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 of the following points have an upward velocity
1, 2, 3, 5, 8

Answer 1

Equation of travelling wave is given by:
$y=Asin(kx-\omega t)$
Differentiating with respect to time.
$v\left(ycomponent\right)=-A\omega cos(kx-\omega t)$
The snapshot is taken at an instant (t is fixed), without any loss of generality let us take t= 0
Then
$v=-A\omega cos\left(kx\right)$
For v to be positive kx must lie between $\frac{\pi }{2}and\frac{3\pi }{2}$
In other words x must lie between $\frac{\lambda }{4}and\frac{3\lambda }{4}$
4, 5, 6 satisfy this.