Reed Instruments

This page and its accompanying Applet are to give a feeling for how a reed type musical instrument works. It displays the developement in time of the sound within the instrument, and how that sound itself controls how the reed opens and closes to maintain the sound.

In a reed instrument, the reed is placed inside the mouth and the mouth is kept under high pressure. The reed is "tongued" to start the flow of air into the instrument. In this process, the high internal pressure in the mouth is suddenly released onto the reed. This launches a sound wave down the tube, which is reflected from the open end of the tube and rebounds back onto the reed. The pressure in this and successive returning pulses helps to control the opening and closing of the reed.

The reed is designed so that under sufficient pressure within the mouth the reed will be forced to close. While playing a note, the reed operates in a regime where it is beginning to close or is closing altogether. Under this condition an increase in pressure within the bore of the instrument opens the reed and lets in more air, while a lower pressure within the instrument closes the reed and lets in less air. It is this counter-intuitive operation (higher internal pressure causes a greater airflow into the instrument) which provides the amplification needed to sustain the sound within the instrument.

While all of the reed instruments behave in the same way, the pitch and shape of the note produced depends crucially on a number of variables. One of these is the shape of the bore of the instrument. A cylindrical bore, like in a clarinet, produces a pitch which whose period corresponds to the time it takes a sound wave to make two round trips up and down the bore. Under higher mouth pressures, the wave is almost exactly a square wave travelling up and down within the instrument.On the other hand, a conical bore, like that in an oboe or a saxaphone, produces a pitch whose period is that of a single round trip travel time, and the wave shape tends to contain more higher harmonics than in the clarinet. Furthermore the shape of the sound wave inside ( and radiated by) the instrument also depends on the size of the opening of the bore, where the sound escapes. A small opening (in comparison to the length of the bore) produces a sound with a much more "jagged", high harmonic shape, while a large opening corresponds to a much more rounded, lower harmonic content shape.

Model System

In the accompanying applet reedapp.html , a reed instrument is modeled and a variety of parameters of the sound within the instrument are displayed. The instrument parameters,- the shape of the bore(conical or cylindrical) can be continuously varied, the mouth pressure can be varied, and the natural opening of the reed ( the embouchure), can all be changed using the Control Panel.

Displayed firstly are graphs representing the pressure (P) and the velocity (V) of the air corresponding to the sound wave within the instrument at any given instant of time. In addition, the pressure within the instrument at the reed (P reed), the velocity of the air flowing through the reed opening (V reed), the width of the reed opening (Reed), and finally the velocity of the air at the open end of the instrument (V open) are also dispalyed as a function of time.

All of the parameters which determine the sound can be varied "live" on the Control Panel to see what their effect is on the sound within the instrument. The P slider increases or decreases the pressure of the inside the mouth (outside the reed).

The embouchure ( the pressure on the reed by the lips to close down the natural opening of the reed) can be varied by grabbing the tip of the reed with the mouse and dragging it up or down. (open or closed).

Similarly the taper of the instrument can be changed by grabbing either top end of the instrument (displayed in black under the "Taper" label) with the mouse and dragging the end up or down. Either the diameter of the open end of the bore, or the reed end of the bore can be changed in this way. Making the reed end very small (minimum 1/20 of the length of the instrument), while leaving the open end larger changes the instrument from being like a clarinet to being like an oboe.

If the graphs overshoot the size of the displays, they can be rescaled using the Scale slider on the control panel. (All except the reed opening graph, which never rescales, are rescaled by the same amount.) Smaller "scale" numbers allow greater variations to be graphed.

Finally, the control panel allows you to Stop the display, Continue the display after you have stopped it, or Restart it with a new "tongueing" at any time. When it is stopped you can Step it forward in time by the fixed number of time steps set on its slider ( where one time step is the time it takes sound to travel roughly 1/30 of the length of the bore).

The Quit button will permanantly stop the applet, and it then cannot be restarted without reloading it.

Experiments

There are a number of experiments which can be carried out with this model One of the most interesting is to compare the very different bahviour of the instrument with a cylindrical bore to that with a conical bore. Run the model as a clarinet (the default) for a while, varying the mouth pressure, and the embouchure to see what their effect is on the sound wave. Try restarting it with a variety of conditions of pressure and embouchure. See what effect varying the diameter of the bore has on the sound wave.

