Like the infinite monkeys typing Shakespeare, but with audio instead.
If there was a program that created a series of sounds at random intervals, pitches, amplitudes, etc., how long would it take to produce an output that sounds like music, some sort of recognisable recording (e.g. a bell ring, a dog barking), or perhaps even a human voice?
Well how fast are your producing it? Is it analog or digital? What is the interval of music / voice that is required? Are you normalizing it? Or are there variations in magnitude as well as frequency? Once you have these params then you should be able to create a closed form method and figure it out with statistics. (Now actually finding all those things out is probably difficult, what kind of random generator are you talking about? If it literally spits out a random wave for each tiny time interval then you could be there a while, if your adding random frequencies then it could be technically done very soon for certain definitions of music)
Edit: i would start with finding how long it takes to get a sign wave because that would be an upper bound on the answer. If that upper bound happens really soon then yay. And can presume some other sound that fits a less strict criteria would happen before it. Don’t know if that information would be helpful in finding the lower bound, but maybe.