Question

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

• A. (A) 15.3GHz
• B. (B) 10.1GHz
• C. (C) 12.1 GHz
• D. (D) 17.3 GHz

Answer 1

Answer: (D)

(D) 17.3 GHz

$f^{\prime }=\left(\sqrt{\frac{1+\beta }{1-\beta }}\right)f,where\beta =\frac{v}{c}$

Hence $\beta =\frac{1}{2}$

and $f^{\prime }=\sqrt{3}\times f$

which implies $f^{\prime }=17.3GHz$