A transverse wave is travelling along a string from left to right… - Vidyadip

MCQ

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
✓
Points $A$ and $E$ have minimum velocity

✓

Answer

Correct option: D.

Points $A$ and $E$ have minimum velocity

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

or $\frac{\mathrm{dy}}{\mathrm{dt}}=-$ wave velocity $\times$ slope of the wave

$(1)$ For upward velocity, $v_{\mathrm{Pa}}=+\mathrm{ve},$ so slope must be negative which is at the points $D,$ $\mathrm{E}$ and $\mathrm{F}$

$(2)$ For downward velocity, $v_{\mathrm{Pa}}=-\mathrm{ve},$ so slope must be positive which is at the points $A, B$ and $\mathrm{H}$

$(3)$ For zero velocity, slope must be zero which is at $\mathrm{C}$ and $\mathrm{G}$

$(4)$ For maximum magnitude to velocity. $|$ slope $|=$ maximum, which is at $A$ and $\mathrm{E}$. Hence, alternative is wrong.

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