Question

A long string under tension of $100N$ has one end at $x=0$. A sinusoidal wave is generated at $x=0$ whose equation is given by
$y=\left(0.01cm\right)\sin [\left(\frac{\pi x}{10}m\right)-50\pi t(sec\left)\right]$
Draw velocity time graph of particle at $x=5m$ .

Answer 1

$y=0.01cmsin(\frac{\pi x}{10}-50\pi t)$

$\frac{dy}{dt}=(-50\pi )\left(0.01\right)cos(\frac{\pi x}{10}-50\pi t)$

$atx=5m$

$V=(-50\pi )\left(0.01\right)sin\left(50\pi t\right)=-Asin\left(50\pi t\right)$