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Question

The equation of a transverse wave traveling on a rope is given by y=10sinπ(0.01x2.000t) where y and x are in cm and t in seconds. The maximum transverse speed of a particle in the rope is about

A
62.8 cm/s
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B
75 cm/s
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C
100 cm/s
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D
121 cm/s
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Solution

The correct option is A 62.8 cm/s
Given a string wave of the form:
y=Aosin(kxωt)

The transverse speed is the rate change of the y coordinate of the particle on the rope
so,
vy=yt

vy=t(Aosinπ(kxωt))

vy=Aoωπcosπ(kxωt)

Now for maximum transverse speed cosπ(kxωt)=1
So, vy(max)=Aoπω

Putting the values
vy(max)=10×π×2.000=62.8cm/s

So A is the right answer.

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