The displacement of particles in a string stretched in the $x -$ direction is represented by $y$ . Among the following expressions for $y$ , those describing wave motion are :

cos k x sin ω t

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k^{2} x^{2} - ω^{2} t^{2}

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{cos}^{2} (k x + ω t)

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cos (k^{2} x^{2} - ω^{2} t^{2})

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Solution

The correct options are
A $cos k x sin ω t$
C ${cos}^{2} (k x + ω t)$
Equation of standing wave is an addition of two moving wave. Hence only A and C are a result of two standing wave (addition of two trigonometric function).

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