What determines the frequency of alternating current?
It's a market evolution, and partly a product of Edison's sour grapes in losing the DC vs. AC war with Westinghouse.
tl; dr version: 40 and lower flickered with lights, 50 was acceptable, 60 worked better with arc lights (flicker again), higher frequencies than those were less compatible with generators and induction motors, based on Tesla's work. So Westinghouse ultimately settled on 60Hz.
Edison, meanwhile, had a hand in AEG (Germany) choosing 50 as a way to create a separate (some would say, monopolistic) market in Europe. Edison was kind of a jerk that way.
More about all that here: https://www.quora.com/Why-is-60Hz-AC-used-in-America-What-are-the-advantages-and-disadvantages-of-using-60Hz