What is the best way for playing audio files stored on server machine?

I uploaded a lot of audio records to my server. Every record has duration about 45 min. I would like to play this files on my website like youtube, but only in audio format. I'm using Web audio API and I heard about html5 local storage. Is it better to use this html local storage, or to play files directly from server storage? How to play file from absolute path on server where is stored my website? Can that be done using xmlHttpRequest or what?