Physics - Wave on String Question with Solution | TestHub

$\begin{array}{l}\text{ Given, }y=3\sin \pi \left(\frac{t}{2}-\frac{x}{4}\right)\\ =3\sin \left(\frac{\pi t}{2}-\frac{\pi x}{4}\right)\end{array}$ Comparing it with standard equation $\begin{array}{l}y=r\sin \frac{2\pi }{\lambda }(vt-x)\\ =r\sin \left(\frac{2\pi vt}{\lambda }-\frac{2\pi x}{\lambda }\right)\end{array}$ We have, $\frac{2\pi \mathrm{v}}{\lambda }=\frac{\pi }{2}$ or $\mathrm{v}=\frac{\lambda }{4}$ and $\frac{2\pi }{\lambda }=\frac{\pi }{4}$ or $\lambda =8\mathrm{m}\therefore \mathrm{v}=\frac{8}{4}=2\mathrm{m}/\mathrm{s}$ So, the distance travelled by wave in $t$ second $=\mathrm{vt}=2\times 5=10\mathrm{m}$