What makes reeds oscillate - part 1

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What makes the reeds oscillate?



1. Asking physics questions


Harmonica reeds are made of metal.
Softly inhaling or exhaling through the instrument is enough to make a blues harp sound.

Can gentle breathing actually move metal?

And how can breathing in one direction cause the reeds to swing back and forth?
The following illustration shows a vibrating reed true to scale. The reed is 0.1mm thick. The maximum deflection from the rest position is 1.5 mm. The reedplate (black hatched) is 1.0mm thick.
Harp reeds protrude slightly from the reedplate. The clearance gap is the distance between the tip of the reed in its resting position (drawn in blue) and the lower edge of the reedplate (dashed green).

The constant breathing pressure (overpressure when blowing, negative pressure when pulling) causes only a small, constant deflection of the reed. This position (orange) differs only a little from the rest position (blue).

But how do the comparatively large reed oscillations develop?
2. Reeds oscillate almost by themselves

2.1 Plucking a reed

First of all, we check that the harmonica reeds oscillate almost by themselves. To do this, we pluck a reed and measure its movement with the help of a guitar pickup. The result can be heard and seen. The following figure shows how the oscillation becomes weaker within the first 0.5 seconds.



Does the oscillation decrease a little or a lot? To answer this question, you need to know how often the reed swings back and forth within these 0.5 seconds. In this figure, the D-reed in channel #4 of a C-harp is plucked and starts oscillating at a frequency of almost exactly 600Hz, which means that the reed oscillates 600 times per second. The illustration shows 300 oscillations.

We now fade in after 0.1 seconds and see the following 20 oscillations "in slow-motion". Obviously, the oscillation decreases only gradually .

In other words, we don't have to do much to make reeds oscillate in the blues harp. The reeds do this almost by themselves!

2.2 Persisting oscillations

If you take the blues harp abruptly off your mouth at the end of a tone, you can hear how the sound reverberates softly. What you hear is the decaying reed oscillation.

With the electronics built into James Antaki's TurboHarp ELX, the reed movement can also be made directly audible and visible (you can find out what else you can do with the TurboHarp on turboharp.com's website or on YouTube).

In the illustration, a note is produced (draw note on channel #4 of a C-Harp) which is maintained for about half a second. Then the instrument is moved away from the mouth and the sound fades out for about half a second.
Below it you can see "slow-motion pictures" of the decaying reed oscillation after 0.1 seconds and (in the same scale) after 0.3 seconds.

Once again, it becomes clear how little energy is lost and has to be replaced a persistent note is played.

3. Physical views

3.1 Energy

In reeds, two forms of energy are continuously transformed into each other: kinetic energy and elastic energy. The oscillation becomes slightly weaker because additional forms of energy occur: The spring heats up slightly (heat energy), the surrounding air is moved (kinetic energy of the air), playing on the blues harp produces sounds (sound energy). These forms of energy are continuously subtracted from the sum of kinetic and elastic energy and only this subtracted energy has to be supplied by the player if a longer lasting note is to be played.

3.2 Force and inertia

In the reed there is a continuous interplay between the inertia of the reed mass and the elastic force generated inside the reed. As long as the reed mass is moving, it "wants" to move on. A deformed elastic body "wants" to reverse the deformation. The oscillation becomes slightly weaker because of additional braking forces. Only these braking forces have to be neutralized by an external force acting on the reed if a longer lasting note is to be played.


3.3 Illustration

The orange illustration shows the oscillation of a plucked harmonica reed as a column diagram: The time runs from left to right, and at regular intervals the deflection of the reed is shown as a column height.
The red columns below illustrate the kinetic energy and the blue columns illustrate the elastic energy. The ideal case of a vibration without energy losses is shown: The sum of kinetic energy and elastic energy is the same at all times. Even without our help, the reed would oscillate indefinitely.

The two physical views are equal: the greater the kinetic energy, the more the mass inertia plays a role. The greater the elastic energy, the greater the elastic forces.


4. The transient response

The illustration shows the transient response of a draw note recorded with the TurboHarp in slow motion. These and many other records show that the reed vibration always builds up gradually.

The energy is supplied "bit by bit". The energy once transmitted to the reed remains stored in it for the most part, so that the total energy increases more and more.

