Question

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

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

Answer 1

The correct option is A 17.3 GHz

According to relative Doppler effect:

${\gamma }_D={\gamma }_0\sqrt{\frac{1+V/C}{1-V/C}}$ where,

${\gamma }_D$ is the observed frequency

${\gamma }_0$ is the frequency of light in the source rest frame

$V$ is the relative velocity between observer and source.

Therefore, ${\gamma }_D=10\sqrt{\frac{1+1/2}{1-1/2}}$

$=10\times \sqrt{3}=17.3$GHz