Question

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency $10GHz$. What is the frequency of the microwave measured by the observer? (speed of light $=3\times {10}^{8}m{s}^{-1}$)

• A. $10.1GHz$
• B. $12.1GHz$
• C. $17.3GHz$
• D. $15.3GHz$

Answer 1

The correct option is C

$17.3GHz$

Explanation for the correct option:

Frequency of the light source, $f_0=10GHz$

We know that speed of the observer​, $v=\frac{C}{2}$

Using relativistic Doppler effect in case observer moves towards the stationary source.

Apparent frequency measured by observer, $f\prime =f_0\sqrt{\frac{C+v}{C-v}}$

$$\begin{gathered} =f_0\sqrt{\frac{C+{\displaystyle \frac{C}{2}}}{C-{\displaystyle \frac{C}{2}}}} \\ =f_0\sqrt{\frac{{\displaystyle \frac{3C}{2}}}{{\displaystyle \frac{C}{2}}}} \\ =10\sqrt{3} \\ =10x1.73 \\ =17.3GHz \end{gathered}$$

Thus, frequency of the microwave measured by the observer is $17.3GHz$

Hence, Option C is correct.