
Scienceblog has a post on the physics of fireworks.
The burst charge can be as simple as more gunpowder, or it could be a more complicated (or even a multi-stage) explosive. The stars, on the other hand, are what actually go off in many directions, producing the beautiful display. When the fuse burns down to the point where it reaches the burst charge, it ignites!
This ignition, depending on how the firework is put together in the first place, will send the stars off into whatever pattern or direction it was designed for....
Just like lightning, the gunpowder explosion superheats the air, causing it to expand and become very rarefied (i.e., have such a low density that it's almost a vacuum). This heating and expansion takes place in a tiny fraction of a second, but it's not the heating and expansion that makes the sound! It's what happens in the instant afterwards. The air from just outside this rarefied area rushes in to fill up this low pressure area. It does so with such great speed that it actually breaks the speed of sound, creating a sonic boom! And that's what makes the "pop" or "boom" sounds that accompanies fireworks.
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