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Question

The displacement of a wave disturbance propagating in the positive x-direction is given by y=11+x2 at t = 0 and y=11+(x−1)2 at t = 2s. Where, x and y are in metre. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is x2m/s. Find the value of x.

A
1
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B
2
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C
3
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D
5
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Solution

The correct option is A 1
y(x,0)=11+x2
y(x,2)=11+(x1)2
If the speed of the pulse is v,
y(x,t)=y(xvt,0)
y(x,2)=y(x2v,0)
Therefore,
11+(x1)2=11+(x2v)2
Comparing LHS and RHS,
v=12m/s2
Hence, x=1

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