Question

A transverse wave is travelling along a string from left to right. The figure below represents the shape of the string at a given instant. At this instant, among the following, choose the wrong statement:

• A. Points D, E, F have upwards positive velocity.
• B. Points A, B and H have downwards negative velocity.
• C. Point C and G have zero velocity.
• D. Points A and E have minimum velocity.

Answer 1

The correct option is D Points A and E have minimum velocity.

Remember that in any wave motion, the wave only appears to be going forward, but the particles do not go forward. They oscillate along with their mean positions. The farthest point is the 1st in oscillating and the nearest is the last.

The X-axis is their mean position and the topmost part of a crest is the positive extreme and the bottom part of a trough is the negative extreme.

The following particles will have upward velocity:

$H\because$ it has finished crossing the negative extreme and is now coming back to the mean.

$B\because$ it is going towards the positive extreme.

$A\because$ it has just started moving towards the positive extreme.

The following particles will have downward velocity:

$F\because$ it has finished crossing the mean and is now heading towards the negative extreme.

$D\because$ it has finished crossing the positive extreme and is now coming back to the mean.

$E\because$ it has just started moving towards the negative extreme.

In any oscillation, the particle has zero velocity at the any extreme and maximum at the mean

Hence $C$ and $G$ have zero velocity and, $A$ and $E$ have maximum speed. The direction of $A$ is upward and for E is downward.
Hence the wrong statement is given in option $\left(D\right)$
So, the correct answer is $\left(D\right)$.