First slide

Doppler

Question

The frequency of a radar is 780 MHz. After getting reflected from an approaching aeroplane, the apparent frequency is more than the actual frequency by 2.6 kHz. The aeroplane has a speed of

Moderate

A

2 km/s
B

1 km/s
C

0.5 km/s
D

0.25 km/s

Solution

$f' = (\frac{c + v_{a}}{c - v_{a}}) f$
where c is the velocity of the radio wave, an electromagnetic wave,
i.e., c = 3 × 1 $0^{8}$ m/s and $v_{s}$ is velocity of aeroplane.
$f' - f = [\frac{c + v_{a}}{c - v_{a}} - 1] f$ $\Rightarrow Δ f = \frac{2 v_{a} f}{c - v_{a}}$
Since approaching aeroplane cannot have a speed comparable to the speed of electromagnetic wave, so $v_{s} < < c .$
$Δ f = \frac{2 v_{a} f}{c}$ $\Rightarrow 2.6 \times 10^{3} = \frac{2 v_{A} (780 \times 10^{6})}{3 \times 10^{8}}$ $\Rightarrow v_{A} = 0.5 \times 103 m / s$ $= 0.5 k m / s$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App