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

Answer 1

The correct option is D $17.3GHz$

Speed of observer, $v=\frac{C}{2}$

where speed of microwave is $C$.

Original frequency of source is given as $f_0=10GHz$

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

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

$f^{\prime }=10\sqrt{\frac{C+\left(C/2\right)}{C-\left(C/2\right)}}$

$=10\sqrt{\frac{\left(3/2\right)C}{\left(1/2\right)C}}$

$=10\times 1.73GHz$

$=17.3GHz$