The cheap, cheap FM transmitter circuits change frequency when you get near them because the are simple and cheap and cheap. My FM transmitter has a transistor added to its output to isolate the tuned circuit from the antenna and to boost its output. It goes more than 2km so it is very illegal. I guess its power can be turned down.
My FRS transeivers were a bargain with their crystal frequencies, rechargable batteries, 38 channels and 3km range. I didn't make them and never looked inside them.