Question:
The driver of a 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.
The driver of a 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.
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The wall first acts as a stationary observer and then as a stationary source: \(f' = f\dfrac{v+u}{v-u}\).
Updated On: Nov 5, 2026
- 91 kmh-1
- 81 kmh-1
- 61 kmh-1
- 71 kmh-1
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The Correct Option is A
Solution and Explanation
Let the bus speed be u and the speed of sound v = 330 m/s.
The wall receives \(f_1 = f\dfrac{v}{v-u}\) and reflects it. The driver, moving towards the wall, hears \(f_2 = f_1\dfrac{v+u}{v} = f\dfrac{v+u}{v-u}\).
\(\dfrac{490}{420} = \dfrac{7}{6} = \dfrac{330+u}{330-u}\Rightarrow 6(330+u) = 7(330-u)\Rightarrow 13u = 330\).
\(u = \dfrac{330}{13} = 25.38\) m/s \(= 25.38\times3.6 = 91.4\) km/h \(\approx 91\) km/h.
Answer: (1) 91 kmh-1
The wall receives \(f_1 = f\dfrac{v}{v-u}\) and reflects it. The driver, moving towards the wall, hears \(f_2 = f_1\dfrac{v+u}{v} = f\dfrac{v+u}{v-u}\).
\(\dfrac{490}{420} = \dfrac{7}{6} = \dfrac{330+u}{330-u}\Rightarrow 6(330+u) = 7(330-u)\Rightarrow 13u = 330\).
\(u = \dfrac{330}{13} = 25.38\) m/s \(= 25.38\times3.6 = 91.4\) km/h \(\approx 91\) km/h.
Answer: (1) 91 kmh-1
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