I went to the nearest village after spawning, started to dig a 3x3 hole and right after reaching the 66th layer (coordinate Y66 which is pretty high from my experience), cave sounds started playing non-stop, one right after another with very short intervals of silence between them.
The longest interval was probably 15-20 seconds, the shortest was around 1-3 seconds.

I think there had been times when I even got two cave sounds simultaneously playing.

I'm not sure if the cave sounds correspond to the sfx or the music, but I usually disable the ingame music while playing so I'm not really sure if this is normal at all.