I was at a jam the other day and heard someone say the old thing about how you need a big speaker to produce low notes, as if the diameter of the speaker is somehow related to the frequency of the wave.
It ain't. A low frequency note means the speaker is going back and forth slowly. Any speaker can do that.
True, it also matters how far the speaker travels back and forth (xmax). A slow moving speaker that's small and doesn't go back and forth very far (small xmax) won't shake much air so it won't be loud on that low note, so cab makers just use more of them. That's why an 8x10 can be loud and low.
Modern speakers with large xmax are rewriting the rules. There are some small cabs that get surprisingly loud and low.
I imagine it's harder to get a big speaker to do high notes. It takes a lot of energy to overcome the inertia of a bigger cone and the air it has to push every time it reverses direction, compared to a smaller cone.
Again, modern technology to the rescue. Super strong neo magnets can provide the power to reverse a bigger cone's motion rapidly through a larger xmax compared to older tech, but smaller speakers will have a natural advantage in high frequencies, all else being equal.
Cab design also matters a lot but I don't know enough about that to say anything more.
I think I've got that right; I'm not an expert and always glad to be corrected by experts.