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Question

The displacement function of a wave travelling along positive x-direction is $$\displaystyle y\, =\, \frac{1}{2\, +\, 3x^2}$$ at t = 0 and by $$\displaystyle y\, =\, \frac{1}{2\, +\, 3\, (x\, -\, 2)^2}$$ at t = 2s, where y and x are in metre. The velocity of the wave is


A
2 m/s
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B
0.5 m/s
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C
1 m/s
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D
3 m/s
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Solution

The correct option is B 1 m/s
Given:
$$y(x,0)=\dfrac{1}{2+3{x}^{2}}$$
$$y(x,2)=\dfrac{1}{2+3{(x-2)}^{2}}$$
If $$v$$ is the velocity of the wave then,
$$y(x,t)=y(x-vt,0)$$
Therefore,
$$y(x,2)=y(x-2v,0)$$
Replacing values we get
$$\dfrac{1}{2+3{(x-2)}^{2}}=\dfrac{1}{2+3{(x-2v)}^{2}}$$
Comparing LHS and RHS,
$$x-2=x-2v$$
$$v=1m/s$$

Physics

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