Author: Bob Phillips
Date: 2011-06-11 16:30
@Jack,
I'm a mechanical engineer with a bit of grad work in acoustics and have done a fair amount of work in vibration problems, and that is what my somewhat intuitive explanation of reed behavior is based on.
Imagine that the pressure wave from the air column is squeezing up into the mouthpiece, and getting further compressed against the moving reed. If the reed is too slow to respond to the air column, it won't be able to resonate with it and transfer energy to the air and keep things vibrating.
If the length of the air column (and therefore its resonant frequency is suddenly changed) the reed has to respond to it to keep things going. We've all had the experience of making a leap (particularly downward) when the reed let us down, and the clarinet either failed to speak, or squeaked.
The poor reed has to change its vibration frequency quickly as the player changes the air column pitch. It can do that only of it is "faster" than the air column. The speed with which this is accomplished also depends upon the reed's damping. I've done some work on the effect of damping in transient resonance conditions, but do not have a clear understanding of how it all works.
Adding damping to the consideration involves at least two sources of energy dissipation. One is the "squirting" of air out of the disappearing gap between the reed and the rails and tip of the mouthpiece --complicated by moisture there. The other is the structural damping of the reed material. Maybe the plastic in a synthetic reed has more damping than cane, and maybe a waterlogged cane reed is both more dense (because of the weight of the entrained water) and more dissipative.
@Mark
(You know this.)
The pitch of the fundamental frequency played on the clarinet depends on both the air columnS frequency and the reed vibration frequency. If that were not the case, then the player could not "lip" the pitch into tune.
We have to remember that the "air column" is not all in the bore of the clarinet. At least two more cells of vibrating air contribute (and complicate) the situation. Pressure on the back side of the reed from the player's mouth affects the reed vibration in two ways: by algebraic summation with the pressure on the other side of the reed, and by forming a "jug." By "jug," I mean a Helmholtz resonator like a long-necked bottle, which when blown like a flute will produce its own musical tone. The player alters this mouth organ to help make it all work.
Another air sac that participates in the tone generation is made up of lungs and throat.
I have yet to see a really comprehensive mathematical model of the lung, throat (and bronchial network), tongue, reed, mouthpiece, clarinet/sax/oboe/flute/bassoon, ... There are pieces around, but the definitive biomechanical doctoral dissertation has yet to be published.
SIGH
Bob Phillips
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