A wave represented by the equation $y = a \cos (kx - \omega t)$ is superposed with another wave to form a…
A wave represented by the equation $y = a \cos (kx - \omega t)$ is superposed with another wave to form a stationary wave such that the point $x = 0$ is a node. The equation of the other wave is
$a \sin (kx + \omega t)$
$- a \cos (kx + \omega t)$
$- a \cos (kx - \omega t)$
$- a \sin (kx - \omega t)$
Solution
$x = 0$, net displacement by both the waves should always be zero for any value of $t$, as it is node. Only option (b) satisfies both these conditions.