Q58 / 66 · JEE Advanced 2007 (Paper 2) · Physics

Paragraph: 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 engine of train $A$ blows a long whistle. Assume that the sound of the whistle is composed of components varying in frequency from $f_1=800 \mathrm{~Hz}$ 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 $340 \mathrm{~m} / \mathrm{s}$.Question: The speed of sound of the whistle is

  • A
    $340 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $310 \mathrm{~m} / \mathrm{s}$ for passengers in $B$
  • Correct answer
    B
    $360 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $310 \mathrm{~m} / \mathrm{s}$ for passengers in $B$
  • C
    $310 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $360 \mathrm{~m} / \mathrm{s}$ for passengers in $B$
  • D
    $340 \mathrm{~m} / \mathrm{s}$ for passengers in both the trains

Solution

$v_{S A}=340+20=360 \mathrm{~m} / \mathrm{s}$ $v_{S B}=340-30=310 \mathrm{~m} / \mathrm{s}$ Therefore, correct option is (b).

Hence, the correct answer is option: 'B'.

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