Question

A transverse wave is travelling from left to right. The shape of the string is shown in the figure at a given instant. The point/points which have maximum magnitude of velocity are

• A. $C$ and $G$
• B. $B$ and $H$
• C. $A$ and $E$
• D. $D$ and $F$

Answer 1

Answer: (C)

$A$ and $E$

This is a sin wave and can be given by $y=A\sin \left(\omega t\right)$.
So the velocity can be given by $v=\frac{dy}{dt}=A\omega \cos \left(\omega t\right)$.
Hence, the amplitude of the velocity is maximum, when $\cos \left(\omega t\right)=\pm 1$ i.e. $\omega t=0,\pi ,2\pi$ etc.
So, the point/points which have maximum magnitude of velocity are A, and E.