The voice coil is the part of the speaker that moves the cone and produces the sound. All it is, basically, is a coil of wire around a cardboard tube. One end of the wire gets hooked to the positive, one end of the wire gets hooked to the negative, and then when it get's placed in the center of the magnet, without touching the magnet.
When electricity goes through the coil, it turns into an electromagnet, and based on where the polarity is, the natural magnet will push or pull the electromagnet (voice coil) up and down, which moves the cone of the speaker, which makes the sound. A dual voice coil is exactly what it sounds like, a speaker with two voice coils connected to the cone, which end up giving you a better sounding sub. More.
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