First slide

Doppler

Question

Two cars moving in opposite directions approach each other with speed of 22 $m s^{- 1}$ and 16.5 $m s^{- 1}$ respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is
$[velocity of sound 340 m s^{- 1}]$

Moderate

A

361 Hz
B

411 Hz
C

448 Hz
D

350 Hz

Solution

The required frequency of sound heard by the driver of second car is given as
$v^{'} = v (\frac{v + v_{o}}{v - v_{s}})$
Where v = velocity of sound
$v_{o}$ = velocity of observer, i.e., second car
$v_{s}$ = velocity of source, i.e., first car
$v^{'} = 400 (\frac{340 + 16.5}{340 - 22}) = 400 (\frac{356.5}{318})$
$v^{'} \approx 448 Hz$

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