there should be many circuits that show how to use a microphone and ampliphier and wires to send signal from one place to another.
there are wireless devices, baby monitors, spy-cams, intercoms, that do this wireless
if you feel you need to invovle an arduino in this is some manner, spend some time with Google use Arduino with your search
Things like that, see what others have done. If you find no one has done what you want then re-read post #2
Just because it is not capable of processing the data, does not mean you cannot use a different chip that can, and use the Arduino to turn that chip off and on.