Actually, the conjecture for sums of multiple sine waves is false. What is true is that the mean square MS = RMS^2 of the sum equals the sum of the mean squares of the component sine waves, with the proviso that the components are orthogonal. The peak value has no bearing on the matter. Consider sin(x)+sin(2x). Lazy guy that I am, I used a spreadsheet to find the peak value 1.76. This divided by sqrt(2) is 1.24. But the RMS of the sum is sqrt(1/2 + 1/2) = 1. -- Gene On Sunday, November 12, 2017, 1:56:12 PM PST, Keith F. Lynch <kfl@KeithLynch.net> wrote: The root mean square (RMS) of a sine wave is always the peak value divided by the square root of 2. The same is true of the sums of multiple sine waves with different frequencies, phases, and amplitudes. But every repeating waveform is equal to the sum of sine waves with different frequencies, phases, and amplitudes. This includes the square wave, i.e. a function which always equals +X or -X, and never takes any other value. But obviously the RMS of that square wave is simply X, not X divided by the square root of 2. Explain. I learn a lot by coming up with such paradoxes then figuring out the solution.