Part of what my group does is to test TCAS after its installed by another group. On our aircraft, you'll hear "Traffic, Traffic" when you're 6nm away from other aircraft at your altitude. If you hear "Descend, Descend" or "Climb, Climb", you are within in 1nm and should probably be a little more concerned. There's another message telling the pilot to do it faster as you get closer.

Was it a male or female voice? It used to be a female voice on a lot of these systems and it was called the B1tchin' Betty. Of course we get a dude and we call it the B1tchin' Bob.