Whoa guys - time out please!
The OP asked the simple question regarding the effect of reversing the connections/polarity and understand this as a phase reversal.
JBL, mathematically you are of course correct, but in this simple case the only (theoretical) difference is in the omission of the first half-cycle and the last. We are not discussing signal generator waveforms here, gated precisely to the last microsecond. Any musical instrument I know of does not instantly start at a perfect set of sine waves (a la Fourier) but takes at least a few cycles to reach pitch (analyses of this all over internet).
Now I know there are some folks who claim they can hear this initial half-cycle business and I will not enter that discussion (again the audibility of the forward or backward motion of a driver at any instant has been debated on internet). But unless Vwguy is writing a mathematical exam paper, why are we making this into a theoretical treatise? After all the maths that can ever be quoted, there is no practical (as in audible) difference between seeing a 180 deg as a reversal in polarity or a phase shift. (Unless I need to return my varsity certificates for an upgrade ....)
Every musical note has a finite beginning and ending.
Recent research shows that the human auditory system is at least an order of magnitude better at determining the beginning of a musical note than the Fourier uncertainly principle would predict.
This has a bearing on our perception of sound quality.
From the OP's original question "How then do some subwoofers have a switch to adjust between 0-180 by degree/percentage?"
With all due respect, this is what I have explained. The difference between phase and polarity.
I did not mention anything about
absolute polarity. That is another can of worms.
Are you saying that as in my 1000 Hz example that it is not possible to differentiate a time difference of 0.5 milliseconds?
For a simple example, taking a conservative estimate, the minimum detectable interaural time difference is 10 microseconds or 0.000010s, corresponding to a shift in sound source location by 1 degree in azimuth relative to straight ahead (consistent with the minimum audible angle).
it is not just the omission of the data in the first and last half cycle, it is the relationship in time of the finite beginning and ending of the musical note.
This does not take into account how important the timing (phase) relationship is when it comes to the fundamental energy of a musical note and its harmonic energy.
The proper relationship in time (phase) of our musical signals is important in the arena of sound stage, imaging and timbre.
"That would be 0,5 mS for a 1kHz signal"
I stand corrected, as I have posted before, I am an old disabled man and the medications that keep what is left of me alive sometimes muddle my mind.
Again, I answered VWGUY's original question, "How then do some subwoofers have a switch to adjust
between 0-180 by degree/percentage?"
It is because phase and polarity are not the same thing.