Question

A wave represented by the equation $y_1=A\cos (kx-\omega t)$ is superimposed with another wave to form a stationary wave such that the point $x=0$ is a node. The equation of the other wave can be :

• A. $y_2=-A\sin (kx-\omega t)$
• B. $y_2=-A\cos (kx+\omega t)$
• C. $y_2=A\sin (kx+\omega t)$
• D. $y_2=A\cos (kx+\omega t)$

Answer 1

The correct option is B $y_2=-A\cos (kx+\omega t)$

$y_1=A\cos (kx-\omega t)$

Thus another wave should be in opposite direction of first wave and amplitude should be negative that is a phase difference of $180\%$, to form stationary wave.

$\therefore y_2=-A\cos (kx+\omega t)$

Hence, option $B$ is correct.