Physics - Wave on String Question with Solution | TestHub

The general equation for wave is $\mathrm{Y}=\mathrm{a}\sin (\omega \mathrm{t}-\mathrm{kx})$ The given equation can be written as $Y=\mathrm{asin}\left(2\pi nt-2\pi \frac{x}{5}\right)$ Comparing both equations, $\omega =2\pi n$ $k=\frac{2\pi }{5}$ Wave velocity is given as $\mathrm{v}=\frac{\omega }{\mathrm{k}}$ $\therefore \mathrm{v}=\frac{2\pi \mathrm{n}}{\frac{2\pi }{5}}=5\mathrm{n}$ Particle velocity can be calculated as follows: $\frac{dY}{dx}=a(2\pi n)\cos \left(2\pi nt-2\pi \frac{x}{5}\right)$ Maximum velocity is ${\mathrm{v}}_{\mathrm{m}}=(2\pi \mathrm{na})$ $\frac{{\mathrm{v}}_{\mathrm{m}}}{\mathrm{v}}=\frac{2\pi \mathrm{na}}{5\mathrm{n}}$ $\therefore \frac{{\mathrm{v}}_{\mathrm{m}}}{\mathrm{v}}=\frac{2\pi \mathrm{a}}{5}$