A person driving car at a constant speed of 15 m/s is approaching a vertical wall. The person notices a change of 40 Hz in the frequency of his car’s horn upon reflection from the wall. The frequency of horn is_____Hz.
(Given : Speed of sound = 330 m/s)

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answer is 420.

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Detailed Solution

Frequency received by

$Wall f_{1} = \frac{V}{V - V_{S}} \times f$

Now wall acts a source for the car driver.

$\begin{array}{l} f_{2} = \frac{V + V_{S}}{V} f_{1} = \frac{V + V_{S}}{V} \times \frac{V}{V - V_{S}} f \\ = \frac{V + V_{S}}{V - V_{S}} f \end{array}$

$Change in frequency = f_{2} - f$

$\begin{array}{l} = f (\frac{V + V_{S}}{V - V_{S}} - 1) = f \times \frac{2 V_{S}}{V - V_{S}} \\ 40 = f \times \frac{30}{315} \\ f = 420 H z \end{array}$