Old English pipian "to play on a pipe" or similar instrument, from Latin pipare "to peep, chirp," of imitative origin (see pipe (n.1)). Compare Dutch pijpen, German pfeifen.
From 1590s, of birds, "to chirp, warble, whistle, sing." Meaning "convey through pipes" is by 1887. Related: Piped; piping. Piping hot is in Chaucer, a reference to hissing of food in a frying pan.
To pipe up (early 15c.) originally meant "to begin to play" (on a musical instrument); sense of "to speak out" is from 1856. Pipe down "be quiet" is from 1900, probably a reversal of this, but earlier (and concurrently) in nautical jargon it was a bo'sun's whistle signal to dismiss the men from duty (1833); pipe in the nautical sense of "to call by the pipe or whistle" is by 1706.