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JEE Main 20139 AprilOnline
Exam
JEE Main
Year
2013
Date
9 April
Mode
Online
Subject
Physics
Chapter
Waves and Sound

JEE Main 2013 · 9 April · Online · Physics · Waves and Sound

When two sound waves travel in the same direction in a medium, the...

When two sound waves travel in the same direction in a medium, the displacements of a particle located at ' xx ' at time ' tt ' is given by : y1=0.05cos⁡(0.50πx−100πt)y2=0.05cos⁡(0.46πx−92πt)\begin{aligned} & y_1=0.05 \cos (0.50 \pi x-100 \pi t) \\ & y_2=0.05 \cos (0.46 \pi x-92 \pi t) \end{aligned} where y1,y2andxy_1, y_2 and x are in meters and tt in seconds. The speed of sound in the medium is :

Options

  1. A92 m/s92 \mathrm{~m} / \mathrm{s}
  2. B200 m/s200 \mathrm{~m} / \mathrm{s}
  3. C100 m/s100 \mathrm{~m} / \mathrm{s}
  4. D332 m/s332 \mathrm{~m} / \mathrm{s}

Correct answer

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

Step-by-step solution

Standard equation y(x,t)=Acos⁡y(x, t)=A \cos\left(\frac{\omega}{V} x-\omega t\right)FromanyofthedisplacementequationSayFrom any of the displacement equation Say\mathrm{y}_1 \frac{\omega}{\mathrm{V}}=0.50 \piandand\omega=100 \pi \therefore \frac{100 \pi}{\mathrm{V}}=0.5 \pi \therefore \mathrm{V}=\frac{100 \pi}{0.5 \pi}=200 \mathrm{~m} / \mathrm{s}
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