A wave represented by the given equation $y = a \cos(kx - \omega t)$ is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is
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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 π π or a path change of $\frac{\lambda}{2}$
So, if $y_{\text{incident}} = a \cos(kx - \omega t)$
⇒ ⇒ $y_{\text{reflected}} = a \cos(-kx - \omega t + \pi) = -a \cos(\omega t + kx)$
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