In dual-core processors. Is it a collective speed or the speed of each core? Let's say 2.33 GHz?

Answer 1

speed of each core.

that doesn't mean that the total speed is 4.66GHz though, it just means that when you multitask you won't have to be afraid of lag. you can do some crazy matlab calculation and burn a cd at the same time!

Answer 2

Each core, like the last person said. So each processor is running seperately at 2.33 each, running seperate things. Unfortunately, they can't both work on the same thing at the same time (as cool as that would be).