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?
When playing the blues harp, a constant flow of air comes out of the lungs (blow note) or a constant flow of air flows into the lungs (draw note). On the other hand, in the oral cavity, in the reed chamber and in the surroundings, the air oscillates (that's why we hear a tone). And the reeds in the instrument also oscillate vigorously. How do these vibrations arise?
In the blues harp, the fluctuating airflow and the oscillating reeds influence each other: airflow acts on reeds, reeds act on airflow. As a result, the pressure fluctuations in the air stream and the reed vibrations can blow each other up. The term "self-excited oscillations" for this process means that airflow and reeds convert the constant airflow from the lungs or into the lungs " by themselves" into oscillations.
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?
This concept is wrong for several reasons. To argue the point, let's imagine that the blues harp sounds at full volume (this makes everything easier). The blues harp reeds are thus supposed to vibrate powerfully already.
1. Each of the two reeds in the channel oscillates almost by itself. It is primarily the elastic force and the inertia of the reed mass that alternate in their influence on the reed movement: Once the reed moves, it "wants" to keep moving. It has "momentum", with which it can run against elastic braking forces.
2. If you take the blues harp away from your mouth, you will hear the reeds keep oscillating for a short time. If a reed in channel #4 of a C-harp continues to vibrate for half a second, it has moved back and forth about 250 times - completely without the influence of a pressure force. From a physical point of view, the reed continues to oscillate for such a long time because only small energy losses occur during the oscillations. Only these energy losses have to be replaced by the pressure force.
3. The elastic force of a reed is approx. 30 times greater than the pressure force (the "Bernoulli force") during a normal draw note. In the case of a draw bend, it is still about 10 times as great. Elastic force and pressure force are therefore by no means equally strong "partners" that alternately push and pull.
4. It is the true role of the pressure force to compensate for the small energy losses of the oscillating reeds. A blues harp reed almost vibrates by itself, but only "almost".
5. The influence of the pressure force ("Bernoulli force") on the reed movement should be thought of more as a kind of "balance". While a reed oscillates back and forth one time, it is - taking everything in account - accelerated more than it is slowed down by the pressure force. Or, physically more correctly: The pressure force adds more energy to the reed movement by accelerating it than it takes away by decelerating it. The energy balance is positive!
6. Since the reed requires only a small amount of energy, a comparatively small compressive force is sufficient.