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Grade 10Wave Motion

. 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)

Hrishant Goswami

12 Years agoGrade 10

1 Answer

Jitender Pal

12 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 v_S / v_S- v_T

Where v_S = Speed of sound = 300 m/s (given)

v’ = 2.2 k Hz = 220 Hz (given)

∴ 2200 = v 300/300 – v_T . . . . . . . . . . . . . (i)

While the train is receding

v^” = v v_S/v_S + v_T

Here, v’ = 1.8 K Hz = 1800 Hz (given)

∴ 1800 = v 300/300 + v_T . . . . . . . . . . . . . . . . . (ii)

Dividing (i) and (ii)

2200/1800 = 300/300 - v_T x 300 + v_T/300

⇒ v_T = 30 m/s

Thanks
Jitender Pal
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