My lecturer said that a standing wave is formed when two waves that travel in the opposite have the same frequency. He said that if the waves are y1 and y2, then the resulting wave y can be given as the sum: y = y1 + y2. y = Asin([tex]\omega[/tex]t - kx) + Asin([tex]\omega[/tex]t + kx). (1) Where the plus and minus kx denotes their direction. However, when (with a bit of trigonometric identity work) equation (1) is simplified it gives: y = 2Asin([tex]\omega[/tex]t)cos(kx). But how can this be? I mean, if x = 0, then the equation tells us that there is an antinode, which (for a string) isn't true. I've seen the equation y = 2Acos([tex]\omega[/tex]t)sin(kx), which makes more sense when I consider a string for example. To get to it you need the equation y = Asin(kx - [tex]\omega[/tex]t) + Asin(kx + [tex]\omega[/tex]t) (2) My question is, why would you use equation (2) and not equation (1)? Thank you in advance for your help!