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Question

A train moves towards a stationary observer with a speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is f1. If the speed of the train is reduced to 17 m/s, the frequency registered is f2. If the speed of sound is 340 m/s , then the ratio f1f2 is

[Assume, medium is stationary ]

A
1819
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B
12
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C
2
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D
1918
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Solution

The correct option is D 1918
Let f0 be the frequency of sound heard by the observer, when both the source of sound and observer are at rest.
Let v be the velocity of sound in the stationary medium and vs be the velocity of the source of sound.

When a source is moving towards a stationary observer, the frequency heard by the observer is given by

fapp=f0(vvvs) .....(1)

From the data given in the question,

Case -1 :

When the speed of train is vs=34 m/s,

Using (1), we get

f1=f0(34034034)=340306f0 .....(2)

Case -2:

When the speed of train is vs=17 m/s
Using (1), we get
f2=f0(34034017)=340323f0 ......(3)

From (2) and (3), we get

f1f2=323306f1f2=1918

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