So as usual, the answer isn't simple, but easy when you know how.
http://linux.seindal.dk/2005/09/12/converting-aac-audio-files-to-mp3/
gives the basics:
youtube-dl lets you capture the entire video
ffprobe examines the contents of the video
ffmpeg strips out the audio and also converts it to a
more favorable format
But as always there are gotchas: under linux the mp3 codec doesn't exist, rather there is a libmp3lame library.
So, step by step:
1. Install youtube-dl, ffprobe, ffmeg, and libmp3lame using your usual process, repositories, whatever.
2. Given a YouTube URL of
http://www.youtube.com/watch?v=abcdefg
at a terminal issue the command (under Linux, do whatever equivalent elsewhere):
cd "directory I want it to be in"
The quote marks protect the path from embedded spaces... Then issue
youtube-dl -o "myyoutubefile.flv" http://www.youtube.com/watch?v=abcdefg
This will save (output: -o) the YouTube video clip as a Flash video (.flv) file containing both the video and the audio. Kaffeine will quite happily play both.
3. Check the audio and video channel formats with
ffprobe "myyoutubefile.flv"
The output of this will contain a string
Stream #0:1(und): Audio: aac (mp4a / 0x6134706D), 44100 Hz, stereo, s16, 147 kb/s
or something similar, indicating that the audio format is aac.
4. Strip out the audio to another format (e.g., here we go to mp3) with
ffmpeg -i myyoutubefile.flv -vn -acodec libmp3lame -ac 2 -ab 128k myyoutubeaudio.mp3
You can do this all in one step with a handy script. Watch this space.
Easy when you know how...