Question

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

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

Answer 1

Answer: (B)

$y=-A\cos (kx+\omega t)$

to create a node at $x=0$ , the other wave should have $-A\cos \left(\omega t\right)$ at $x=0$ .
Also , the wave should be moving in the opposite direction .
so , the angle should be $(kx+\omega t)$