If you have two sine waves with peak amplitdes V1 and V2, at the same frequency f, with an arbitrary phase difference between them, is the sum always a sine wave? Can anyone provide a proof or reference to this.
If you have two sine waves with peak amplitdes V1 and V2, at the same frequency f, with an arbitrary phase difference between them, is the sum always a sine wave?
Thank you. I see a derivation of something in a book, and I could see the proof relied on the fact that the sum of two sine waves would be a sine wave, but it was not stated. So I got a bit concerned perhaps the proof was invalid, but it seems not the case.
If you have two generic sinusoid with amplitude "A" and "B" and same argument "x" and arbitrary phase "θ" between them, the sum will be a sinusoid having amplitude let say "M" and phase "φ" so that:
Well, in general it can still be considered a sine way - it just happens to have an amplitude of zero.
I must admit, intuately I though that if there was some phase difference between them, then the sum would no longer be a pure sine wave, but it seems my intuition was wrong.
In signal processing field, usually we decompose signals into sine wave form. This in other view to see, or actually more professionally, is in the form of exponential function.
Thus, here I will use the method of exp function. This simplifies the calculation since it avoids two pure sine form wave summation. Also this is why Euler solves a very important question with his Euler equation.