A person with perfect pitch sits on a bus bench listening to the 450 Hz horn of an approaching car. If the person detects a Frequency of 470 Hz, how fast is the car moving

Explanation:

Let the velocity of car be v . Let the velocity of sound be V .

We shall apply theory of  Doppler's effect to solve the problem . Expression for apparent frequency of car is as follows .

n = n₀ x V / (V-v )

here n is apparent frequency , n₀ is real frequency . V is velocity of sound .

Given n = 470 , n₀ = 450 , V = 340 m /s

Applying the given data in the given expression ,

470 = 450 x 340 / (340 - v )

340 - v = 325.5

v = 14.5 m /s .

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