Exercise 27 calls for you to destroy a small 2" speaker... the way these speakers are designed, I don't think you'll be repairing it after you've made the required cuts to tear it apart and see how it works. I've taken video of the process if you'd rather not destroy your own speaker.
The coil of wire wrapped around the small cardboard tube is surprising. It's very fine and wrapped nice and tight, obviously by a machine. If I understand my reading of Exercise 27, the electric current sent to the speaker will create a magnetic field in the coil that will fluctuate... these fluctuations will cause the magnet to move up and down, with the air waves created moving the black paper cover that I cut away from the speaker. The paper cover's movement is what creates the sound waves that the listener hears.
A very simple device... only two moving parts as far as I can tell - the magnet and the paper cover. Amazing.