Hi Thunder,
You can demonstrate the effect of an inverted sound wave easily by reversing the two wire connections to a speaker. It will sound exactly the same, but will no longer be in phase with other speakers that are connected.
If you add a non-inverted sound wave with an inverted one, they cancel. You can demonstrate this with a stereo. If you connect one of its speakers out-of-phase as above, the bass will be reduced unless the room is very echoy.
Put the two speakers facing each other about 2cm apart. When they are in-phase, the bass will be loud. Now reverse the connections of one speaker so that it is out-of-phase, and the bass cancels.