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

Answer: (D)

$17.3GHz$

According to Doppler's law, when source or observer is in relative motion, apparent frequency is slightly different from real one;

${\nu }^{\prime }=10\sqrt{\frac{c+\nu }{c-\nu }}$

Here,

${\nu }^{\prime }=10\sqrt{\frac{1+\frac{1}{2}}{1-\frac{1}{2}}}$

${\nu }^{\prime }=10\times \sqrt{3}GHz$

${\nu }^{\prime }=17.3GHz$