Can I just be clear about one thing...
These 10 spaces and the sound: Am I right in inferring that you want a "logical OR" situation? I.e. it doesn't matter which or how many of the spaces are "invaded"... you get the same sound?
As the how the sound is made: The Arduino, in simple terms.... I like "simple" (matches my nature).... can close a switch. With the silicon intelligence of a 1980s PC, it is quite capable of cleverness in the closing, i.e. close for "x" seconds, not close again until "y" seconds have passed, etc, etc, but it is still, basically, a switch closure. That closing switch can be wired to lots of things.... a doorbell ringer might suit, for instance.
What sound: If you just use the Arduino to close a switch, we're done with the sound bit. Probably best to start there, as your sensors are not simple. But remember that the Arduino is clever. You might use it to generate the sounds that emerge when the switch closes. Maybe even "play" a short "audio recording". Subject for another time, another thread.
Sensors: PIR is probably going to be your best bet, if I guess your application right. Ultrasonic might "do", but as someone else said, they might confuse one another.... but!... can you mount the sensors on the ceiling, looking down? That might have all sorts of advantages, and might bring ultrasonics back into consideration.
Sparkfun has a little PIR, 0- 255 inches, $25
But their PIR is only $10, and I'd lean towards PIR anyway...
"At the risk of being totally boring...." (as Mrs. Wilknson says in the magnificent Billy Elliot musical), what does the Arduino bring to the party? Why not just connect some PIRs to a doorbell? Perhaps if you expand on the "why Arduino" side of things, forum members can help refine your design.