When a sinusoidal sound wave passes through a tube open at both ends, it will get reflected when it reaches the end of the tube. The reflected wave will itself reflect when it reaches the opposite end of the tube, and so on, generating infinitely many reflection waves that interact which each other and the fundamental. This website allows you to see the reflection waves end their sum.
I know the fundamental is described as $\cos \left( k x - \omega t \right)$, but I can't figure out an equation for the reflected waves. How would I do that, as a function of the wavelength and the length of the tube? I want to sum each of the equations mathematically and see for which values of the wave and tube length the resulting wave is 0 everywhere.