I like Prof Kirk's explanation from another board.
The Whistler works on the same principle as when you blow across a pop bottle and make a tone. The less volume of liquid in the bottle (thus the more air) the deeper the sound. So, you put the engine at BDC and "whistle" across it to make a tone, and the frequency of the tone is measured; that measurement correlates to a specific air volume (well known by pipe organists the world 'round). Then you put the engine at TDC and whistle it again, getting another (higher) tone/volume. Once you know the BDC and TDC volume, a simple division calculation tells you the compression ratio... - GA