I looked into this on my laptop which I'd never really bothered about setting any sounds for as a matter of interest . . . . . and came across this post on launchpad, alerts were not added for the stated reason. https://bugs.launchpad.net/linuxmint/+bug/1186624
I enabled login sounds/fails etc in the login preferences window as clem mentions under the accessibility tab, you should also just be able to add extra wav soundfiles into the appropriate folder I imagine if you want something else.
Thunderbird worked fine for me, make sure its a .wav or compatible file, only time I couldn't add a sound file was not realising it was an mp3.......
I thought I might have to get and install a load of sound files but it turns out there's a whole load i never knew were there already in /usr/share/sounds however, in sound settings and alert volume they can't be selected, and if I'm reading that link right, it's just set like that, for now at least. I assumed the command in the link mentioned as a terminal command so for the crack i entered it lol..... it basically came back with a message saying it hadn't completed or denied something... bizarrely wheni went back into sound/sound effects and choose default sound, the selector now works. . .. . . . . can't see how to get alerts for firefox though so if anyone else does feel free to chip in, I probably wouldn't bother but nandayo might !
Hope that helps somewhat . . . . . .
Lenovo ThinkPad T61 LM14 & 15 (different HDDs) Intel T7500/2.2GHz/Cinammon 1.6/1.8 Intel GM965. Toshiba Satellite M70: Dual boot Zorin OS & Elementary.Desktop:LM13/15 Geforce 9500 GT, Athlon 7750 Dual-Core 2700mhz,3gb RAM.Linux Registered #562462