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To keep things simple, let's talk about plane acoustic waves in one dimension. If we solve the wave equation in one dimension , we find that the acoustic pressure as a function of space and time is of the form $$P(x,t) = Ae^{i(kx -\omega t)}$$ where $A$ is the maximum amplitude, $x$ and $t$ are the displacement and time respectively, $\omega$ is the ...

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You may consider reading about Aharonov-Bohm effect. This is one of those cases, where the phase of the wave function, in sum with the electromagnetic 4-potential, is extremely important, as it gives different physical results. This effect was also checked experimentally, so it is not a pure theoretical abstraction.

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A single measurement like this has a lot of noise on it - and random signal is always going to have some random correlation. You should definitely not pay too much attention to the stuff that is in the tail of the correlation distribution - it's all noise. The fact that the built in function does not produce negative values is related to you only looking at ...

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