First slide

Doppler's effect

Question

Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of 72 km/hr and 36 km/hr. If first car blows horn of frequency 280 Hz, then the frequency of horn heard by the driver of second car when line joining the cars make 45° angle with the roads; will be

Difficult

A

321 Hz
B

298 Hz
C

289 Hz
D

280 Hz

Solution

Here $v_{A} = 72 km / hr = 20 m / \sec$
$v_{B} = 36 km / hr = 10 m / \sec$
$n' = n (\frac{v + v_{B} \cos 45^{o}}{v - v_{A} \cos 45^{o}})$
$\Rightarrow n' = 280 (\frac{340 + 10 / \sqrt{2}}{340 - 20 / \sqrt{2}}) = 298 Hz$

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