Physics - Wave on String Question with Solution | TestHub

The given wave equation is $y=A\sin 2\pi \left(nt-\frac{x}{10}\right)$

Comparing this with the standard wave equation $y=A\sin (\omega t-kx)$, we get:

Angular frequency, $\omega =2\pi n$

Wave number, $k=\frac{2\pi }{10}=\frac{\pi }{5}$

Maximum particle velocity is given by $v_{p,max}=A\omega =A(2\pi n)$

Wave velocity is given by $v_w=\frac{\omega }{k}=\frac{2\pi n}{\pi /5}=10n$

The ratio of maximum particle velocity to wave velocity is:

$\frac{v_{p,max}}{v_w}=\frac{A(2\pi n)}{10n}=\frac{\pi A}{5}$

Answer: $\frac{\pi A}{5}$