12d: Woodwind Instruments

Probably the earliest instruments were simple flutes. The earliest known flute comes from Europe and is dated at about 35,000 years old. Other woodwind instruments include the clarinet, oboe, bassoon and saxophone families of instruments.

In woodwind instruments (as in all instruments) there is something that vibrates to create sound and a resonating body which selects a fundamental frequency and overtones and amplifies them. From the above discussion we know that the tube itself is the resonating body. What creates the initial vibration? In the clarinet and saxophone family of instruments a single reed, clamped to a mouthpiece vibrates to create the initial sound. Most reeds, shown on the left, below, are made from a type of cane plant.

freq freq

On the right above is a picture of a double reed. This is the vibrating device for oboes, bassoons and bagpipes. In most reed instruments the reed or double reed is clamped in the mouth so that the mouth can change the frequencies being produced. The adjustment of the performer's mouth to correctly produce the initial sound is called embouchure. Even with this control, however, a reed mouthpiece without the instrument sounds basically like a duck call (and in fact many duck calls are based on a simple reed). Most reed instruments are blown closed, meaning that the air flowing past the reed tends to force it shut after which it springs open due to its own stiffness.

There does not appear to be anything that vibrates on a flute but we know vibrations are the source of all sound. So what vibrates? Most flutes have a sharp edged hole called a fipple that splits a stream of air. Initially the air stream goes into the flute cavity. As pressure builds up the stream will suddenly shift to flow to the outside of the flute. When the air pressure inside drops the stream re-directs back into the cavity. It is this back and forth motion of the air (which occurs very rapidly) that is the source of vibration for a flute. The sound produced (before resonance with the body of the flute) is called an edge tone.

Other kinds of flutes, including pan flutes and the modern orchestral flute, have a hole across which the musician blows. The edge of the hole acts the same way as the edge of a fipple with air first going into the flute, then building up pressure to make the flow go out. This rapid back and forth air flow causes the vibration that makes the initial sound. The picture on the right, below, shows an air stream being divided by a sharp edge. Notice the turbulent pattern generated as air first goes above and then below the edge.

One way to change the fundamental frequency of a tubed instrument is to put holes in the tube which can be closed or opened with the fingers. As shown in the figure below, a hole allows a displacement anti-node of air to occur at the hole location, changing the resonant frequency. Flutes, clarinets and saxophones all use this method to change the fundamental frequency being played.

There are several problems with putting holes in a tube to get different resonant frequencies. The size of the hole affects the shape of the wave inside the tube which changes the overtones that are present. The result is small errors in pitch that vary with the range and volume of the notes being played. Early flutes and recorders from the Renaissance had holes of varying size to correct for these errors. Modern flutes have hole sizes that get slightly larger at the end furthest from the fipple which give more uniform changes in pitch. By using mechanical keys to cover the holes the hole size can be adjusted for sound quality rather than convenience of the performer. Covering and opening holes also changes the amount of impedance mismatch between inside and outside the instrument, so that different notes may sound slightly louder or softer, depending on the fingering.

A second problem for tube instruments with holes is that the human hand is of finite size. For a longer tube this becomes problematic; a normal hand cannot reach the hole locations necessary to make a specific note. Most modern instruments use levers called keys attached to pads on springs to cover holes that are further away than can be reached by a normal sized hand. A second reason to use keys is that more holes can be used. Human hands can only cover ten holes at one time because we only have ten fingers. To be capable of playing all 12 notes of an octave some keys are normally closed unless pressed to open them.

Flutes tend to have uniform diameter along their length but other wind instruments do not. The diagrams below show the difference in cross sectional shape between a flute, clarinet and saxophone. Bassoons are shaped more like a flute (the same cross section along the length) whereas oboes are more shaped like a saxophone with an increasing diameter and a bell on the end. Notice that the saxophone and oboe are flared along their entire length, the clarinet is flared only at the end and the flute has no flaring. As discussed above, the flaring changes the impedance mismatch between waves inside the instrument and sound transmitted away from the instrument. Notice that the lengths are different for these instruments as well. Not shown in the cross section diagram of the flute is the cork which provides an adjustable end to the left of the mouth (or embouchure) hole of the flue. The cork allows the resonances inside the flute to be tuned so that reflections from cork end reinforce sound generated at the embouchure hole.

