WoW API: PlaySoundFile

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Plays the specified audio file once. Unlike PlayMusic, you cannot stop the playback.

PlaySoundFile("path"[, "channel"])

Arguments

path: String – The path and name of the sound file you'd like to play, relative to the WoW directory; both ogg and mp3 formats are accepted. The file must exist prior to logging in to WoW.
channel: String – Either "Master" (this will play the sound also with disabled sounds like before 4.0.1), "SFX", "Ambience", "Music".

You can play a sound file included with your addon:

PlaySoundFile("Interface\\AddOns\\MyAddOn\\mysound.ogg")

Or one of the ones shipped with WoW (Power of the Horde, in this case):

PlaySoundFile("Sound\\Music\\ZoneMusic\\DMF_L70ETC01.mp3")

There does not appear to be a bad error if the file is missing - it just won't play. There is a return status, which is 1 if the sound was OK and nil if it couldn't be found.
This API call was broken in patch 1.11 and was fixed in patch 1.11.2.
As of 4.0.1, custom .wav files are no longer supported.
As of 6.0.2, custom .mp3 files are no longer supported.