The Clarinet BBoard

Re: Soft Reeds --High Notes?

Author: mrn  Date:   2008-12-09 14:47 kdk wrote: <<I'm not convinced that a reed really behaves like an airplane wing, mostly because (a) it isn't attached at its edge - the ligature holds the reed over an area that starts near the reed's midpoint and ligature design is predicated on the theory (whether it's true or not) that the entire reed vibrates; and (b) the force driving the reed - assuming it's provided by the player's airstream - doesn't seem to be periodic - in fact one of the staples of effective technique is the ability of the player to produce a steady airstream.>> While these things are true, they don't really invalidate the physical analogy with a mass and spring. Even if the whole reed vibrates to a certain degree, the major component of reed motion is still the bending of the vamp portion of the reed--the fact that the rest of reed may experience other vibrational modes doesn't change that. The biggest assumption that I made was that the spring action is *linear* (that is, there is a spring constant, as opposed to something more complicated). A real reed (and a real airplane wing, for that matter) is nonlinear. Nonetheless, in a surprisingly high number of applications (in fact, probably most of the time) a linear model will suffice to explain the basic operation of a physical system in a qualitative way. So that is a simplifying assumption I'm making, but I think it's probably good enough here to explain what happens--you have to make the same kind of simplifying assumptions in the airplane case, too, and since I never acutally relied on the assumption that only part of the reed vibrates, reeds and wings are not really as different for our purposes as they might seem. Besides, real airplane wings (along with the fuselages they're attached to) vibrate along their whole length, too. As far as the airstream being constant, while that may be true from the player's perspective, once the reed starts to move because of the airstream, the reed is subject to constantly changing forces from both sides (since pulses of air pressure in the mouthpiece reflected back from the bore also have an effect), and it happens that the forces are periodic (and thus mathematically decomposable into sums of sinusoids). Also the mathematical theory behind linear systems says that as long as we assume the system is linear, we need only figure out what the response of the reed will be to a sinusoid to know what response we'll get with other types of stimuli, so the nature of the player's airstream doesn't really affect the analysis. In fact, if you solve the equation on paper, you can change the input stimulus to anything you want and still get the same result. Now as I said, the reed/mouthpiece system is not really linear (neither is an airplane wing--they are both quite non-linear in operation), but a linear model will quite often give you a reasonably good qualitative picture of how a physical system like this will operate (especially if the amplitudes are relatively small), and there some good mathematical theory (Taylor's theorem) that explains why this is true. In electronics, which is my primary field of engineering expertise, we routinely use linear models to predict behavior of negative-resistance oscillators (which is what a reed/mouthpiece system is), even though we realize that ultimately the system is non-linear--it's good enough to make it work, though. But that's also why I said that what I gave was a partial answer to the question. Sometimes that's the best we can do, even as engineers--that's why people build prototypes! A lot of engineering analysis design involves figuring out what properties change when you tweak certain parameters and then tweaking them with a prototype or computer simulation to get what you want. Getting an exact analysis on paper almost never happens. It took me a while to figure this out when I was in college, but it was an a-ha moment when I did! Analyzing a real reed with its complex internal structure and complex shape would be quite difficult to do, and we'd still only be able to approximate what it does, even if using sophisticated software to do it. Ultimately, though, I'll admit that to a certain extent you simply have to take my word for it that this is a decent enough approximation to yield useful results. You're also right that this won't necessarily be of any benefit to a young student. I just included it here because Norbert asked about it, and, for me anyway, it was more illustrative than a simple reference to another person's statement about it.

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