Physics - Wave on String Question with Solution | TestHub

Given, $y=10\sin \left(\frac{\pi x}{4}\right)\cos (\pi t)$ Compare with standard equation formed after superposing $\begin{array}{rl}& y=A\sin (kx+\omega t)\text{ and }y=A\sin (kx-\omega t)\\ & y=2A\sin (kx)\cos (\omega t)\end{array}$ Therefore, $k=\frac{\pi }{4}$ We know, the propagation constant is: $k=\frac{2\pi }{\lambda }=\frac{\pi }{4}$ $\Rightarrow \lambda =8\mathrm{cm}$ The distance between two consecutive nodes is given by half of wavelength: $\frac{\lambda }{2}=4\mathrm{cm}$