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Question

The amplitude of a wave disturbance propagating in the positive x−-direction is given by:
y=11+x2 at t=0 and y=1[1+(x−1)2] at t=2 sec. Where, x and y are in meters. If the shape of the wave disturbance does not change during the propagation, what is the velocity of the wave?

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

The correct option is D 0.5 m/s
From the given y(x) equations at two different times we can see that the value of y is maximum (=1 m) at x=0 at t=0 and at x=1 at t=2.
So, the peak of the wave pulse has travelled a distance of 1 m (from x=0 to x=1) in 2 s along positive x - direction.
Hence, the wave velocity is:
v=12=0.5 m/s
The correct answer is Option C:0.5 m/s

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