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JEE Advance - Physics (2007 - Paper 2 Offline - No. 14)

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 speed of sound of the whistle is
$$340 \mathrm{~m} / \mathrm{s}$$ for passengers in $$\mathrm{A}$$ and $$310 \mathrm{~m} / \mathrm{s}$$ for passengers in $$\mathrm{B}$$
$$360 \mathrm{~m} / \mathrm{s}$$ for passengers in $$\mathrm{A}$$ and $$310 \mathrm{~m} / \mathrm{s}$$ for passengers in $$\mathrm{B}$$
$$310 \mathrm{~m} / \mathrm{s}$$ for passengers in $$\mathrm{A}$$ and $$360 \mathrm{~m} / \mathrm{s}$$ for passengers in $$\mathrm{B}$$
$$340 \mathrm{~m} / \mathrm{s}$$ for passengers in both the trains

Explanation

IIT-JEE 2007 Paper 2 Offline Physics - Waves Question 9 English Explanation

$$v_{\mathrm{SA}}=(340+20) \mathrm{m} / \mathrm{s}=360 \mathrm{~m} / \mathrm{s} $$

$$v_{\mathrm{SB}}=(340-30) \mathrm{m} / \mathrm{s}=310 \mathrm{~m} / \mathrm{s} $$

where, speed of sound in air = 340 m/s

Hence, the speed of sound depends on the frame of reference of observer.

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