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JEE Main 201226 MayOnline
Exam
JEE Main
Year
2012
Date
26 May
Mode
Online
Subject
Physics
Chapter
Waves and Sound

JEE Main 2012 · 26 May · Online · Physics · Waves and Sound

The disturbance y(x, t) of a wave propagating in the positive x...

The disturbance y(x,t)y(x, t) of a wave propagating in the positive xx-direction is given by y=11+x2y=\frac{1}{1+x^2} at time t=0t=0 and by y=1[1+(x−12)]y=\frac{1}{\left[1+\left(x-1^2\right)\right]} at t=2 st=2 \mathrm{~s}, where xx and yy are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of wave in m/s\mathrm{m} / \mathrm{s} is

Options

  1. A2.02.0
  2. B4.04.0
  3. C0.50.5
  4. D1.01.0

Correct answer

C. 0.50.5

Step-by-step solution

The equation of wave at any time is obtained by putting X=x−vty=11+x2=11+(x−vt)2\mathrm{X}=x-\mathrm{vt}\mathrm{y}=\frac{1}{1+x^2}=\frac{1}{1+(x-v t)^2}We know at t=2sect=2 \mathrm{sec}, y=11+(x−1)2\frac{1}{1+(x-1)^2}On comparing (i) and (ii) we get vt=1v t=1 V=1t\frac{1}{t}As t=2sect=2 \mathrm{sec} \therefore V=12=\frac{1}{2}=0.5  m\mathrm{~m}/ s. \mathrm{s} \text{. }
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