First slide

Doppler

Question

A speeding motorcyclist sees traffic jam ahead him. He slows down to 36 km hour $^{- 1}$ . He finds that traffic has eased and a car moving ahead of him at 18 km hour $^{- 1}$ is honking at a frequency of 1392 Hz. If the speed of sound is 343 m $s^{- 1}$ , the frequency of the honk as heard by him will be

Easy

A

1332 Hz
B

1372 Hz
C

1412 Hz
D

1454 Hz

Solution

Here speed of Motorcyclist speed is
$v_{m} = 36 km {hour}^{- 1} = 36 \times \frac{5}{18} m s^{- 1} = 10 m s^{- 1}$
Speed of car,
$v_{c} = 18 km {hour}^{- 1} = 18 \times \frac{5}{18} m s^{- 1} = 5 m s^{- 1}$
Frequency of source, $ν_{0}$ = 1392 Hz
Speed of sound, $ν =$ 343 m $s^{- 1}$
The frequency of the honk heard by the motorcyclist is
$v^{'} = v_{0} (\frac{v + v_{m}}{v + v_{c}}) = 1392 (\frac{343 + 10}{343 + 5}) = \frac{1392 \times 353}{348} = 1412 Hz$

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