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?