Question

# The amplitude of a wave disturbance propagating in the positive xâˆ’-direction is given by:y=11+x2 at t=0 and y=1[1+(xâˆ’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/sFrom 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/sThe correct answer is Option C:0.5 m/s

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