There are 2 times the sound cue is given.
When you get in range of the shiny, which is 50 meters, the sound will play. This is simply because 50m is the LZA spawn radius.
The 2nd sound cue is not distance-based, but rather when the shiny enters your line of sight, the sound plays again (if it wasn't within your sight before; otherwise, the sound only plays once).