Question

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

• A. Point D, E and F have upward velocity.
• B. Point A, B and H have downward velocity
• C. Point C and G have zero velocity
• D. Point A and E have minimum velocity

Answer 1

The correct option is D Point A and E have minimum velocity

Since the wave is travelling from left to right, the positions of the points at the next instant is as shown below.


Particle velocity, $v_p=\frac{dy}{dt}=-v\left(\frac{dy}{dx}\right)$

or $v_p=$ - (wave velocity) × slope of the wave

Here, wave velocity ($v$) is positive.

(a) For upward velocity of particle, $v_p=+ve,$ so slope must be negative which is at the points D, E and F.

(b) For downward velocity of particle, $v_p=-ve,$ so slope must be positive which is at the points A, B and H.

(c) For zero velocity, slope must be zero which is at C and G.

(d) For maximum magnitude of particle velocity, slope = maximum, which is at A and E.

Hence, statement (d) is wrong.

Why this question? Tip: You can also find the particle velocity by superposing the wave forms at two successive instants & determing the required direction of motion of the particle located at a point. Particles at the peaks & troughs are instantaneously at rest.