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I'm familiar with the uncertainty principle in harmonic analysis, which states that you can't localize the support of a function in both the time domain and the Fourier domain. One of the physical manifestations of this principle is the Heisenberg uncertainty principle, which states that you can't localize the position and momentum of a particle.

But the harmonic analysis version of the uncertainty principle applies to other physical phenomena too. For example, there is a musical version of the uncertainty principle that says that you can't localize a signal in both the time domain and frequency domain.

So my question is this: what happens if you set something like the wheeler delayed choice experiment up, where you take some sort of measurement of a faraway sound (like, someone playing a trumpet from far away), but don't decide on a "time window" for your measurement until after you have seen them blow into the trumpet? Will your choice of measurement window affect the way the sound waves travel before reaching the measurement apparatus?

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Sound wave are classical objects. There is no wave-particle duality there.

The choice of time window will affect the precision with which you can measure your frequency (This is what comes out of Fourier analysis.) as well as the integrated intensity of sound that you measure.

For a given time interval (assuming that you trumpet is loud enough so that you get a good signal) you can measure the frequency within a certain interval. Both intervals obey some kind of uncertainty relation.

But there is nothing quantum about this!

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In my opinion (and I state that not for my ego but to express that it can include mistakes), you take it a bit wrong way.

Psychoacoustical point of view: There is no such thing as a strict frequency or time domain. In our physiology and connected cognitive processes you can't think in terms of Fourier transform. For example: yes, it takes some time between the moment of the first, "rough" sound sensation and the moment of true awareness of all its aspects but it is not the same mechanism as the choice of window according to the signal frequencies, sampling (etc. etc. engineerging etc.). If you really prefer to transform human hearing principles to a simple signal processing operation, then I would recommend - well, not to do it, but... - I would recommend the autocorrelation (so the questions like: what is the difference between this time interval and the last one? Which actually includes Fourier analysis).

General physics point of view: Beware of mixing things. There are many really fascinating similarities in physics and its mathematical formulation but don't let them fool you. Again an example: calculating energies of a particle in a potential well is basicaly the same as finding the acoustical eigenmodes of rectangular room. Correct? Well, the maths is very close! But the physical principles, basics and interpretation are bloody different!

I am not a quantum physicist but I that the features of the system you have proposed are way too large-scale for these questions and I can assure you that in practical music acoustics measurements we don't take them into account. :-)

But well, anyway, it was my pleasure to try to untangle your question.

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  • $\begingroup$ Thanks! I actually know very little about the physical principles involved here. I know much more about harmonic analysis than I do about physics. Actually, I heard that human hearing is sort-of similar to a wavelet transform, but I'm not sure how true that is. $\endgroup$ – Rob F Sep 9 '15 at 17:02
  • $\begingroup$ My pleasure! If you are satisfied, mark the question as answered. $\endgroup$ – Victor Pira Sep 9 '15 at 17:58

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