So really want the AC going thru a relay that is Normally closed, and have some of that same AC be rectified into a low level DC (say by having the same AC drive a cheap wallwart as a 5V/12V source) , and have wallwart DC output go thru a current limit resistor to charge up a cap and eventually drive the relay into the open state to turn off the AC to your alarm bell.
System resets on power loss.
Shouldn't be that hard.
(or just a cheap radio turned up really loud!)
wallwart power supply to drive relay (or as needed for the relay you pick)http://www.mpja.com/prodinfo.asp?number=15178+PD
resistor & capacitor from your favorite supplier such that 1/2PiRC = 5 seconds (or something like that, maybe need a square root of 2 or something in there too, I'm a digital guy, go google it - big cap, small R)
(is it just me, or is turn-on current/voltage not shown on the data sheet?)
Okay, this one is simple to followhttp://www.mpja.com/prodinfo.asp?number=18474+RL
5V across coils, 120V across the relay itself, good 1A (for that 125W radio, good & loud!)
Don't forget another R in parallel with cap to ground to make sure it bleeds off on a timely manner.