Since WordPress version 3.6 WordPress added the ability to embed audio into posts and pages by automatically wrapping the link (URL) to your audio file in your media library with an audio short-code. If you use Visual mode this is a behind the scenes kind of magic where all you would see is a graphical play button in your post/page that would play your audio file when you clicked it. If you’re comfortable in the Text mode (HTML) then you would see the following:
[audio mp3="ABSOLUTE LINK TO MY AUDIO FILE"][/audio]
Recently I’ve been hearing people having issues with this not working for them. A temporary solution is to either add your media, audio in this case, as a “Link to media” from the “Embed or Link” drop down when you’re adding your media OR choose “Embed media player”. Then when back in the text editor select Text mode and change the embed code from what you see above to this:
[audio:ABSOLUTE LINK TO MY AUDIO FILE]
Then you will get the following, with your own audio file of course.[audio:http://pccweb.ca/test-site/files/2013/03/01-Glenview-Podcast-March-24-2013.mp3]
This issue could be caused by a conflict with the theme you’re using or a plugin, but until that is resolved I suggest using the above work around.