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

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$\cos (k^{2} x^{2} - ω^{2} t^{2})$

$k^{2} x^{2} - ω^{2} t^{2}$

$coskxsinω t$

$\cos (kx + ω t)$

answer is A, C.

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Detailed Solution

$y = coskx sinω t$ and $y = \cos (kx + ω t)$ represent wave motion, because they satisfies the wave equation $\frac{\partial^{2} y}{\partial t^{2}} = v^{2} \frac{\partial^{2} y}{\partial x^{2}}$ .

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