I have trouble with the embedding of equations! So I would like to give you only some remarks to the German page “Mathematik”:

It deals with the superimposition of two sine waves. Some general theorems are introduced; (1) and (2) are leading to (3). Some cases of the interaction of two sine waves are treated:
a) different amplitudes
b) slightly different frequencies (> beat, the German “Schwebung”)
c) different phase
d) different amplitudes, different phases