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freixas
Keymaster

This topic relies on background information in The Compressibility of Air and Mass Flow, Speed, and Pressure.

This post provides a some background into melodica reeds and how they work. Because I am relying on information I’ve gleaned from various sources (and which are sometimes contradictory), I would appreciate any corrections or additions.

Melodicas use reeds to create sounds. A reed is a thin piece of material that can be made to vibrate through the use of moving air. The reeds used in saxophones and clarinets are called “beating reeds” because the reeds beat against the mouthpiece. Melodicas use “free reeds”, reeds that are free to move without colliding with anything; instead they move through a hole in a reed plate.

More specifically, melodicas use “Western free reeds”, which are reeds that are suspended above the reed plate. “Eastern free reeds”, in contrast are cut from the reed plate. Eastern free reeds can produce sound regardless of the direction of the airflow, but they usually need a resonator to be heard. Western free reeds only work with the airflow in one direction, but they don’t need resonators and thus can support more compact instruments.

Actually, this is a topic for further investigation. Organs use Western free reeds and pipe resonators. The harmonica also uses Western free reeds, with the mouth acting as a resonator. I’ve opened my melodica and sounded a reed using a stream of air from an air brush. The sound is very quiet, implying that the exhaust port, air chamber, or both might be acting as a resonator and amplifying the sound.

Let’s look at a generic melodica reed.

The reed is attached to a reed plate using a rivet or screw. The long, flexible strip that produces the sound is called the tongue. It sits above an opening just slightly wider than the tongue. The exact dimensions are probably important. A Yamaha site on harmonica reeds (which are similar) claimed that the tongue clears the sides of the plate by 0.03 mm and the end of the plate by 0.1 mm.

Typically, the tip of the tongue rests above the plate at a height equal to the thickness of the tongue. This is not an absolute rule.

The dimensions for the reed above were assembled from various sources, including my Suzuki M37-C’s F3 reed and the Yamaha site mentioned above. This is intended as a starting point for investigating how reeds work. I wouldn’t rely on it to actually produce an F3 note. For example, the thickness of the tongue is incorrect for the F3 note, which is actually thicker at the ends than the middle. You can view the exact dimensions of my generic reed in this PDF:

Here’s how I believe the reed works (mostly taken from an article on concertina reeds):

• When all exhaust ports on the melodica are closed, the pressure throughout the air chamber and the space past the reed is equal. Air velocity is 0.
• When an exhaust port opens (from pressing a key) and you blow into the melodica, airflow begins.
• As we’ve learned from the background articles, the velocity of the air varies by the cross-section of the system. It will be very slow in the air chamber, which has a large cross-section.
• To exit, the air has to flow through the gap below the reed.
• Let’s assume that you blow at a rate of about 0.5 liters per second. This means that 0.5 L/s will flow past any cross-section in the system. Using the formula $V=Avt$, where $V$ is volume in cubic meters, $A$ is the cross-section’s area in square meters, $v$ is the velocity and $t$ is the time in seconds, we can calculate the speed as $v=\frac {V}{At}$. The reed, at rest, provides about 1.215-05 m2 of area. This yields an air speed of about 41 m/s.
• As we know from Bernoulli’s equation, as airflow increases, pressure drops. The region just below the reed now has lower pressure than the region above and the reed is pushed down into (but not touching) the reed plate.
• Once it drops this far, the area available for the air to flow drops to 1.552-06 m2. The speed of the air would now be about 322 m/s, which is close to the speed of sound. Air flowing at speeds above Mach 0.3 (0.3 of the speed of sound) behaves differently than slower air and so at this point the physics gets more complicated.
• Most people claim that the airflow stops. I’m not sure if this is possible but it might be true for a very short period of time. There may be some compression in our normally incompressible air, which would increase the pressure on the reed, causing it to continue to bend.
• Once it has bent far enough, the reed will provide a bigger cross-section to the air and air speeds will drop. This will reduce the pressure differences between the top and bottom of the reed. In addition, the reed will have stored mechanical energy, which will want to restore it to its rest position.
• The combination of more equal pressure and mechanical energy combine to speed the reed up through the reed plate, despite the fact that it will block the airflow again.
• The reed will continue moving past its rest position. Again, tension in the metal will slow this movement. If there were no further airflow, the reed would bounce up and down a few times until friction brought it back to its rest position. But if the airflow continue, then as the reed comes down it will again create a region of low pressure and the vibration will continue.

The vibration creates small regions of compressed and rarefied air—a sound wave.

I still have a lot of holes in my understanding of the process. Let’s say the gap is too large. This would mean that, for any given volumetric flow, the airflow through the gap will be slower, resulting in less pressure difference between the top and bottom of the reed. I might guess that I would need more air to start the reed sounding and that the reed would sound weaker. For a too-small gap, I would think the reed would sound with less air and have more volume.

A reed with no gap won’t sound, however, and it’s not clear to me why. The common explanation is that it blocks the airflow, which would be correct if the tongue made an airtight seal with the reed plate, but it doesn’t. Unless the seal is airtight, the air will find a way out.

As a related topic, why do some reeds sometimes “block” (refuse to sound)?

I know people have explanations for these things, but it’s not always clear whether the explanations are based on science or “common-sense” ideas of how things should work. Let me quote from the concertina article:

In the first part of the swing cycle, the reed moves down in the direction of the frame. When the reed gets closer to the frame the air flow diminishes greatly. When it enters the frame the air flow is at its minimum.

In this quote, the phrase “…air flow diminishes greatly,” is disturbing. One of the first things one learns in fluid dynamics is the continuity equation. Unless you are compressing air, there is no way to reduce air flow—what flows in is exactly what flows out. What is really happening could be much more complex.

The complete answer might be buried in this research paper: Aerodynamic excitation and sound production of blown-closed free reeds without acoustic coupling:The example of the accordion reed. Unfortunately, it probably requires an actual physicist with a background in fluid dynamics and acoustics to translate the findings for lay people.

Note: Sounds like I need to research a background article on sound waves.

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