This is one of the most misunderstood concepts for the audiophile, perpetuated because manufacturers such as Conrad Johnson and many others use the terms incorrectly. It is also very difficult to explain without pictures of the waveforms.
In a stereo system the signal alternates between being positive and negative, ultimately causing the speaker cone to move back and forth creating sound pressure waves. Polarity refers to whether a signal is positive or negative. Inverting polarity means that what was positive is now negative and vice versa. If the speaker cone was moving out at certain point in time it is now moving in. Swamp is correct that reversing the speaker wires will invert (reverse) polarity.
One problem in understanding this is that many describe this as a phase reversal, which is incorrect. Phase refers to time. If something is out of phase then it is occurring at a time different than the original signal.
Take two identical speakers being fed the identical signal. They are moving in and out in lock step. If I reverse the connections to one speaker, while one is moving in the other is moving out. This is an inversion of the polarity to one speaker, but most people will describe this incorrectly as a phase reversal. They will say that the speakers are out of phase when the correct terminology would be that one speaker has had it's polarity reversed. This terminology is so widely accepted that it is probably impossible to correct.
Take the same two identical speakers being fed the same identical signal but one goes through a slight delay network. They are moving out and in but one lags a little behind the other. They are now out of phase. Your sub has an adjustment to vary the amount of this delay.
When attempting to integrate a sub with the main speakers, you want the positive pressure wave from the sub to coincide with the positive pressure wave from the main speakers at the frequencies that they are both reproducing (around the crossover frequency). Since they are different distances from the listening position, moving in and out at the same time is not enough since the pressure waves have to travel different distances to reach you. By delaying one of the waves (using the 0-180) phase control it may be possible to get these waves to overlap. If the amp to the sub inverts polarity and the main amp does not (or vice versa), then using the polarity inversion switch on the sub will put the polarity correct. You can then use the phase control to fine tune it to make up for the difference in distance.
In a stereo system the signal alternates between being positive and negative, ultimately causing the speaker cone to move back and forth creating sound pressure waves. Polarity refers to whether a signal is positive or negative. Inverting polarity means that what was positive is now negative and vice versa. If the speaker cone was moving out at certain point in time it is now moving in. Swamp is correct that reversing the speaker wires will invert (reverse) polarity.
One problem in understanding this is that many describe this as a phase reversal, which is incorrect. Phase refers to time. If something is out of phase then it is occurring at a time different than the original signal.
Take two identical speakers being fed the identical signal. They are moving in and out in lock step. If I reverse the connections to one speaker, while one is moving in the other is moving out. This is an inversion of the polarity to one speaker, but most people will describe this incorrectly as a phase reversal. They will say that the speakers are out of phase when the correct terminology would be that one speaker has had it's polarity reversed. This terminology is so widely accepted that it is probably impossible to correct.
Take the same two identical speakers being fed the same identical signal but one goes through a slight delay network. They are moving out and in but one lags a little behind the other. They are now out of phase. Your sub has an adjustment to vary the amount of this delay.
When attempting to integrate a sub with the main speakers, you want the positive pressure wave from the sub to coincide with the positive pressure wave from the main speakers at the frequencies that they are both reproducing (around the crossover frequency). Since they are different distances from the listening position, moving in and out at the same time is not enough since the pressure waves have to travel different distances to reach you. By delaying one of the waves (using the 0-180) phase control it may be possible to get these waves to overlap. If the amp to the sub inverts polarity and the main amp does not (or vice versa), then using the polarity inversion switch on the sub will put the polarity correct. You can then use the phase control to fine tune it to make up for the difference in distance.