MCQ
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 observer?.......$GHz$ ( speed of light $= 3 \times  10^8 $ $ms^{-1}$)
  • A
    $10.1 $ 
  • B
    $12.1 $ 
  • $17.3$ 
  • D
    $15.3$ 

Answer

Correct option: C.
$17.3$ 
c
Use relativistic doppler's effect as velocity of observer is not small as compared to light

$f=f_{0} \sqrt{\frac{c+v}{c+v}}$ ; $V=$ relative speed of approach

$f_{0}=10\, \mathrm{GHz}$

$\therefore f=10 \sqrt{\frac{c+\frac{c}{2}}{c-\frac{c}{2}}}=10 \sqrt{3}=17.3\, \mathrm{GHz}$

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