Firefox does not control what sounds are made unless you have an add-on that is being used targeting what site(s) your emails are coming from, in which notify you with a special sound. If this is not the case and the site does not allow you to change the sound, there is nothing more that can be done but to leave feedback to Microsoft to implement such changes.

It's Friday night, time for a little mischief.

You can hack that page to swap the default WAV file for another one, by changing the address of the sound file to a new address of your choice. At least, you can do it after the first time OWA plays its default sound. In my case that occurs when the notifications list drops down. When I tried to preemptively modify it, my change was blown away.

The following worked with OWA on Exchange 2010, but I don't know about your version:

Select and copy the following long line of script:

var tgt=document.querySelector("#divSoundContainer audio"); tgt.src="//www.jeffersonscher.com/gm/snd/Bicycle Bell Ringing-SoundBible.com-607558103.wav";

Open the web console below your mailbox by pressing Ctrl+Shift+k.

Next to the caret (>>) paste the script and press Enter to run it. Firefox should retrieve a WAV file from my web server and play it. (http://soundbible.com/292-Bicycle-Bell-Ringing.html)

Then you can close the console and that sound should be used until you reload the page.

Now... it's a little awkward hacking the email site by hand. You could use a bookmarklet to make it a one-click operation from the Bookmarks toolbar, or a userscript to make it automatic.

But could you test first and see whether that approach even works on yours? Also, you'll need to find a sound you like and some hosting for it (Firefox is unlikely to load a sound file from your hard drive for security reasons).