Let’s say I play the same sound several times per second at equidistant intervals. How many times can I play it per second until I’m no longer able to distinguish that they’re discrete sounds and they start blending together?
Second, if I were to analyse the sound I play, would I find that it only seems continuous because it’s composed of its own repetitions which are too rapid for me to resolve? Is it turtles all the way down?
The human brain seems to top out at both vision and sound somewhere around 1/10th to 1/15th of a second, with a bit of variation between individuals. Sounds that occur less than 1/15th of a second apart seem simultaneous, just as images that change faster than 1/15th of a second seem like motion and not individual images.
TV and movies use a slightly faster frame rate than that since even though 10 to 15 frames per second is “good enough” for most people, your brain still perceives a bit of flicker. Getting up above 30 frames per second gets rid of the flicker.
Similarly, at about 10 to 15 beats per second, your sounds will blend together.
I don’t understand your second question.
I know precious little about acoustics or phonology; but I believe you would benefit from reading the works of Herrman von Helmholtz, who actually made these things a science.
Humans can usually hear sounds between about 20-20000 Hz, so once in that range you should be hearing a distinct pitch; the record, under ideal laboratory conditions, for hearing a musical tone is 12 Hz. There is also a phenomenon called temporal masking where a strong sound causes you not to perceive a weaker sound for a short time before (20 ms) or after (up to 200 ms) it.
If you analyse an arbitrary sound sample, for example with a Fourier transform, it is true that it is composed of a spectrum of frequencies, but it is subject to complicated psychoacoustics when you hear it. But, yes, physically you can regard it as a combination of repetitive sine waves.