A wave represented by the equation $y_1 = a\,cos(Kx-\omega t)$ is superimposed 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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at $x=0$ node is formed
So, wave is reflected from rigid end.
$\Rightarrow \quad y_{i}=a \cos (k x-\omega t)=a \cos (\omega t-k x)$
$\Rightarrow \quad y_{r}=-a \cos (\omega t+k x)$
$\boxed{{{\text{y}}_{\text{r}}} = {\text{a}}\cos (\omega {\text{t}} + {\text{kx}} + \pi )}$
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