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Flute

Another instrument in which time delay is used to create a negative resistance ( air flow in when pressure inside is high, and out when it is low) is the flute. But in this case the delay comes not because of the delayed response due to mass, but to the time it takes the air to flow across the mouthpiece while blowing across it.

The flute is an pipe, which has one opening at one end, or at a finger hole, and the other opening is in the side of the flute very near one end. This second hole is the one which the flautist blows across to make the flute create its continuous tone. The flautist chooses the mode of the air vibration which she/he wants to amplify and adjusts the velocity of the air coming out of the mouth so that it travels across this mouthpiece hole in about 1/4 of a period vibration of the air in that mode. (flautists play primarily the first and second modes, and occasionally a good flautist can play the third mode for special effects).

Let us see how the time delay works in this case. The flautist directs the air stream coming out of the mouth so that it bisects the far side of the mouth piece hole. If there were no vibration of the air inside the instrument, about half would flow into the instrument, and half out.

Now let us look at what happens to this air stream as a mode of vibration of the air inside the instrument occurs. The modes of air vibration inside a tube are such that the pressures variations tend to small near the open end of the tube, but the velocity variations of the air due to the vibrations of the mode tend to be large. Thus it is not the variations in pressure which control the air flow into the instrument ( as it is for reed and lip-reed instruments) but the variations in the velocity of the air in that mode at that open end. As the blown air leaves the lips, the oscillations of the air in the vibrating mode deflect that air. If, just as the air leaves the lips, the air flow due to the mode's vibration is a maximum out of the hole, then the blown air is deflected out of the instrument. But due to the time delay due to the time it takes that blown air to get across the mouthpiece, that blown air actually enters the instrument about 1/4 period later. Since it was deflected out, less air enters the instrument at that time. However, 1/4 of a period later is when the pressure just at the outlet is the lowest. Since the air stream was deflected out by the out-flowing air, less air enters the instrument at this time when the pressure inside is lowest. Similarly, if the air leaves the lips just as the flow into the instrument due to the mode vibration is largest, the blown air stream is deflected into the instrument. Again it actually gets in about 1/4 of a period later. When it enters the instrument, it gets in just as the pressure inside is at its highest. Since it was deflected in, more air thus enters the instrument when the pressure at the mouthpiece is at its highest. Ie, once again the blown air enters when the pressure is high and is deflected out when the pressure is low. This again gives the negative resistance which causes the amplitude of vibration to grow (rather than decay) and continue to sound as long as the air blown across the instrument.

In order to play one of the higher modes, one must arrange that the air stream crosses the mouth hole in about 1/4 period of the frequency of that mode to get maximum amplification for that mode. Ie, to play the higher modes, the flautist must change the velocity of the air leaving the mouth, or must decrease the distance the air must travel. They tend to do both. They purse the lips more, to make the hole smaller, so that the same amount of air must leave the lips with a higher velocity, and they move their lips closer to the far edge of the mouth hole on the flute (either by rotating the flute to bring the far edge closer, or by moving the lips closer).


next up previous
Next: Violin Up: Negative Resistance or Negative Previous: Trumpet
Bill Unruh 2002-04-12