I think the problem with this suggestion is that the speed in which a question is resolved is not necessarily instantaneous. Posts may take hours, days or even weeks to be resolved. In such a case, having an audible notification system is simply not feasible. Sure this is not always the case, but when implementing a feature like this, one has to take into consideration all possible consequences...
A feature like this would be much better suited to a chat like area and believe it or not, there is already a system like this in place on the chat servers. Communications there are meant to be faster than the usual
- post a question
- receive a comment requesting more information
- answer the comment
- edit the question
- get an answer
- comment on the answer requesting clarification
Another thing to note here (speaking only for myself), is that people might not be 100% focused on the site the whole time that they are here. They might be at work, multi-tasking (as we do) and alt+tabing through multiple browser tabs only returning to Stack Overflow every so often to check for updates. So they might not want to be interrupted by a bleep every time someone mentions their name.
Oh, so you're on Stack Exchange?
Let me sing you the song of my people...