The current comes into the speaker motor assembly
through the speaker terminals. Then the voice coil receives the
current. When the current is running through the voice coil, the current
creates a magnetic field. This magnetic field attracts and repels away
from the magnet's magnetic field. The attraction and repulsion is based
on the direction of the current. The voice coil which is attached to the
cone will either push or pull the cone. The cone moving in and out is
what causes the air to move or vibrate. The vibration in the air is what
actually makes sound. This is how speakers work and subsequently how
subwoofers work seeing as subwoofers are a type of speaker.