On many sound cards and mixers there is a button "Phase invert". What is its purpose? When should we use it?
To avoid the effect of Phase Cancellation, as pictured below:
This happens when you record with multiple microphones and their phases are cancelling each other.
You should use it when visually you notice that one signal is cancelling the other, inverting one of the channels should solve the issue.
When you are combining several microphones capturing the same sound sources that happen to have different phase conventions.
I've recently made a comparison between Røde and Oktava mics placed right beside each other and matching their gain pretty well on the mixer. When you added the signals without phase reversal, most of the bass was gone.
Now the point here was for comparison purposes, so the end product contained either one or the other, but if I had wanted to create a musically useful product by combining two microphones, I'd have been pretty annoyed (my mixer doesn't have phase inversion switches, but my DAW has). Also when switching in full sound, a phase mismatch would cause loud clicks.
In contrast, there is the trick of tying two microphones to each other, sing straight into one, and combine them phase inversed. That make most sound from a larger distance cancel and helps against acoustic feedback.