An observer is moving with half the speed of light towards a stat… - Vidyadip

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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