The Intermatic SP440B is a magnetically actuated security alarm... very loud.
The response time of the combined circuit is fast... with no noticeable delay.

One note on adapting the SP440B to this application:  The SP440B alarm sounds when
the alarm's magnetically actuated switch opens, not when it closes as one might expect. 
Unsolder and remove the magnetic switch and connect 2 wires in its place.  Bring these
to the relay and switch as drawn but notice that since the alarm only sounds when these
2 wires are not connected, the 2 labels on the switch will be wrong and must be reversed.

The switch used in the unit pictured below does not have a center (off) position. 
It is not needed.  The SP440B has its own off/on switch.

This is all there is to it, inside and out. This is the Trouble Finder unit I have used for years.

(The small white Box glued to the top of the bigger gray box is the SP440B.)

Above is my grandson Atticus.