Then close down the reed end of the bore to its minimum size, leaving the open end larger to produce an "oboe". Note firstly the change in frequency of the oboe in comparison to the clarinet. Note also that the clarinet settled down to its final "shape" for the sound wave inside very quickly, while the oboe takes a much longer time to settle down (recall that "long here means many periods, where a period for these instruments might be 1/300 of a second).

Note especially the difference in the behaviour of the pressure and the velocity within the instrument when played as an oboe in comparison to it being played as a clarinet during the first few periods. In the oboe, the initial pressure pulse is a brief pulse which travels down the instrument, while in the clarinet, the initial pressure pulse is broad and roughly constant. The pulse height drops as the pulse approaches the open end because the larger bore at that end has spread the pulse over a much larger area. Note that in the oboe, returning pulse is a broadened negative pressure pulse. It is broadened because the higher frequency components have tended to escape out the end of the bore while the lower frequencies are reflected.

This negative pulse might be expected to close the reed. However, note that the interference between this incoming (toward the reed) pulse and its reflected image pulse at the reed produces a positive pressure of the reed on the first first return trip of the pulse. In the clarinet, a positive pressure is produced at the reed (and thus opening the reed) only on the second return of the wave from the end of the tube. It is this behaviour which creates the higher frequency of the oboe (one octave or twice the frequency higher) over that for the clarinet for exactly the same bore length. You can also vary the bore taper between that of a clarinet and an oboe continuously to see the effect on the frequency of the instrument and the shape of the sound wave.

It is also interesting to examine the situation in which one "inverts" the oboe, and makes the open end much smaller than the reed end. In this case the instrument is converted into a "Helmholtz resonator" and the period of the sound wave becomes very long, corresponding to a very low pitch. One can thus create a reed instrument of very low pitch even though the instrument is of normal length (ie much much shorter than the wavelength of the sound produced). Such an instrument would not be very useful as the small opening, together with the low pitch would produce a very poor coupling to the outside air, and a quiet sound. Furthermore, the placement and use of "finger holes" would be problematic. ( The pitch would depend more on the total open area of the finger holes, rather than their placement along the bore.)

In general, just play with this model to get a feel for the way in which a reed instruments operates, and the variety of waveforms produced by the instrument under different playing conditions.

Technical Details

The model used here is deliberately simplified. The reflection from the open end of the tube is assumed to be a simple "single pole" reflection function, rather than the more complex form expected from a real opening. I.e., the reflection is assumed to be of essentially constant unit amplitude for frequencies below the "knee" ( which is taken as f=c/D, where c is the velocity of sound, and D is the diameter of the opening), and the reflection amplitude falls at 6dB per octave for frequencies higher than the "knee". Thus no account is taken of the influence of any flares or bells as the end of the instument.

The reed is assumed to very overdamped, with a damping time of 1/30 of the travel time of sound down the tube (ie 1/60th to 1/120 of the period of the note). The mass of the reed is assumed to be unimportant to its its dynamics. Its restoring force is of course not negligable. A pressure of half way along the pressure scale (ie, a pressure of 50) is assumed to be just sufficient to close off the reed completely with the initial "embouchure". Thus tongueing the reed (pressing Restart)with a pressure of greater than 50 initially results in no air flow into the instrument. However, after the sound wave is intiated, the mouth pressure can be increased to its maximum value and the instrument will continue to play (louder).

The air flow through the reed is assumed to be proportional to the width of the opening, and to the square root of the pressure difference across the reed (turbulent flow). Note that this gives a flow characteristic through the reed very similar to the experimental one as shown for example in Benade (p***).

No account is taken of the effects of the shape of the reed cavity on the sound produced, nor of the effects of the closed or open tone holes.

The two controls on the main page are the delay slider and the Contol Panel Show/Hide button. The delay control controls how fast the images are displayed. Although "the faster the better" might seem reasonable, java can display things faster than the graphics can accomodate them, leading to incomplete displaying of especialy the pressure-and- velocity-along-the-bore graphs. Smoother animation may require a longer delay than the default minimum. This control can also be used to run the display in slow motion in case particular features of the motion of the air in the bore requires closer examination.

The Control Panel Show.Hide button can be used to hide the control panel for a more uncluttered display, with it being unhidden (shown) only when needed.

These graphs are best displayed on a 1024X768 or larger display. On that size the whole of the graphs fit onto the screen. However on smaller displays, the graphs can be scrolled. It is also best displayed on faster computers.

Further References