Physics - Sound Wave Question with Solution | TestHub

The equation of the standing wave formed due to superposition of $Y=A\sin (\omega t-kx)$ and $Y=A\sin (\omega t+kx)$ is given by, $Y=[2A\cos (kx)]\sin (\omega t)$ Location of the nodes is dictated by condition: $[2A\cos (kx)]=0$ Therefore, $\begin{array}{rl}& kx=\left(\frac{2\pi }{\lambda }\right)x=(2n+1)\frac{\pi }{2}\\ & \Rightarrow x=\left(n+\frac{1}{2}\right)\frac{\lambda }{2};n=0,1,2,\dots .\end{array}$