Hello, I have a wave of the form y = Asin(x-vt) + Asin(x+2vt) which I substituted into the wave equation to find out if it satisfies it. It didn't because of the speed of the left travelling wave being equal to 2v. What I got was: A[-sin(x-vt)-sin(x-2vt)] = 1/v2 * A[-v2sin(x-vt) - 4v2sin(z-2vt)] So the v2 terms cancel on the RHS but we're still left with factor of 4 which mean they aren't equal. According to the superposition principle, if two individual waves satisfy the wave equation then their sum should also satisfy it. Individually they do but together they don't. I'm trying to think of why, physically, this wave wouldn't satisfy the wave equation as putting the equation into Desmos creates what looks like a perfectly normal wave travelling in the negative x direction as t>0. Any help would be awesome.