Your expectations are about to be dashed. That is, how would said sensor know it's 6 inches and not 8?
Most folk go with switches to doors and such. i.e. your basic alarm/security system.
I'm wondering if the technology exists to be able to place sensors around my home that would sense a sound in a 6 inch radius and send a signal to a mobile app that identifies which sensor detected the sound?
For example, if I had one sensor in my bedroom closet and one in my kitchen cupboard, a sound originating w/in 6 inches of the closet sensor would send a signal the the mobile app identifying the sound came from the closet sensor ... and the kitchen sensor would not pick up the sound.