A policeman is chasing a thief from behind, while riding on a bike which is moving with a speed of 54 kmh -…

A policeman is chasing a thief from behind, while riding on a bike which is moving with a speed of 54 kmh - 1. The thief is also riding on a bike moving with a speed of 72 kmh -1. When the policeman blows horn of the bike having frequency of 200 Hz. Find the apparent frequency heard by the thief. (Take, speed of sound = 330 ms - 1).

Solution

Sol. Given, $v_s = 54\ \mathrm{kmh}^{-1} = 15\ \mathrm{ms}^{-1}$, $v_o = 72\ \mathrm{kmh}^{-1} = 20\ \mathrm{ms}^{-1}$, $v = 330\ \mathrm{ms}^{-1}$ and $f = 200\ \mathrm{Hz}$ Therefore, Apparent frequency observed by the thief, $f' = \left(\frac{v - v_o}{v - v_s}\right) f = \left(\frac{330 - 20}{330 - 15}\right) \times 200$ $= \frac{310}{315} \times 200 = 196.82\ \mathrm{Hz}$ Answer: 196.82 Hz

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