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JEE Advanced 2007Paper 2
Exam
JEE Advanced
Year
2007
Paper
Paper 2
Subject
Physics
Chapter
Waves and Sound

JEE Advanced 2007 · Paper 2 · Physics · Waves and Sound

Paragraph: Two trains A and B are moving with speeds 20 ~m / s and...

Paragraph: Two trains AA and BB are moving with speeds 20 m/s20 \mathrm{~m} / \mathrm{s} and 30 m/s30 \mathrm{~m} / \mathrm{s}, respectively in the same direction on the same straight track, with BB ahead of AA. The engines are at the front ends. The engine of train AA blows a long whistle. Assume that the sound of the whistle is composed of components varying in frequency from f1=800 Hzf_1=800 \mathrm{~Hz} to f2=1120 Hzf_2=1120 \mathrm{~Hz}, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus 320 Hz320 \mathrm{~Hz}. The speed of sound in still air is 340 m/s340 \mathrm{~m} / \mathrm{s}.Question: The spread of frequency as observed by the passengers in train BB is

Options

  1. A310 Hz310 \mathrm{~Hz}
  2. B330 Hz330 \mathrm{~Hz}
  3. C350 Hz350 \mathrm{~Hz}
  4. D290 Hz290 \mathrm{~Hz}

Correct answer

A. 310 Hz310 \mathrm{~Hz}

Step-by-step solution

For the passengers in train BB, observer is receding with velocity 30 m/s30 \mathrm{~m} / \mathrm{s} and source is approaching with velocity 20 m/s20 \mathrm{~m} / \mathrm{s}. ∴f1′=800(340−30340−20)=775 Hz and f2′=1120(340−30340−20)=1085 Hz\begin{array}{ll} \therefore& f_1^{\prime}=800\left(\frac{340-30}{340-20}\right)=775 \mathrm{~Hz}\\ \text{ and }& f_2^{\prime}=1120\left(\frac{340-30}{340-20}\right)=1085 \mathrm{~Hz} \end{array}\thereforeSpreadoffrequencySpread of frequency=f_2^{\prime}-f_1^{\prime}=310 \mathrm{~Hz}\therefore$ The correct option is (a).
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