you can buy those PIR beams for shop doorways etc, they are ded cheep.... from ebay, when the beam is broken they say "Bing Bong!"
They use Batteries of course and how long they last could be an issue
Or these.. Hallway Alarm
I use those little wireless doorbells for our garden gate and garage door, simply wired a door contact across the button and arranged that the magnet swiped across the contact rather than holding it closed in any position, the receiver can travel anywhere in the house.. The batteries in the receiver last well over a year and only one transmitter so far has needed a battery (twice) in about 6 years!Wireless Doorbell