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JEE Main 2021 (20 Jul, Shift 1) · Progressive Wave Equation

Progressive Wave Equation question from JEE Main 2021 (20 Jul, Shift 1)

Q79JEE Main 2021 · 20 JUL · SHIFT 1Difficult

Progressive Wave Equation

The amplitude of wave disturbance propagating in the positive x-direction is given by $y = \frac{1}{1 + x^2}$ at time t = 0 and $y = \frac{1}{1 + (x - 2)^2}$ at t = 1 s, where x and y are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be ___________ m/s.

Numerical answer type. Work it out, then open the answer.

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Answer: 2

The peak ( $y = 1$ ) is at $x = 0$ at $t = 0$ and at $x = 2\text{ m}$ at $t = 1\text{ s}$ .
Shape is unchanged, so the pulse moves $2\text{ m}$ in $1\text{ s}$ .
$v = 2\text{ m/s}$

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