JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Waves & Sound

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The driver of bus approaching a big wall notices that the frequency of his bus's horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is

330 ms^{- 1}

(A) $90 kmh^{- 1}$ ✓ Correct
(B) $80 kmh^{- 1}$
(C) $61 kmh^{- 1}$
(D) $71 kmh^{- 1}$

Answer: (A)

Solution

The bus is both the moving source of the horn and the moving observer of the echo from the wall, so the reflected frequency is

f_{2} = (\frac{v _{s} + v}{v _{s} - v}) f_{1}

. Substituting

v_{s} = 330 m s^{- 1}

f_{1} = 420 Hz

and

f_{2} = 490 Hz

gives

\frac{330 + v}{330 - v} = \frac{7}{6}

, so

6 (330 + v) = 7 (330 - v)

and

13 v = 330

. Hence

v \approx 25.4 m s^{- 1} \approx 90 km h^{- 1}

JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Single correct option

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