b
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 \(y_{\text {incident }}=a \cos (k x-\omega t)\)
\(\Rightarrow y_{\text {incident }}=a \cos (-k x-\omega t+\pi)\)
\(=-a \cos (\omega t+k x)\)
Hence equation for the other wave 

\(y=a \cos (k x+\omega t+\pi)\)