Good ol' Herman VonHelmholtz. I did a science project in High School building band-pass sub-woofers using the Helmholtz Equation to try and calculate optimal port length. That was some crazy stuff!

I had read an article on Natural Resonant Frequency (NRF) as it pertains to motorcycles sometime in the past but can't remember the details. I found a great link from California Sciences that discusses the application and importance of NRF to motorcycle air-boxes in particular. Its got more equations than you can shake a stick at!

If you have 10 minutes, it's quite short and really worth reading.

http://motorcycleinfo.calsci.com/Airboxes.html

Some quotes:

"...In the '70s, the US government started making noise regulations tighter. At some point, the manufacturers realized that the noise from the air intake was part of their problem. They started to look for ways to muffle not only the exhaust, but the intake roar too. Sound waves are pressure pulses in the air. Pistons pull in air on their intake stroke, creating a low pressure pulse in the air box. Then on the compression, power, and exhaust strokes the intake valve is closed and the air box is free to return to atmospheric pressure. These alternating low pressure and normal pressure pulses are sound waves. The manufacturers needed some way to dampen them out."

"... So at resonance, air flows through a tuned air box almost without resistance. This is as close as we can get to a superconductor of air. "

"The idea that the snorkel makes for a significant impediment to air flow into the engine is questionable at best. Drilling holes to let in more air is exactly equivalent to drilling holes in your speaker cabinets to let out more sound. Removing the snorkel from your air box is the exact same thing as removing the port in your speakers, the tube that's carefully engineered to have just the right diameter and length to reinforce the bass on your speakers at low frequencies. By altering your air box in any significant fashion, you're most likely going to cost yourself three to five hp in the mid range, and gain nothing measurable at high rpms. "

Paz,
CC