A transverse wave is travelling along a string in the positive x-axis. The

shows the photograph of the wave at an instant. Find
(a) the points moving upwards
(b) the points moving downwards
(c ) the points which have zero velocity
(d) the points which have maximum velocity

Explanation

The dotted curved in the figure reprensents the position of the wave at a later instant. It can be easily obtained from the figure that

(a) Point D,E, and `F` move upward. (b) points `A,B,H,` and `I` move downward. (c ) points `C`, and `G` have zero velocity. (d) points `A,E,` and `I` have the maximum velocity
Method `2:` particle velocity `V_(p)=-wave velocity xx(dy)/(dx)`
As the wave travel in positive `x-`direction. the point having `dy//dxgt0` will move down, `dy//dxlt0` will move up and `dy//dxgt0` the points having will be at rest. the points having maximum magnitude of `(dy)/(dx)` will have maximum magnitude of speed.