If a person's eardrum vibrates, let's say, 440 times per second for 1 second, how does the brain know its because 1 sound source vibrated 440 times, as opposed to 440 sources vibrating once, one after the other, or 2 objects vibrating 220 times per second, but out of sync with each other, or any other combination? Thanks.
If the sources have different locations then they won't reach the 2 ears at the same time, won't have the same loudness and spectral content (although here you describe a pure tone), so your brain will be able to tell them apart. There is a whole field of neuroscience interested in "causal inference", which describes how your brain makes this type of guesses. For example have a click and a flash been produced by the same source of different sources?
But I think this is not exactly what you were asking. If the signals are identical when reaching the ears then it becomes more of a philosophical question. If you place a microphone in the observer's ear and receive a perfect sine, does it matter that it has, in facts, been produced by multiple sources? That's the classical philosophical question of whether a tree falling in a forest produces a sound or not, if no one is around to hear it. Is a sound a physical signal or is it the percept it elicits in an observer? Take the example of color. If you compare 2 lights, one monochromatic red and one complex spectrum that looks exactly the same red. Do they have the same color or not? Due to the physiological limitations of your sensory organs they elicit the exact same response. Yet they are physically different. There is of course no clear or easy answer to this question as on one extreme you will end up arguing that there is no objective reality and on the other extreme you deny the obvious fact that we experience the world differently.
Shams, L., & Beierholm, U. R. (2010). Causal inference in perception. Trends in cognitive sciences, 14(9), 425-432.