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JEE Advance - Physics (2007 - Paper 2 Offline - No. 15)

Two trains $$A$$ and $$B$$ are moving with speeds $$20 \mathrm{~m} / \mathrm{s}$$ and $$30 \mathrm{~m} / \mathrm{s}$$ respectively in the same direction on the same straight track, with $$B$$ ahead of $$A$$. The engines are at the front ends. The engines of train A blows a long whistle.

Assume that the sound of the whistle is composed of components varying in frequency from $$f_{1}=800 \mathrm{~Hz}$$ to $$f_{2}=1120 \mathrm{~Hz}$$, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus $$320 \mathrm{~Hz}$$. The speed of sound in still air is $$340 \mathrm{~m} / \mathrm{s}$$.

Two trains $$A$$ and $$B$$ are moving with speeds $$20 \mathrm{~m} / \mathrm{s}$$ and $$30 \mathrm{~m} / \mathrm{s}$$ respectively in the same direction on the same straight track, with $$B$$ ahead of $$A$$. The engines are at the front ends. The engines of train A blows a long whistle.

Assume that the sound of the whistle is composed of components varying in frequency from $$f_{1}=800 \mathrm{~Hz}$$ to $$f_{2}=1120 \mathrm{~Hz}$$, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus $$320 \mathrm{~Hz}$$. The speed of sound in still air is $$340 \mathrm{~m} / \mathrm{s}$$.

Two trains $$A$$ and $$B$$ are moving with speeds $$20 \mathrm{~m} / \mathrm{s}$$ and $$30 \mathrm{~m} / \mathrm{s}$$ respectively in the same direction on the same straight track, with $$B$$ ahead of $$A$$. The engines are at the front ends. The engines of train A blows a long whistle.

Assume that the sound of the whistle is composed of components varying in frequency from $$f_{1}=800 \mathrm{~Hz}$$ to $$f_{2}=1120 \mathrm{~Hz}$$, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus $$320 \mathrm{~Hz}$$. The speed of sound in still air is $$340 \mathrm{~m} / \mathrm{s}$$.

The distribution of the sound intensity of the whistle as observed by the passengers in train $$\mathrm{A}$$ is best represented by
IIT-JEE 2007 Paper 2 Offline Physics - Waves Question 7 English Option 1
IIT-JEE 2007 Paper 2 Offline Physics - Waves Question 7 English Option 2
IIT-JEE 2007 Paper 2 Offline Physics - Waves Question 7 English Option 3
IIT-JEE 2007 Paper 2 Offline Physics - Waves Question 7 English Option 4

Explanation

Since all the passengers in train A are moving with a velocity of $$20 \mathrm{~m} / \mathrm{s}$$ therefore the distribution of sound intensity of the whistle by the passengers in the train $$A$$ is uniform.

Trick : Total frequency $$=(1120-800) \mathrm{Hz} =320 \mathrm{~Hz}$$

IIT-JEE 2007 Paper 2 Offline Physics - Waves Question 7 English Explanation

There is no relative motion between source and observer.

Therefore, all the passengers will hear the sound of same intensity.

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