World's Largest Horn Shatters Glass

ELI20 version: I answered why you want a large outlet area but not necessarily why it curves like that. Anytime you have a sudden change in cross-sectional area in the horn you will get waves reflecting back at the source. You don't want that because that is wasted energy that could have moved forward. Even if it goes from a small cross-section to a larger, if you do it suddenly you get those wasted waves. So you want the horn to basically be asymptotic at the exit so you never have a jump in discontinuity when it exits to the wide open air. So a directors cone isn't as good as the curved shapes I showed because it still has the sudden change when it dumps into the open air.
Summary: I made a huge horn and broke glass with it and explored why horns are shaped the way they are.