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A train approaching a hill at a speed of 40 km/hr sounds a whistle of frequency 580 Hz when it is at a distance of 1 km from a hill. A wind with a speed of 40 km/hr is blowing in the direction of motion of the train Find (i) The Frequency of the whistle as heard by an observer on the hill, (ii) The distance from the hill at which the echo from the hill is heard by the driver and its frequency. (Velocity of sound in air = 1,200 km /hr

A train approaching a hill at a speed of 40 km/hr sounds a whistle of frequency 580 Hz when it is at a distance of 1 km from a hill. A wind with a speed of 40 km/hr is blowing in the direction of motion of the train Find
(i) The Frequency of the whistle as heard by an observer on the hill,
(ii) The distance from the hill at which the echo from the hill is heard by the driver and its frequency.
(Velocity of sound in air = 1,200 km /hr

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
Hello Student,
Please find the answer to your question
(i) The frequency of the whistle as heard by observer on the hill
n1 = n[v + vm/v + vm – vs]
236-2462_6.png
= 580 [ 1200 + 40/1200 + 40 – 40] = 599 Hz
(ii) Let echo from the hill is heard by the driver at B which is at a distance x from the hill.
The time taken by the driver to reach from A to B
t1 = 1 – x/40 . . . . . . . . . . . . . . . (i)
The time taken by the echo to reach from hill
t2 = tAH + tHB
t2 = 1/(1200 + 40) + x/(1200 – 40) . . . . . . . . . . . . . . . (ii)
where tAH = time taken by sound from A to H with velocity (1200 + 40)
tHB = time taken by sound from H to B with velocity 1200 – 40 From (i) and (ii)
t1 = t2 ⇒ 1 – x/40 = 1/1200 + 10 + x/1200 – 40
⇒ x = 0.935 km
The frequency of echo as heard by the driver can be calculated by considering that the source is the acoustic image.
n” = n[(v – vm) + vs/(v – vm) – vo]
= 580 [(1200 – 40) + 40/(1200 – 40) – 40] = 621 Hz

Thanks
Aditi Chauhan
askIITians Faculty

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