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Clarinet reed

This section really applies to all the reeds- whether clarinet, oboe, sax, bagpipe,.... This technique uses a light reed with relatively high stiffness, so that the resonance of the reed itself is well over 2 kHz. This means that the reed essentially responds immediately to any pressure difference across the reed. What is important for this reed is the difference in pressure between the outside of the reed and the inside. As this pressure difference increases the reed begins to close.

This leads to two regimes of air flow through the small gap between the reed and the instrument. If the pressure difference between the outside and inside is small, with more pressure outside than inside, this difference in pressure will begin to force air in through the gap. The larger the pressure difference at first, the larger the air flow through the gap, as one would expect. However as the pressure difference gets larger, the reed begins to close. Thus there is a competition between the amount of air flowing through the reed between the increasing pressure difference and the decreasing gap ( because of that pressure difference) through which the air is forced.This means that when the pressure difference is low, the higher the pressure difference the more air is forced through. However once the reed really begins to close due to the pressure difference, the air flow begins to decrease. The smaller and smaller gap more than makes up for the pressure difference, and the flow decreases with increasing pressure difference (because the gap gets smaller and smaller). Eventually when the pressure difference is sufficiently large, the gap closes completely and no air flows at all.

Now, let us assume that we put enough pressure on the outside of the reed that the reed is almost closed. What happens if the pressure inside the instrument increases for some reason. Since the pressure inside has become higher, the pressure difference drops, and the reed opens more. This lets through more air. Ie, when the pressure in the instrument gets higher, more air flows into the instrument. Alternatively when the pressure inside drops, the pressure difference increases, and the reed closes further and less air goes in. Ie when the pressure inside is higher, more air flows in, and when the pressure is lower, less air flows in. Since more air flowing in tends to increase the pressure inside, we have the contrary operation, that higher inside pressures grow still higher, and lower pressures inside get even lower. This is just like the negative resistance I was mentioning. The air flow tends to make small pressure fluctuations larger and larger. As long as the air flows through the gap, this amplification will continue. The oscillation will continue to grow until finally the natural damping is of about the same effect as this anti damping due to the reed.

Figure 1 gives sketch of the behaviour of the reed. This is a plot of the air flow into the instruments as a function of the difference in pressure between the inside of the instrument and the outside the reed (usually in the mouth). The beginning rising part is where the higher pressure difference drives more and more air through the open reed. The falling part to the right is where the closing reed ( pushed shut by the difference of pressure between the outside and inside of the reed) pinches off the air flow.

To play the instrument, the player increases the pressure in his/her mouth until with no oscillation of the air inside the instrument, the difference in pressure would lie at about point A. The reed has started to close, but not completely and some air flows in. Now the player tongues the reed- closes off the gap with the tongue, and then rapidly withdrawing the tongue to let a burst of air into the tube. This starts the air inside the tube vibrating. Without the reed this vibration would rapidly die out. However, each time in its oscillation the air inside produces a higher pressure near the reed, more air flows into the instrument and increases the pressure still more. Each time the pressure inside, in the oscillation of the air inside, goes lower, the reed closes still more and the amount of air flowing in decreases, making that lower pressure even lower. Ie, just like pushing the child in the direction it is traveling, the air flow "pushes the pressure, making its oscillations even higher, and amplifying the sound. If one plays the instrument loudly, the pressure differences become high enough that the reed spends most of its time closed completely. It is only at the highest pressures inside that the reed opens and amplifies this high pressure.

Instead of having to decide each time the pressure gets high inside to let in more air, (as one does with the child on the swing in deciding to push in the direction of motion each time the child swings by), the reed does this automatically, and it will keep producing the sound as long as the air pressure outside is maintained around the point A.

Note that in the clarinet, one can control how large the gap is with no pressure difference, and thus how low a pressure closes the reed, by controlling how strongly the lips press against the reed. Ie, one can play using only a little bit of mouth pressure by almost closing the reed with lip pressure. This allows quiet playing. Similarly by relaxing the lips, the opening is larger and more pressure in the mouth is needed to get to the operating point and the instrument plays louder.

The primary difference between the various instruments (eg oboe and clarinet) is the natural modes of the instrument which this reed anti-damping amplifies. In the clarinet the modes are primarily those of a pipe closed at one end. The lowest mode has a frequency given by the velocity of sound divided by four times the length of the instrument. The higher modes have frequencies of three, five, seven,... times this frequency. At least for the lowest modes, it is therefor just the odd harmonics of the note come out of the clarinet.

The oboe, with its conical bore ( like a cone), the modes inside an oboe are very different from those inside a clarinet. If we compare the oboe with the same length clarinet, one reduces the diameter of the bore (inside cavity of the instrument) near the mouthpiece, where the pressure fluctuations are highest, and increases the bore near the end of the tube where the velocity fluctuations are highest. Both of these increase the frequency of the modes. The oboe is such that the frequency of the lowest mode is given by the velocity of sound divided by twice the length (instead of four times the length as for the clarinet). The higher modes have frequencies which are close of all of the integer multiples of this- ie twice, three times, four times, etc. Ie the modes inside the oboe have frequencies which are very similar to those of a pipe which is open at both ends (except of course the oboe is not. It is closed at one end, the apex of the cone).

The oboe reed, in this case a double reed in which two reeds close against each other instead of one against the case of the instrument, operates in exactly the same way as the clarinet reed does. Ie, blowing hard enough on the reed it operates near the point where it closes which again produces the same kind of negative resistance as does the clarinet reed. However in this case, because of the very small diameter of the bore near the reed, the amplification process is not nearly as efficient, and the oboe is much harder to play than is the clarinet. Again the modes are amplified, but in this case, the fundamental tends to be very weak. Instead one gets the primarily the second, third and fourth harmonics sounding strongest.

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Next: Trumpet Up: Negative Resistance or Negative Previous: Negative Resistance or Negative
Copyright Bill Unruh 2002-04-12