Currently Being ModeratedJul 6, 2012 10:07 AM (in response to ggabay)
There is no option to stream only sound. If you are playing a video on your device and you turn ON Airplay, that will stream that content to your desired Apple TV. It will not be possible to split audio from a video.
Currently Being ModeratedJul 6, 2012 10:47 AM (in response to ggabay)
It's actually very easy and doesn't even require splitting the video stream and extracting the audio track from it (which is pretty easy if you have a desktop computer).
If you don't want to play back protected content (non-music videos purchased from iTunes Store), all you need to do is getting GoodPlayer, letting it play audio in background (Settings > Background Audio) and connect to your ATV in non-AirPlay mirroring mode. It'll happily play back the audio track of the video while you can do anything in the foreground. (Note that, in addition to GoodPlayer, other background audio-playback players may also work - it's just that I've tested GoodPlayer in this regard between my ATV3 and iPad 3. Let me know if you need more - for example, a list - info on them.)
Currently Being ModeratedJul 6, 2012 12:42 PM (in response to ggabay)
What about streaming YouTube Video's soundtrack and keep watching it on the iPad?
Will GoodPlayer help me somehow with that?
Currently Being ModeratedJul 6, 2012 12:49 PM (in response to ggabay)
Nope, it doens't play back YouTube (browsed from the built-in browser) in the background.