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

Answer 1

Answer: (D)

Particle velocity, $\frac{dy}{dt}=-v\left(\frac{dy}{dx}\right)$
or $\frac{dy}{dt}=-$ wave velocity $\times$ slope of the wave
(a) For upward velocity, $v_{pa}=+ve$, so slope
must negative which is at the points $D,E$ and $F$.

(b) For downward velocity, $v_{pa}=-ve$, 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 velocity,
$\mid$ slope $\mid =$ maximum, which is at $A$ and $E$.
Hence, alternative is wrong.