It is not possible to increase the amount of RAM on an Arduino board.
You are stuck with the 1KB that is there. You can interface to different memory media like SD and USB memory, but they are probably too slow for audio use.
The Ada fruit wave board is as far as i know a playback device only.
To have one sound stored on Arduino and at the same time capture a second sound and compare it to the first one is simply too much for Arduino to handle.