How can I tell when an HTML5 audio element has finished playing?

Using HTML:

<audio id="music" src="https://stackoverflow.com/questions/9346579/blah.mp3" onended="yourFunction()"></audio>

Using Javascript:

document.querySelector("#music").addEventListener("ended", yourFunction, false);

Using jQuery:

$("#music").on("ended", yourFunction);

Read more about Media events on MDN