Question

A transverse sinusoidal wave is generated at one end of a long, horizontal string by a bar that moves up and down through a distance of $1.00cm$. The motion is continuous and is repeated regularly $120$ times per second. The string has linear density $90gm/m$ and is kept under a tension of $900N$. Find:
The maximum value of the transverse speed $u$.

Answer 1

The distance from the bottom to the string is equal to$1cm$

$y(x,t)=Asin(Kw-wt)$

Transverse speed is given by

$u=\left|\left(\frac{dy}{dt}\right)\right|=wAcos(Kx-wt)A=\frac{1cm}{2}=\frac{1}{2}\times {10}^{-2}m$

and$w=2\pi f=2\pi 120\left(Hz\right)$

$\therefore$u(maximum)$=wA=2\pi \times 120\times \frac{1}{2}\times {10}^{-2}=3.77m/sec\left(approx\right)$