Question

What is the velocity of a particle of the string at position $x=1.5$cm and $t=9/8$ sec?

Answer 1

We know,

$v=\frac{dy}{dt}$

$v=5\sin \left(\pi x/3\right)\times -40\pi \sin \left(40\pi t\right)$

At $x=1.5cm,t=9/8s$

$v=-200\pi \times 1\times \sin \left(45\pi \right)=0$. As$\left[sin\right(n\pi )=0]$

Hence $v=0$