## Standing Waves

If you have a solid understanding of what Traveling waves are (click here if you need a refresher) then when you add up a sine wave moving to the right with a wave moving to the left, you get a standing wave. $ y(x,t) = \sin(kx-\omega t) + \sin(kx + \omega t) $ Using $ \sin(a) + \sin(b) = 2 \sin((a+b)/2) \cos((a-b)/2) $ and simplifying the above equation we get : $y(x,t) = 2\sin(kx)\cos(\omega t) $ A plot of this…