Waves

JEE Main level, single correct, medium

44 of 142

Question 44 of 142

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

Show answer and solution

Answer: (C) 0.50.5

The equation of wave at any time is obtained by putting X=x−vt\mathrm{X}=x-\mathrm{vt}
y=11+x2=11+(x−vt)2\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)2y=\frac{1}{1+(x-1)^2}
On comparing (i) and (ii) we get vt=1v t=1
V=1tV=\frac{1}{t}
As t=2sect=2 \mathrm{sec}

∴V=12=0.5 m/s. \therefore V=\frac{1}{2}=0.5 \mathrm{~m} / \mathrm{s} \text {. }

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Standing waves on a string simulationDrag the sliders and watch the numbers in this question change.

More Physics practice

JEE Main Physics practice question on Waves (Travelling Waves), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.