Is it possible to set alert sound for new incomming messages and notifications associated with my Ask Ubuntu account?
If you are using Chromium or Firefox, try the Desktop Notifications for Stack Exchange extension, written by Rob Wu. A picture says more than a hundred words, so here is a screenshot (taken from the Stackapps.com site):
I cannot remember hearing sounds, but it should be easy to implement. When I see him later this day, I will ask him about it.