In my earlier post The Besler Steam Plane I mentioned, "What impressed spectators the most was the silence of the airplane. That was an important selling point, because in those days before radar planes were located and tracked acoustically."
The site Retronaut has an article, Listening Before Radar, that shows several examples of these old acoustic dection and tracking contraptions. I've included a few and there are more to see at the Retronaut article.
As an aside, while poking around the web for information about acoustic aircraft tracking I discovered that it is still being worked on. The EU is working on a system called SAFE-AIRPORT that uses phased arrays of microphones to track airplanes. The system is intended to be used in air traffic control around airports.