I empathise - drove me completely nuts as well, and I cursed myself for being loyal to the brand and noy buying a BlackBerry. Moreover, the pathetically inadequate User's Guide is no help at all!
Press the Home key, which will take you to the Main menu
Choose Ctr Panel (it's red)
Scroll down to Tones (should be the 3rd one there)
Scroll down to Warning Tones (should be the 12th one there)
Change On to Off
Back, Back, Back etc.....
wait a couple of secs...
Hopefully, that wretched tune will have been silenced!