Physics - Wave on String Question with Solution | TestHub

The given equations of motion are $\begin{array}{rl}& y_1=2a\sin (\omega t-kx)\\ & y_2=2a\sin (\omega t-kx-\theta )\end{array}$ Now the resultant equation of wave is given by $\begin{array}{rl}& y=y_1+y_2\\ & =2a\sin (\omega t-kx)+2a\sin (\omega t-kx-\theta )\\ & y=2a\left[2\sin \frac{(\omega t-kx+\omega t-kx-\theta )}{2}\times \cos \frac{\omega t-kx-(\omega t-kx-\theta )}{2}\right]\end{array}$ $y=4a\cos \frac{\theta }{2}\sin \left(\omega t-kx-\frac{\theta }{2}\right)$ ...(1) Now comparing equation (1) with $y=A\sin (\omega t-kx)$, we have Resultant amplitude $A=4a\cos \frac{\theta }{2}$