Question

# The equation of a wave disturbance propagating in the positive Y-direction is given by y=11+x2 at t=0 and y=1[1+(x−1)2] at t=2 s, where x and y are in metres. 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
1 m/s
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Solution

## The correct option is C 0.5 m/sGiven: At t=0, y=11+x2 or x=√1−yy=x1 At t=2 s, y=1[1+(x−1)2] or x=1+√1−yy=x2 Since the shape of the wave doesn't change during propagation, we can find velocity of the wave by calculating the distance travelled by a point having certain displacement y in given time interval. ∴v=x2−x1t2−t1=1+√1−yy−√1−yy2−0=12=0.5 m/s Hence, the correct answer is option (c).

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