Hi. I have been reading about the superposition of simple harmonic vibrations of different frequencies and what entails to make the their combination periodic. This is quoted from the book Vibrations and Waves by A.P. French: "The condition for any true periodicity in the combined motion is that the periods of the component motions be commensurable-i.e. there exists two integers n1 and n2 such that T = n1T1 = n2T2 The period of the combined motion is then the value of T as obtained above, using the smallest integral values of n1 and n2..." This is quite understandable. However, when it comes to the beat phenomena we can't find out the time period of the combined motion through this. For example if we have frequencies 255 Hz and 257 Hz, the time period of the superposed motion is 1/256 s which isn't something you would arrive at using T = n1T1 = n2T2. I think i need a little bit guidance here to help me through because even though on the surface it seems easy to understand the beat phenomenon given the equation for the superposed, equal amplitude vibrations, however i can't see how the two time periods of the combining waves are commensurable? It is, it seems, a necessary condition to be fulfilled for periodicity after all.