You're talking about using a mechanical compressive wave in a medium to transmit information. Whether the medium is 'air' or 'stick', the rate at which such waves travel is generally called 'the speed of sound in [medium]'.
Wifi signals to Mars travel at the speed of light in a vacuum. This is faster than any mechanical wave because the changing forces of compression between the atoms in the medium must still obey the speed of light.
mechanical compressive wave ,traveling at the speed of sound? Why do u introduce these? What has sound to do with my example? Imagine the stick not tapping on ground but just getting close. to it. Not an audio, but a visual way for the receiver to tell the 2 different singnal states. Then he'd grab his end of the stick and do the same. I am sure what you say is correct by itself but.. it feels there is just something from it that doesn't fit with my example.. Edit: reading again your comment and trying to understand what you say.. if i get it right then it's totally misleading to call it "speed of sound": it should be called speed of mechanical compressive waves