Physics - Sound Wave Question with Solution | TestHub

Since the point $x=0$ is a node and reflection is taking place from point $x=0$. This means that reflection must be taking place from the fixed end and hence the reflected ray must suffer an additional phase change of $\pi$ or a path change of $\frac{\lambda }{2}$. So, if $y_{\text{incident }}=a\cos (kx-\omega t)$ $$\begin{array}{rl}\Rightarrow y_{\text{incident }}& =a\cos (-kx-\omega t+\pi )\\ & =-a\cos (\omega t+kx)\end{array}$$ Hence equation for the other wave $$y=a\cos (kx+\omega t+\pi )$$