Posted by Rick Denney on April 19, 2002 at 14:50:44:
In Reply to: Re: Re: Re: Re: Re: Re: Re: diaphragm placement/bore size? posted by Brian Frederiksen on April 19, 2002 at 14:30:46:
You are right, of course, but so am I. We are speaking of the same law. Boyle's law is usually expressed as v1p1=v2p2, where v1 is the volume in one condition, v2 is the volume in another condition, p1 is the pressure when the volume is v1, and p2 is the pressure when the volume is v2. If we are talking about the same air molecules, it applies. When the volume in the lungs increases (expansion as a result of diaphragmatic contraction, etc), the pressure decreases in accordance with the above relationship. If your mouth and glottis are open, then the air pressure will equilize--that is the outside air and the air in the lungs will settle on the same pressure. Where Boyle comes in is that it takes more molecules of air to do it--this is the flow of air going into the lungs--without more air the pressure cannot equalize. When you exhale, the volume contracts, the pressure increase, and the flow goes the other way to equalize the pressure.
As it flows, if the pressure is really close to atmospheric pressure, then it will approximately follow the relationship I mentioned. For a given flow, speed can only be changed by changing the area of the pipe, and so on.
So, Boyle explains the difference in pressure resulting from contraction (expansion), and that difference explains the flow exiting (entering) the lungs, and the Q=VA relationship I described explains what air speed will result from that flow with a given aperture size in the embouchure.
This process is why we are advised to use the "toe" syllable to shape our mouths and throat--it opens the throat and reduces airspeed and resulting turbulence and friction. As airspeed increases, so does friction, which means that the flow will be diminished a bit to the detriment of the sound. The concept of warm air really means slow air--but lots of it.
I hope you understand that I'm agreeing with you, but explaining the science a bit from an engineering perspective.
Rick "the hip bone's connected to the thigh bone..." Denney