Question

solve this and explain in detail
Q.1) When the maximum particle velocity for a transverse wave is 3 times the wave velocity? Take transverse wave as $y=y_0\sin 2\mathrm{\pi }\left(\mathrm{ft}-\frac{\mathrm{x}}{\mathrm{\lambda }}\right)$.

Answer 1

$$\begin{gathered} DearStudent, \\ Given, \\ \mathrm{we}\mathrm{know}\mathrm{standard}\mathrm{equationof}\mathrm{wave}: \\ \mathrm{y}=\mathrm{r}\sin 2\mathrm{\pi }\left(\mathrm{vt}-\frac{\mathrm{x}}{\mathrm{\lambda }}\right) \\ \mathrm{given}{\mathrm{v}}_{\mathrm{p}}=3\mathrm{v} \\ {\mathrm{y}}_{\mathrm{o}}\mathrm{\omega }=3\left(\frac{\mathrm{\omega }}{\mathrm{k}}\right) \\ {\mathrm{y}}_{\mathrm{o}}=\frac{3}{\mathrm{k}} \\ \mathrm{we}\mathrm{know},\mathrm{k}=\frac{2\mathrm{\pi }}{\mathrm{\lambda }} \\ \mathrm{thus} \\ {\mathrm{y}}_{\mathrm{o}}=\frac{\mathrm{\lambda }}{2\mathrm{\pi }}\times 3 \\ ora=\lambda =\frac{2\mathrm{\pi }}{3}{y}_o \\ Regards \end{gathered}$$