$y = a\cos (kx + \omega t)$ superimposes on another wave giving a stationary wave having node at $x = 0.$ What is the equation of the other wave
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(c) $a\cos (kx + \omega \,t)$
hence ${y_{{\rm{reflected}}}} = a\cos ( - kx + \omega \,t + \pi ) = - a\cos (kx - \omega \,t)$
hence ${y_{{\rm{reflected}}}} = a\cos ( - kx + \omega \,t + \pi ) = - a\cos (kx - \omega \,t)$
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