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JEE Advanced 2006
Exam
JEE Advanced
Year
2006
Subject
Physics
Chapter
Waves and Sound

JEE Advanced 2006 · Physics · Waves and Sound

Paragraph: Two plane harmonic sound waves are expressed by the...

Paragraph: Two plane harmonic sound waves are expressed by the equations. y1(x,t)=Acos⁡(0.5πx−100πt)y2(x,t)=Acos⁡(0.46πx−92πt)\begin{aligned} & y_1(x, t)=A \cos(0.5 \pi x-100 \pi t) \\ & y_2(x, t)=A \cos(0.46 \pi x-92 \pi t) \end{aligned} (All parameters are in MKS)Question: What is the speed of the sound?

Options

  1. A200 m/s200 \mathrm{~m} / \mathrm{s}
  2. B180 m/s180 \mathrm{~m} / \mathrm{s}
  3. C192 m/s192 \mathrm{~m} / \mathrm{s}
  4. D96 m/s96 \mathrm{~m} / \mathrm{s}

Correct answer

A. 200 m/s200 \mathrm{~m} / \mathrm{s}

Step-by-step solution

Speed of wave v=ωRv=\frac{\omega}{R} or v=100π0.5π\quad v=\frac{100 \pi}{0.5 \pi} or 92π0.46π=200 m/s\frac{92 \pi}{0.46 \pi}=200 \mathrm{~m} / \mathrm{s}
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