First slide

Doppler

Question

A radar sends a radio signal of frequency 9 x 10⁹ Hz towards an aircraft approaching the radar. If the reflected wave shows a frequency shift of 3 x 10³ Hz, the speed with which the aircraft is approaching the radar, in m/s is (velocity of the radio signal is 3 x 10⁸ m/s

Moderate

A

150
B

100
C

50
D

25

Solution

Let v_s, be the velocity of jet, then change in frequency dn is given by
$dn = n (\frac{2 v_{s}}{c}) or 3 \times 10^{3} = (9 \times 10^{9}) \times \frac{2 v_{s}}{(3 \times 10^{8})} v_{s} = \frac{(3 \times 10^{3}) \times (3 \times 10^{8})}{2 \times (9 \times 10^{9})} = 50 m / s$

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