b
(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 \({y_{{\rm{incident}}}} = a\cos (kx - \omega \,t)\)

==> \({y_{{\rm{reflected}}}} = a\cos ( - kx - \omega \,t + \pi )\)\( = - a\cos (\omega \,t + kx)\)