Paper is a form of cellulose , which is one of many naturally occuring polymers . Of course, if you look at the high quality speakers like this subwoofer, then you'll find cones made of a plastic called polypropylene . An alternating field makes it vibrate, and the vibration can be made to produce sound. Here's an assembled speaker for those who don't feel like building their own. It's cabinet is made of wood.
Wood is another form of cellulose .
The mesh fabric that covers the speaker is made of nylon , and it's stretched over a polystyrene frame. That's because it's protected by a a hard shell. The outside housing is made from a special kind of polystyrene high-impact polystyrene . It's a graft copolymer of polystyrene with a rubbery polymer, polybutadiene . It's much less brittle than regular polystyrene.