Finally, one comes into a saturation range. The mechanism for the energy supply works there no longer. The maximum volume is reached at a given blowing or suction pressure.
5. Stationary oscillations

The illustration shows a "slow-motion recording" of the reed oscillation for a longer lasting note of constant volume.

The player must replace only the comparatively low energy losses of the vibrating reed. The reed oscillates almost by itself.

6. The oscillation starts

How can an oscillation be stimulated by constant blowing or drawing?

The video shows the model of a blues harp reed: a metal strip that is clamped at one end.

The role of a constant overpressure or underpressure during blowing or drawing is played by a weight which is applied to the free end of the metal strip.

A constant weight only causes the strip to bend. An initially excited oscillation gradually decays and finally disappears completely.
Caution: In the video the bending of the metal strip is exaggerated ( so that you can see it clearly ). In fact, a constant breathing pressure would bend a blues harp reed only very slightly: In a true-to-scale drawing, the resting position (blue) and the deflection by our constant breathing pressure  (orange) are almost indistinguishable.


The abrupt onset of breathing pressure is excessively overdone in the video. In fact, pressure builds up continuously from zero. But this doesn't change the basic result either: an initial oscillation fades away, leaving a constant bend.

Vividly: a constant force can cause the blues harp reed momentarily to vibrate by "pushing", but this vibration disappears again.

How can a continuing strong vibration of the reed nevertheless occur? The answer will be: feedback!

7. The slots

The slots between the reed and the reed plate are decisive for the occurrence of a continuing oscillation. The closer the reed is to the reed plate, the less space there is for the air that has to squeeze through the slots. This in turn influences the pressure that ultimately prevails on the surface of the reed. (Why does the air not congest in front of the narrowed slots and simply wait there until the slots open again? The reason is difficult. In any case, the fact is that instead the pressure difference increases and the air is accelerated by the constriction.)
 
So maybe we can create a constant pressure in our lungs, but the pressure at the reeds varies with time. This can work because you always have to see pressure and air flow simultaneously: With a blow note, there is constant overpressure in the pulmonary alveoli and a constant flow of air is generated. On the way through the trachea, oral cavity, reed channel and slots, pressure and air flow begin to fluctuate in the same rhythm.

To be more precise: the fluctuations of air flow and pressure have the same frequency, but are time-shifted. The reasons for this "delay" are the inertia of the air mass and the resonance characteristics of the vocal tract (the vocal tract is the mouth and throat area). Why this is so and why delay is important cannot be said in one sentence. A separate essay on this topic is planned ...
8. Feedback

The reed is more or less deflected from its resting position by the blowing or suction pressure in the reed channel: the pressure influences the deflection.
 
The deflection of the reed affects the size of the slots. This changes pressure: the deflection influences the pressure.


Deflection influences pressure - pressure influences  deflection - deflection influences pressure - deflection influences  pressure...   

If everything works out well, this reciprocal influence results in the reed oscillations and the pressure oscillations blowing up each other. This is called feedback.

The much-feared feedback noise on stage is a prime example of how tiny causes can build up in their effect: Some noise is picked up by the microphone, comes amplified from the loudspeaker, is picked up by the microphone, comes amplified from the loudspeaker ...

Warning of a misunderstanding: The feedback noise on stage blows up because the microphone sound is amplified.  So the amplifier plays a decisive role.
The fact that the reed oscillations and the pressure fluctuations influence each other does not mean that they have to blow up. And indeed there is no amp inside the harp. So: blowing up without an amp!
(How does it work? The reason is the already mentioned delay, see above...)

9. Longer lasting notes

If a note lasts longer, we blow or draw just enough to compensate for the energy losses in the vibrating reeds. This is again possible because reed oscillations and pressure fluctuations influence each other and because there is a delay between the two.

Just like the annoying feedback noise on stage, the reed oscillations do not blow up arbitrarily high. One of the reasons for this is that the reeds cannot be bent arbitrarily.

10. The answer - Summary

  • By blowing or drawing we "push" the reeds just a little bit at the very beginning.
  • Through feedback, the initially tiny oscillations grow rapidly, while the reeds are supplied with energy  "bit by bit" from our lungs.
  • The reeds oscillate almost by themselves, because the elastic and the kinetic energy are continuously transformed into each other.
  • With a longer lasting note we only have to constantly replace the very small energy losses in the reeds.


 
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