I'm an electrical engineer, and I understand wave propagation, interference patterns, and so on. But I'm missing something basic, so perhaps my understanding isn't as good as I believe. I'll show my thinking; please tell me where I am mistaken.
Say that I have two guitars. Each one is precisely tuned. Each guitar has somebody play an open-string E note.
The result is a louder note, which implies to me constructive interference. But, if this is true, why is there never a destructive "noise cancelling" effect? Obviously, both guitar strings aren't always going to vibrate in the same phase.
Best Answer
You correctly diagnosed the problem in the last sentence. The problem is with the phase.
There is no interference happening here. The two sources do not maintain a constant phase difference. When interference occurs (with a constant phase relation between the two sources), you will have a net intensity of $(E_1 + E_2)^2$, which is four times either if they are equal. In the destructive case, the net result gives $0$ intensity (for a phase difference of $\pi$). However, when there is no constant phase relation, the phase difference would be randomly distributed between $0$ and $2\pi$, and in this case, you just have the average intensity adding up, to give $\langle E_1^2 \rangle + \langle E_2^2 \rangle$, which is 2 times either if they are equal. That's what you hear, and mistake it for constructive interference.