The Physics of Music: How do reeds work?

This blog post attempts to answer the question, “How do reeds work?” I used to think that a reed “buzzes” and that buzz gets amplified and colored by the horn. That’s true…but not quite right! As with any substantial discussion we need to establish some background and context.

Factors in tone production

Let’s begin by establishing what you need to produce sound. Arnold Jacobs, sets out the 3 factors of tone production [1]

1. Motor function
2. Vibration
3. Resonance

Instrument	Motor function	Vibration	Resonance
Horn	Breath	Lips buzzing	Instrumental partial
Woodwind	Breath	Reed	Instrument
Singer	Breath	Vocal folds	Vocal column
Piano	Depressing key	Hammer	Vibrating string
Violin	Bow	Bow pulling string	Vibrating string

As an aside, the piano, harpsichord, and pizzicato strings have no sustaining motor function – once a note is played, you cannot put energy back into sustaining the sound and the note will diminuendo.

So what is responsible for producing a tone? The answer is all three factors working together: reed, motor function (air/bow), and instrument.

Air and reed

A flag fluttering in the wind is a good mental picture of how a reed vibrates [2]. The analogy is quite good, a stiffer flag needs a faster wind speed to flutter. A strong wind induces strong vibrations – often faster as well (as in the bassoon reed).

As air flows past the reed, into the mouthpiece and out the horn, it drops in pressure. This lowered pressure in the mouthpiece causes the reed to close off and narrow the gap. The pressure drop comes from the Bernoulli Equation and is related to the air speed not air volume. 

The dashed line indicates the position of the lips on the bottom and teeth on top. Air which flows into mouthpiece and out the horn has a lower pressure than the air in the oral cavity.

The reed resists further closing of the reed-mouthpiece gap and the result is a stationary reed in a flexed position with air flowing through the horn. Sound is not produced in this picture.

It is possible to balance the reed flexing with flowing air without producing sound!

Reed and Instrument

Putting air through the horn is not sufficient to produce a tone. We need instrumental resonance too!

The effect of an instrument resonance is a reverse puff of air in the opposite direction. Since sound is pressure waves, when one of these pressure waves (a note, like A = 440 Hz, is a pressure wave) reflects back into the mouthpiece, it relieves the pressure keeping the reed shut off and the reed springs open. As the reed opens, more air is let in, reinforcing the resonating wave traveling up and down the instrument.

Importantly, the reed vibrates in sync with the note and not at it's natural crow or buzz. For example, to play an octave above A 440, the reed must vibrate 880 Hz. It is a physical fact that stiffer reeds can vibrate faster, thus supporting high register pitches.

Conclusions

1. Lip buzz or reed vibration is sustained by air velocity. 
2. Have your air ready immediately to start a note.
3. Light tonguing may be required to kick start notes.
4. A smaller aperture (small mouthpiece/stiffer reed) requires more air pressure for a high enough air speed. 
5. A larger aperture (large mouthpiece/softer reed) requires more air volume to sustain air speed
6. A stiff reed may be required for the high register, conversely: a soft reed may be needed for the low register

References

1.  Instruments - Arnold Jacobs "Almost Live."  http://youtu.be/xfJAvhTwNNE
2.  Sound in Motion. David McGill