"Flow-controlled Valve" Model for Pipe Excitation

The process of sounding a flute or a flue-type organ pipe employs an airstream directed at an edge. However, the process differs so much from the process of directing an airstream on an isolated edge that it is modeled in different ways and different language is used to describe it. Rossing's Science of Sound uses the term "air reed" to describe the situation in which the oscillating air stream is the means for excitation of the pipe sound. In using the "air reed" terminology, it is pointed out that the oscillation is controlled not by pressure, but by the air flow. The edge structure represents an "open end" for the pipe, and thus is a pressure node. The open end is an antinode for air motion (air displacement antinode) and this maximized air flow associated with the standing waves of the pipe can drive the oscillation of the airstream. By contrast, the mouthpiece end of a clarinet with its reed constitutes an acoustical "closed end", a pressure antinode which provides pressure feedback to help stabilize and control the reed oscillation.

The description of the excitation process as a "flow-controlled valve" or "flow-controlled oscillator" dates back to Helmholtz in his investigation of cavity resonance. The tone you produce by blowing over a coke bottle involves air oscillation in and out of the mouth of the bottle which can be described as "flow controlled". When the air is flowing out of the bottle, it directs the airstream outward, and when the airflow associated with the resonant vibration is inward, it directs the airstream inward to provide energy to sustain the oscillation. Helmholtz described the flute excitation in the same sort of way, with the air motion from a standing wave forcing the players airstream out of and into the flute periodically.

Benade comments on the shortcomings of Helmholtz's model, explaining that the player's airstream lags considerably behind these air motion changes from the pipes standing waves. He cites the work of Coltman and Fletcher as clarifying some of the details of the "flow-controlled valve" action at the flute's embouchure hole. Their work highlighted the importance of the transit time from the players lips to the side of the embouchure hole and its relationship to the periods of oscillation of the sound components (harmonics) present in the tone.

Hall discusses the nature of edges and the excitation of organ pipes. The role of the eddies or swirls in the air at the edge is explored and some illustration is given of feedback mechanisms which presumably contribute to the oscillation of the airstream and help with the sounding of the pipe at its resonant frequencies.

The difference between the "edgetone" as envisioned in the sounding of a flute, recorder, organ pipe, etc. and the tones produced by directing air over an edge which is not coupled to an air column has been a subject of considerable discussion and investigation. Benade comments "Until recently there has been a tendency ... to confuse the sounds produced by blowing a narrow air jet against a sharp edge when the edge forms part of a flute or an organ pipe (air reed behavior) with those produced when the system is run in isolation (edge-tone behavior). In the latter case a type of repetitive eddying called vortex shedding takes place on alternate sides of the air jet, and a sound is produced if a sharp edge is used to separate the two sets of vortices. Vortex phenomena have only a secondary influence on flute-type sound production; moreover, at ordinary musical blowing pressures the edge-tone frequencies are so high as to be nearly inaudible".

Some of the literature which addresses the differences between the free edgetones and the behavior of the edges in flutes and organ pipes:

1. Coltman, John W., "Sounding Mechanism of the Flute and Organ Pipe", J. Acoust. Soc. Am. 44 (1968)
2. Fletcher, N. H., "Nonlinear Interactions in Organ Flue Pipes," J. Acoust. Soc. Am. 56 (1974)
3. Bouasse, H., Instruments a' Vent, 2 vols., Paris: Librairie Delagrave, 1929,1930.
4. Cremer, L. and Ising, H., "Die selbsterregten Schwingungen von Orgelpfeifen," Acustica 19, 143-153,(1968)
5. Elder, S. A., "Edgetones versus Pipetones," J. Acoust. Soc. Am. 64, 1721-1723, (1978)

Oscillations at a Free Edge

If you directed air or a liquid toward a sharp edge, you might expect it to divide evenly and smoothly at the edge. But nature doesn't behave that way. You tend to get oscillations of the flow back and forth across the edge. This has long been associated with the the formation of swirls or vortices in the flow. It is observed that the frequency of the oscillation tends to go up linearly with the flow velocity, but that the frequency for a larger diameter "edge" is lower.

This fluid driven oscillation is observed in a wide variety of settings. One of the most familiar is the singing of tightly stretched electric wires in the wind. My wife and I lived in North Wales for a year and heard this sound daily. Outside the bedroom of our third floor "flat" was a thin, tightly stretched electric wire which was constantly exposed to the wind off the Menai Strait. We awoke every morning to the sound of the wire singing in the wind, so we had an instant weather report since a higher pitch meant higher wind speed. Our common line was "The wire is up to an F this morning! Let's stay in bed!"

Other common examples of fluid-driven oscillations:

1. The strap you use to tie a load on a pickup truck will vibrate in the wind. Often you can see examples of the fundamental string mode of vibration in a tightly stretched strap in the wind.
2. If you tried to use plastic to cover the load described above, you find out that any exposed edge of the plastic will oscillate wildly in the wind, so that it is hard to keep a load covered if any edges are exposed. Corners of a cover or loose ends of a strap will flap so wildly that they tend to fray.
3. A flag on a flagpole will flutter in the wind. A steady wind will generate a rapid fluttering of the cloth of the flag.
4. A kite in the wind demonstrates the diameter dependence of the fluid-induced oscillation. The kite material will flutter rapidly from the component of wind directed toward its edge, but will also bob slowly back and forth in the wind, presumably from the component of wind directed toward the full area of the kite. Acting as a larger barrier, the body of the kite experiences a slower oscillation.
5. If you dip your fingers in water and move your hand quickly through the water, your fingers will beat together, presumably because of fluid-induced oscillation.
6. Direct the stream of a hose on a twig or stalk. If you hold the stream steady, you will observe the twig to start an oscillation back and forth in the stream.
7. A fluid oscillation you can feel is in the experience of mounting a slalom water ski. As the ski breaks the surface of the water and begins to plow through the water, it will begin to oscillate back and forth. That's when you usually fall! If you make it through the oscillation period and get the ski up on a plane, it ceases to oscillate.

If you blow with increasing air stream velocity on a whistle composed of a slit and an edge, you will note that you get jumps in pitch and experience several ranges of edgetones. Associated with the vortices in the flow, there are several regimes of edge tones . The illustration below is adapted from Hall, who references the work of Coltman. It associated the different edgetone regimes with patterns of vortex formation and feedback to the slit from the edge.