There were few options, but here is the process that worked for me.
first I installed the ffmpeg converter, as usual by,
$ sudo apt-get install ffmpeg
Then i downloaded the YouTube video to my home folder. Lets call it myVideo.flv (when you are watching YouTube video the flv file gets downloaded in to /tmp directory but i prefer DownloadHelper). Although DownloadHelper has a option of converting the video to mp3 format, it didn't work for me.
then convert the video by,
$ ffmpeg -i ~/myVideo -acodec copy convertedFile.mp3
Now listen to your new mp3 file using your favorite mp3 player.
(make sure that you are not violating any copyright issues when converting media)