Question

A rocket is going away from the earth at a speed $0.2c$, where c = speed of light. It emits a signal of frequency $4\times {10}^{7}Hz$. What will be the frequency observed by an observer on the earth?

• 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 $3.2\times {10}^{7}Hz$

Frequency observed by an observer on earth will vary as function of speed of rocket and speed of light as follows-
$v\text{'}=v\left(1-\frac{v}{c}\right)=4\times {10}^7\left(1-\frac{0.2c}{c}\right)=3.2\times {10}^{7}Hz$