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. A whistling train approaches a junction. An observer standing at junction observes the frequency to be 2.2 KHz and 1.8 KHz of the approaching and the receding train respectively. Find the speed of the train (speed of sound = 300 m/s)

. A whistling train approaches a junction. An observer standing at junction observes the frequency to be 2.2 KHz and 1.8 KHz of the approaching and the receding train respectively. Find the speed of the train  (speed of sound = 300 m/s)   

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
7 years ago
Hello Student,
Please find the answer to your question
Let the speed of the train be v T
While the train is approaching
Let v be the actual frequency of the whistle. Then
V = v vS / vS - vT
Where vS = Speed of sound = 300 m/s (given)
v’ = 2.2 k Hz = 220 Hz (given)
∴ 2200 = v 300/300 – vT . . . . . . . . . . . . . (i)
While the train is receding
v = v vS/vS + vT
Here, v’ = 1.8 K Hz = 1800 Hz (given)
∴ 1800 = v 300/300 + vT . . . . . . . . . . . . . . . . . (ii)
Dividing (i) and (ii)
2200/1800 = 300/300 - vT x 300 + vT/300
⇒ vT = 30 m/s

Thanks
Jitender Pal
askIITians Faculty

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