If $y_1=A\sin(\omega t-kx)$ and $y_2=A\sin(\omega t+kx)$ are superpose…

Question

If $y_1=A\sin(\omega t-kx)$ and $y_2=A\sin(\omega t+kx)$ are superposed, the resultant displacement is

Accepted Answer

C. $y=2A\sin\omega t\cos kx$

Using $\sin C+\sin D=2\sin\frac{C+D}{2}\cos\frac{C-D}{2}$, with $C=\omega t-kx$ and $D=\omega t+kx$, we get $$y=2A\sin\omega t\cos kx.$$ This is the standard equation of a standing wave.

Answer

$y=2A\sin\omega t\sin kx$

Answer

$y=2A\cos\omega t\cos kx$

Answer

$y=A\sin\omega t$