The Mozilla-specific Audio Data API was theoretically deprecated in March 2012 when it was agreed that the draft standard Web Audio API would be implemented in Gecko. In practice, Gecko didn't start warning that the API was deprecated until Firefox 22 when bug 855570 landed.
Bug 927852, containing a simple default preference change to disable the Audio Data API by default, has just landed on mozilla-inbound and will make its way to mozilla-central overnight. This means that uses of the Audio Data API that triggered a warning in the developer console will now fail by throwing an exception.
Changing the default value of this preference gives us an easy way to revert the change if anything critical arises as the change filters through the release trains. Once this change has reached the released Firefox 28 and then baked through a couple of additional release cycles, the code implementing the Audio Data API will be removed from the tree.
The Mozilla Audio Data API was started back in December 2009 by David Humphrey, being announced here and implemented in bug 490705. David kindly posted a series of articles as the API was under development, you can find them under this category of his blog. The patches implementing the API landed in August 2010 and shipped in the stable release of Firefox 4 in March 2011.
David and his team's work provided an outlet for web developers to express interest in developing audio applications for the web, and provided an impetus for the W3C to form the W3C Audio Incubator Group chaired by Alistair MacDonald. This working group started on 12 May 2010 and closed on 28 March 2012, ultimately becoming the W3C Audio Working Group.
The (now draft standard) Web Audio API was proposed to the Audio Incubator Group by Chris Rogers in June 2010. Once it became clear that the Web Audio API would win out and become a standard, the Gecko implementation was started in bug 779297 in August 2012. Ehsan Akhgari, Paul Adenot, and Karl Tomlinson have been working on it since then, with the first stable version shipped in Firefox 25.