Question

A wave represented by the equation $y=a\cos (kx-\omega t)$ is superimposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for other wave is

• A. $a\sin (kx+\omega t)$
• B. $-a\cos (kx+\omega t)$
• C. $-a\cos (kx-\omega t)$
• D. $-a\sin (kx-\omega t)$

Answer 1

The correct option is B $-a\cos (kx+\omega t)$

To form a stationary wave with $y=a\cos (kx-wt)$ the wave should be in the opposite direction of this wave and amplitude should be negative that is the phase difference should be of $\pi$

$y=a\cos (kx+wt+\pi )[y=-a\cos (kx+wt)]$

Hence option (B) is correct