A speaker has two terminals on it, one terminal is - (negative) and the second terminal is + (positive, if you wire the speaker polarity backwards, so the + is connected to the - and the - is connected to the + the cone of the speaker will move inwards instead of moving outwards. The speaker will still work if wired backwards and no damaged can be done to it, however it would not be in phase with other speakers.
When a current is given to a speaker, it energizes the electromagnet, which makes it repel as a permanent magnet causing the cone of the speaker to move outwards. The movement of the speaker cone causes positive pressure wave air, this travels right throughout the air around us, then our ears pick up the sound produced by the speaker cone. So if you wired a speaker backwards, with reverse polarity, the amplifier sends a positive signal, so this means that the speaker cone will still produce sound. Nevertheless, the amplifier will get confused and think it is transmitting a positive pulse, making the cone move outwards, creating a positive pressure wave, this will result in the speaker cone to pull itself inwards, towards the magnet, creating negative air pressure.
So wiring a speaker backwards will create a negative air pressure, this means that it will cancel out other speakers that are wired correctly and create a positive air pressure, this can cause multiple speaker to become out of phase. A human can't really tell if a speaker is wired backwards by using their ears, unless they see the movement of the cone. But if you wire a subwoofer backwards, you can tell because it won't give proper bass response and output because the cone will pull itself in.
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