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Q.
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:-
Solution:
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, $v_{p a}=-v e$, 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.
