I had the same problem and I found this very simple solution.
audio_file.onchange = function(){
var files = this.files;
var file = URL.createObjectURL(files[0]);
audio_player.src = file;
audio_player.play();
};
<input id="audio_file" type="file" accept="audio/*" />
<audio id="audio_player" />
You can test here:
http://jsfiddle.net/Tv8Cm/