How does the Bernoulli’s Principle apply to brass playing? I’m not a physicist (almost completely self-taught in that area), so I must acknowledge that this is an area where I just may be way off base. So rather than try explain this in detail, I’m going to simply offer my understanding at this time and ask my readers to help me fill in the gaps and correct any misinformation. I’ve heard contradictory statements about this from sources I trust, so perhaps this is another area where even experts still disagree.
First, what is the Bernoulli Principle? The relevant part for brass playing is that a fluid (or air, in our case) moving with a change in pressure will also be accompanied by a change in speed. This physical law is often cited (including by me) as the reason why brass players change the level of tongue arch according to the range being played. The higher the register, the higher in the mouth the tongue will arch, resulting in the air moving through a smaller area inside the mouth. The general reasoning here is that this results in the air striking the lips with faster speed/higher pressure, making the faster vibrations for the high register easier.
I recently got an email from Darryl who is trying to help me come to grips with why this might be wrong.
The pressure that one can create by lung pressure is the maximum pressure that will exist just before the embouchure, regardless of how one “narrows” the path before the aperture. The total pressure of the air is, at best, exactly the same as the lung pressure. Regardless of the air’s velocity of flow as it approaches the aperture.
As I understand things, he’s definitely correct that there is a maximum pressure that can be created in the thoracic cavity before internal mechanisms engage to protect you from an internal injury. I’m going by memory here, but I recall Arnold Jacobs writing about how this maximum amount of internal pressure is actually quite small (the context was, I believe, how we need not work as hard as we sometimes feel to breathe well for playing).
But I get a little lost trying to understand fully the context of Darryl’s corrections. Some of my confusion may be due to certain assumptions that I’m making regarding the dynamics of how the air behaves prior to striking the lips. First, I’m assuming that friction and viscosity aren’t changing around the model enough to be irrelevant to the tongue arch. Secondly, I’m assuming that the air behaves similarly to how it would traveling through a tube of varying size. For the sake of increasing my understanding, for now let’s just assume that this is the case. I think we can all agree that there are lots of variables here and that it’s not only impossible, but also unnecessary to consider them at this time. We’ll start burning those bridges later.
This web site has a nice description for us laymen regarding Bernoulli’s Principle. From it, I’ve learned some new things.
As a fluid passes through a pipe that narrows or widens, the velocity and pressure of the fluid vary. As the pipe narrows, the fluid flows more quickly. Surprisingly, Bernoulli’s Principle tells us that as the fluid flows more quickly through the narrow sections, the pressure actually decreases rather than increases!
First, it appears that I had an important point backwards. As the air gets forced through a smaller opening (e.g., in the oral cavity because of a higher tongue arch) the pressure actually decreases as it flows faster. Still, I’m left a bit confused because assuming the air flow through the body behaves as a fluid passing through a pipe, then Bernoulli’s Principle would indicate a difference in speed or pressure as it gets blown through the smaller “pipe” created by a raised tongue arch, contrary to Darryl’s correction.
Another web site addresses my confusion somewhat by differentiating between what’s called static pressure and ram pressure.
Static pressure should not be confused with ram pressure, which is the pressure felt by an object because it is moving relative to the fluid. Basically, the fluid is ramming into the moving object, or vice versa.
The ram pressure increases when the speed increases. This explains the stronger force felt by your hand when it is held a fast moving current. In the faster current, your hand is deflecting more flowing fluid from its original path.
So perhaps what we need to consider with regards to the tongue arch and how it affects the air pressure isn’t so much the static pressure inside the mouth, but the ram pressure of the air as it strikes the compressed embouchure formation. Again, assuming that the air inside the body behaves similarly to a fluid moving through a tube of varying sizes, I don’t understand Darryl’s corrections.
Can Darryl or any other physicist types out there with expert understanding of these principles want to chime in and help me better understand what’s going on? What is actually happening to both the static pressure of the air as it moves through a more narrow path due to the raised tongue arch? How does this affect the ram pressure of the air against the lips? Lastly, how does this make it easier for brass players to play in the higher register? Please leave your comments below.