Questions about blues harp physics
Are there practical applications for instrument making?
There is little that manufacturers or customizers do not already know and much better from practical craft experience. Physically, the playing performance of a blues harp comes from the reeds and the airflow, which is influenced by the blues harp's construction. Reed properties, especially their eigenfrequency, which can be heard when plucked, can actually be calculated using physical formulas. I do not know whether manufacturers really do it that way. The airflow through the blues harp is so complicated that it cannot yet be simulated with today's computers. There are equations (the Navier-Stokes equations), but they can't be solved. Systematic experimentation on the PC (for example, systematically changing the channel shape or the reed shape), as is practiced in other industries, is likely to be a thing of the future for a long time to come.
What are self-excited oscillations?
In the blues harp, the fluctuating airflow and the oscillating reeds influence each other mutually: airflow acts on reeds, reeds act on airflow. As a result, the pressure fluctuations in the air flow and the reed oscillations can blow each other up. The term "self-excited oscillations" for this process means that nothing intervenes from the outside, for example, no tiny motor that moves the reeds back and forth. The air flow and the reeds cause their oscillations without any external help, i.e. "by themselves".
Are there Bernoulli forces in the blues harp?
Bernoulli forces usually play a role when an air stream accelerates along a surface. An example is air flowing through a narrowing pipe. If the velocities in the pipe are less than about 30% of the speed of sound, the air does not accumulate and must therefore flow faster through the bottleneck. This results in a pressure drop at the constriction. Static pressure and velocity upstream of the bottleneck and within the bottleneck are related to each other via a Bernoulli equation.
If the pressure on the wall inside the constriction is lower than the pressure acting on the wall from the outside, the flowing air exerts a suction force perpendicular to the wall. In this context, one speaks of a Bernoulli force.
It has been known for some time that practically no air flows along the surfaces of the blues harp reeds. The truth is that the air flows out of or into the reed channel (when blowing or drawing) more or less vertically through the slots between the reeds and the reedplate. To highlight it once more: There is no airflow along the surfaces, so in this sense there can be no Bernoulli forces.
On the other hand, the airflow is indeed vigorously accelerated as it passes from the reed channel into the slots (or vice versa), and a Bernoulli equation can be applied, resulting in a compressive force on the airflow through the slots.
The currently existing physical models for the blues harp assume that there is a uniform pressure in the reed channel. Therefore, if a compressive force acts on the airflow at the slits, then this compressive force acts throughout the entire reed channel, and thus on the reeds as well. Thus, a pressure force acts on the reeds, which is calculated using a Bernoulli equation. In this sense, one could again speak of "Bernoulli force", but the airflow does not sweep along the surfaces of the reeds, but along their lateral rims, whereby the suction forces on the two lateral edges cancel each other out.
By the way, the pressure force on the air stream and on the reed surfaces is likewise not anything that "magically" arises within the blues harp. The origin of this force is actually that we blow or draw while playing.
Conclusion: The pressure force on the surfaces of the reeds occurs in a Bernoulli equation, but should not be called a "Bernoulli force".
The Bernoulli force pushes, the elastic force pulls back - is this true?
"Bernoulli force" is a term for the pressure force acting on the reeds. The elastic force is a force with which the reed "defends" itself against deformation.
Does the pressure force push the reed toward the reed plate, and does the elastic force pull it back?
Since both forces basically act simultaneously and together, the question can be rephrased: Does the pressure force prevail on the way there and the elastic force on the way back?
When the blues harp sounds at full volume (in the "steady state"), the elastic force for a normal draw note is about 30 times greater than the pressure force (the "Bernoulli force"). In the case of a draw bend, it is still approx. 10 times as large. And it does so all the time, i.e. backwards and forwards. The forces do not alternate, but the elastic force always prevails. How then does the reed make its way to the reedplate (and beyond)?
When the reed oscillates through the middle position on its way to the reed plate, it is fast (it was previously accelerated by the elastic force). It gets to the reed plate because it has "momentum". The reed has mass, and the mass "wants" to move on - even if the elastic forces brake more and more. Finally, the reed is actually slowed down, is then accelerated by the elastic force towards the center position, moves through the center position, and the game is repeated on the other side in inverse direction.
The role of the pressure force is actually much more subtle. It does not act exactly in sync with the elastic force, but slightly offset. The reed movement has - compared to the pressure force - a slight latency. Latency is known to everyone who has ever tried to make music with each other via the Internet. Latency means: comes later, lags behind. This allows the pressure force to add energy to the oscillating system of reeds and airflow. Since blues harp reeds oscillate almost by themselves, very little energy input is needed per oscillation, and the fluctuations of the pressure force are sufficient for this.