 3.2 $\times$ 10${}^7$ Hz

$\Delta$v = $\frac{\nu }{c}\times$

$v=\frac{0.2c}{c}\times 4\times {10}^7$ = 0.8 $\times {10}^7$ Hz

$v^{\prime }=v-\Delta$v = $4\times {10}^7-0.8\times {10}^7$ = 3.2 $\times {10}^7$ Hz