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Question

A transverse wave is travelling along a string from left to right. The fig. represents the shape of the string (snap-shot) at a given instant. At this instant . Which points have zero velocity
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Solution

Equation of travelling wave is given by:
y=Asin(kxωt)
Differentiating with respect to time.
v(y component)=Aωcos(kxωt)
The snapshot is taken at an instant (t is fixed), without any loss of generality let us take t= 0
Then
v=Aωcos(kx)
For v to be zero kx must be equal to either π2 or 3π2
In other words x must be equal to λ4 or 3λ4
3 and 7 satisfy this.

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