# Standing Waves

If you have a solid understanding of what Travelling waves are (see previous sub-section 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 looks like the following:

For the most part when one is referring to standing waves, it is customary to just talk about the resultant wave that you see above.

But one should understand that the way you form this is by taking a right moving wave and adding it up with a left-moving wave: