The displacement of a particle in string stretched in $X$ direction is represented by $y.$ Among the following expressions for $y,$ those describing wave motions are
IIT 1987, Medium
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(d) $y = \cos kx\sin \omega \,t$ and $y = \cos (kx + \omega \,t)$ represent wave motion, because they satisfies the wave equation $\frac{{{\partial ^2}}}{{\partial {t^2}}} = {v^2}\frac{{{\partial ^2}y}}{{\partial {x^2}}}$.
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