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Question

The displacement function of a wave travelling along positive x-direction is y=12+3x2 at t = 0 and by y=12+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)=12+3x2
y(x,2)=12+3(x2)2
If v is the velocity of the wave then,
y(x,t)=y(xvt,0)
Therefore,
y(x,2)=y(x2v,0)
Replacing values we get
12+3(x2)2=12+3(x2v)2
Comparing LHS and RHS,
x2=x2v
v=1m/s

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