The frequency of a car horn encountered a change from 400Hz to 500Hz, when the car approaches a vertical wall. If the speed of sound is 330 m/s. Then the speed of car is_________km/h.

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Alok Kumar Singh | Contributor-Level 10

6 months ago

Initially wall will act as observer, so with the help of Doppler's effect, we can write

$f' = \frac{c}{c - v_{0}} f_{0}$

Now wall will act as source of sound of frequency f', so With the help of Doppler's effect, we can write

$f'' = \frac{c + v_{0}}{c} f^{'} = \frac{c + v_{0}}{c - v_{0}} f_{0}$

$\Rightarrow 500 = (\frac{c + v_{0}}{c - v_{0}}) 400 \Rightarrow 5 c - 5 v_{0} = 4 c + 4 v_{0} \Rightarrow v_{0} = \frac{c}{9} = \frac{330}{9} m / s = \frac{330}{9} * \frac{18}{5} k m / h = 132 k m / h$

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