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Re: Physics

Author: mschmidt
Date: 2007-08-18 00:22

Let us say we were going to construct a consensus understanding of how a reed works, and explore the consequences of such an understanding. I'm not SURE about any of these things, but I think most of them are mostly true. You are welcome to disagree, and if there is substantial disagreement, then we'll have to do some real research.

1. The tip of the reed closes and opens at the fundamental frequency of the note being played, which is selected by the fundamental frequency of the instrument air cavity. Therefore: (a) The tip must be able to vibrate at a wide variety of frequencies. (b) The tip must neither be so stiff, and the reed so open, that the opposite sides of the reed can come together to cut off the air, nor must the tip be so non-resilient and the reed so closed, that the tip cannot reopen. (c) The flexibility of the tip (which is a function of both thickness and length), and the opening of the reed (either "natural" or as changed by lip pressure), affects the speed of air necessary for the Bernoulli effect to close the reed. These are the primary determinants of the "resistance" of the reed. Note that there are already four ways to affect the resistance of the reed: tip thickness, tip length, and opening caused by the reed itself, and opening as adjusted by the embouchre.

The opening and closing behavior of the tip may be further modified by couplings to the other parts of the reed, which could be considered secondary determinants of resistance. I am not absolutely sure that the secondary determinants will always have a smaller effect than the primary determinants, but it's a starting hypothesis. More about coupling later.

2. The opposite blades of the reed do not touch each other except at the side edges and the tip. Therefore, the function of all scraped areas behind the tip is either to (a) affect the vibrational behavior of the tip through direct through-reed vibrational coupling, (b) modify the shape of the cavity formed behind the tip in a static sense, (c) couple directly with the vibrations of the air column itself to selectively reinforce or cancel particular vibrational modes of the air column, or (d) couple simultaneously with both the tip and the air column to affect vibrations of both.

For all you non-physicists out there, a brief word about coupling. "Vibration" involves oscillatory motion. The tip of a reed oscillates. A clock pendulum oscillates, too; it goes back and forth. If your clock pendulum had another pendulum hanging from the end of it, the behavior of the clock pendulum would be affected. How it would be affected would depend on the relative weights of the two pendula, length of the arms of the pendula, and so forth. These two pendula are coupled oscillators. The reed and the air column of the oboe are coupled oscillators; together they determine the fundamental frequency and the distribution of partials of the sound. The length of the air column (and the harmonic, selected by register keys) is the biggest determinant of the fundamental frequency, but you can make a reed that plays flat, because the reed couples with the air column and can slow down the vibration. But the reed itself can be considered as a system of multiple coupled oscillators.

OK, that's enough for now on the basics. There's a lot of mystery in choosing amongst the options in #2, although I think that (b) is relatively minor. I think the heart of understanding the heart has to do with affecting the degree of (a) and (c) and (d), but I'm still thinking about mass vs. stiffness.

Mike

Still an Amateur, but not really middle-aged anymore

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