You haven't let us know all the details. There has to be a reason why 12 AAA batteries are specified. Do you have the characteristics of the buzzer?
Mosaness said:
The buzzer would be parallel to one side of the window and the voltage source will be parallel to another side of the window. There will be resistors in series in between the wire connecting the buzzer and the voltage source.
If the burglar cuts the wire along the top frame (say through the top resistor), how does the peizo get the power to sound off?
I can see two ways to secure a window with just wire: one is to detect broken glass by running wire around the glass at a smallish outline and the other is to detect an open window by running wire from the frame to the window edge, maybe in more than one place. Both depend on breaking the wire to detect a problem (as you already mentioned), which means your circuit needs to detect an open circuit from a safe short circuit. It also means you can use the same length of wire to circle the glass and frame, and perhaps it can be run past several windows and doors, since any break anywhere should set off the alarm. If you need to have an idea of where the break occurred, then you need separate wires to detect problems in separate zones.
The fellow in the other thread already mentioned this, but to spell it out, you want to short out the buzzer with the wire so that 0 volts appears across the buzzer under normal operation. When the shorting wire is broken, the buzzer sees some voltage across it and sounds off.
Next you might want to look at how to make things tamper proof. Can the burglar do anything to foil the alarm if he has access to the wires running along the window? (I don't see how to detect this without using an amplifier using a wheatstone bridge to compare the resistance of the wire network to a reference). The thing is powered using AAA batteries... can you do something to extend battery life or detect a low power condition to alert the customer to replace batteries (again, normally I would say make the buzzer chirp but you can't do that with just resistors and sounding off the buzzer constantly may be a way to kill the battery while the customer is away from home).
Then see if there are any gotchas... you mentioned adding resistors in the loop to prevent false alarms. I think the place you read this from was concerned about flux through loops of wire or maybe changing capacitance between objects moving with respect to the wire. This is not going to be enough energy to sound off a buzzer and would only matter to sensitive pickups. For example, if the amplifier and wheatstone bridge I mentioned was in play, it may detect induced voltages along the wire and falsely set off an alarm.