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Standard X

Physics

Doppler Effect

Two trains ...

Question

Two trains $A$ and $B$ are moving with speeds $20 m / s$ and $30 m / s$ respectively in the same direction on the same straight track, with $B$ ahead of $A$ . The engines are at the front ends. The engine of train $A$ blows a long whistle.
Assume that the sound of the whistle is composed of components varying in frequency from $f_{1} = 800 H z$ to $f_{2} = 1120 H z$ as shown in the figure. The speed in the frequency (highest frequency lowest frequency) is thus $320 H z$ . The speed of sound in still air is $340 m / s$ .
The speed of sound of the whistle is :

340 m / s

for passengers in

A

and

310 m / s

for passenger in

B

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360 m / s

for passengers in

A

and

330 m / s

for passenger in

B

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310 m / s

for passengers in

A

and

360 m / s

for passenger in

B

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340 m / s

for passengers in both the trains

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Solution

The correct option is B $360 m / s$ for passengers in $A$ and $330 m / s$ for passenger in $B$
Applying concepts of relativity
relative velocity $= 30 - 20$
$= 10 m / s$ .
Speed of second of whistle for passenger in $A$
$340 + 20$
$= 360 m / s$ .
Speed of second of whistle for passenger in $B$
$= 340 -$ relative velocity
$= 340 - 10$
$= 330 m / s$ .

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A train running at 108 km $h^{- 1}$ towards east whistles at a dominant frequency of 600 Hz. Speed of sound in air is 340 m/s. What frequency will a passenger sitting near the open window hear ? (b) What frequency will a person standing near the track hear whom the train has just passed ? (c) A wind starts blowing towards east at a speed of 36 km $h^{- 1}$ . Calculate the frequencies heard by the passenger in the train and by the person standing near the track.

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The correct option is B 360 m/s for passengers in A and 330 m/s for passenger in BApplying concepts of relativity relative velocity =30−20=10 m/s.Speed of second of whistle for passenger in A340+20=360 m/s.Speed of second of whistle for passenger in B=340− relative velocity =340−10=330 m/s.