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?

To illustrate this, a toy spring will play the role of the blues harp reed. The figure shows a comparison of what the spring looks like in a relaxed state and under the influence of its own weight.
The weight of the spring takes over the role of the constant blowing or drawing force on the blues harp reed. In the first part of the video you can see how this weight deforms the spring.

In the second part of the video, the weight force acts abruptly on the spring, just as the blowing or drawing pressure acts abruptly on the reed. Now the spring is additionally accelerated and receives kinetic energy. With this additional energy package, the spring starts to oscillate as described in section 3. The constant weight force only causes it to be stretched additionally. The weight has no influence on the oscillation itself.
In other words: A constant force can cause the bluesharp reed to vibrate by "pushing" it.

7. Feedback

The reed is more or less deflected from its resting position by the blowing or drawing pressure in the reed channel. The pressure affects the deflection.

When the reed approaches the reedplate, the slots between the tongue and the reedplate become narrower. Blowing air through narrow slots or sucking in air through narrow slots requires more pressure difference between the reed channel and outside space. The deflection thus influences the pressure. (Why does the air not jam in front of the narrowed slots and just waits there until the slots open again? The justification is difficult. In any case, the fact is that instead the pressure difference grows and the air is accelerated and forced through the constriction.)
Deflection influences pressure - pressure influences deflection - deflection influences pressure - deflection influences pressure...   

If everything goes well, this reciprocal influence leads to the deflection and pressure swaying up against each other.


By the way, the feared feedback on stage is also generated in the same way:
Microphone sound influences loudspeaker sound - loudspeaker sound influences microphone sound - microphone sound influences loudspeaker sound...


If everything goes wrong, this will cause microphone and speaker sound to bounce up.

The picture shows a wave file of feedback noise. In "slow motion" you can see how the whistling starts within a few hundredths of a second out of nowhere. The sound frequency was 2300Hz, which corresponds to the blow note on channel #10 of a D-harp.

The analogy with the transient response of the blues harp reed (section 4) is obvious.

8. Longer lasting notes

If a note lasts longer, we blow or draw just enough to compensate for the energy losses in the vibrating reeds.

Just like the annoying feedback noise on stage, the reed oscillations do not escalate arbitrarily. This is partly due to the fact that large deviations of the reed would require very high forces.

9. The answer - Summary

  • By blowing or drawing we "push" the reeds 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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