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A wave represented by the given equation $y = a \cos (k x - w t)$ is superposed 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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$y = - a \sin (k x - w t)$

$y = - a \cos (k x + w t)$

$y = - a \cos (k x - w t)$

$y = a \sin (k x + w t)$

answer is B.

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Detailed Solution

$y_{1} = a \cos (k x - ω t),$ if we take

$y_{2} = - a \cos (k x + ω t)$ , then

$y = y_{1} + y_{2} = 2 a \sin k x \cos ω t$

$= A \cos ω t$

For $x = 0$ , $A = 0$ , which represents node.

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