What effect does the changing diameter have on the simple standing waves that we saw for a tube with constant diameter? The result, shown in the graphs below, is that the wave amplitudes are squeezed a little bit. Compare these results for the first few harmonics of a tube with constant diameter to those for the flute, above. We know from Fourier analysis that more overtones have to be present to get the more complicated wave shapes shown below. So a changing tube width will greatly affect the timbre of the instrument.

Video/audio examples:

12e: Brass Instruments

Brass instruments use the vibration of the player's lips with the proper embouchure to initiate the sound. As in the case of a reed instrument, buzzing the lips creates a broad spectrum of sound. Resonances in the instrument select one of these frequencies to be the fundamental of a note. Unlike most reed instruments in which the vibrating part is blown closed, for brass instruments the lips are blown open. Air rushing between the lips lowers the pressure and the lips close. Then pressure builds up and the lips open again. Blown open and blown closed vibrators both depend on the Bernoulli effect; moving air has lower pressure causing the reed or lip to close.

We know that tubes of different lengths have different resonant frequencies. Brass instruments change the length of the tube using one of two mechanisms. Slide trombones have a set of double tubes that slide over each other to make the length longer. Trumpets, french horns, tubas and other brass instruments use a set of valves to change the length of the tube. There are usually three and occasionally four valves on most brass instruments. The diagram below shows one of several ways to construct a valve that changes the effective tube length. Pushing the valve down causes the air path to detour through a section of pipe making the total path longer.

Brass instruments tend to have large bells and are louder than woodwinds on average because of better impedance matching as mentioned above. End effects due to the large bell also tends to shift the frequency spectra significantly from what would be expected from a simple tube. Although we expect a tube closed on one end to only have odd multiple overtones, the measured frequencies of a trumpet are harmonic. The table below compares the predicted frequencies of a simple tube of length 1.4 m (the approximate length of a trumpet) and the measured frequencies of a real trumpet. Notice that the predicted overtones are odd multiples of the fundamental but the real instrument has all harmonics.

Why do the frequencies shift so much? For higher frequency overtones the standing wave extends further out into the bell region as shown in the diagram below. Since in effect higher harmonics 'see' a longer tube, the frequency of these overtones are shifted downward a little. The fundamental, because it 'sees' a shorter tube shifts up a little. The impedance mismatch for different overtones will also be different because of this effect. Higher frequencies escape more easily than lower frequencies because higher frequencies extend out further into the bell region of the instrument (as mentioned above, the amount of reflection at the end of a tube is affected by the diameter of the tube relative to the wavelength - so longer wavelengths reflect further out from the end of the bell). This means the overtones of a brass instrument are louder than in the case of a saxophone or clarinet. The effects of the bell on various overtones also gives brass instruments their unique timbre in addition to shifting the frequency spectrum.

The mouthpiece also has an effect on the frequencies present in a brass instrument. The mouthpiece forms a small Helmholtz cavity with a volume resonance with a low Q-factor. As you may recall from Chapter Four on resonance, a low Q-factor means a very broad resonance. For modern instruments this resonances tends to weaken the lower harmonics (including the fundamental) so that the higher harmonics have a larger effect on the timbre.

As a final complication, brass instruments sometimes use mutes to change not only the volume but also the frequency spectrum radiated by the instrument. A mute does not seal up the bell end of a brass instrument but it does weakly produce extra frequencies corresponding to a tube that is closed on both ends. This changes the timbre of the instrument in addition to reducing the volume.

Video/audio examples:

Slow motion of vibrating lips.
How to buzz your lips.
How valves work.
How to make an instrument from a straw.
Wikipedia on trombones, trumpets, french horns, tubas, and sousaphones.
The following web sites have pictures, sound samples and information about modern musical instruments used in bands and orchestras: one, two, three, four.

12f: Pipe Organs and other reed instruments

Although technically a keyboard instrument, pipe organs are based on tubes. Instead of changing the length of a single pipe (with holes or other mechanisms) to get different frequencies there is a large collection of pipes of different lengths and a mechanism to blow air through them. The sound generating part may be either a fipple or a reed and some organs have different pipes with each type. The tubes may be made of wood or metal, may be open or closed on the end and have various shapes, as shown below. A variety of methods are used to tune an individual pipe by slightly changing its length or modifying the end of the pipe. As in the case of reed instruments different pipe shapes lead to different overtones that change the timbre of the note being played. Because a large number of pipes can be employed (the Wanamaker Pipe Organ has 28,604 pipes), pipe organs can produce a wide variety of sounds. The longest pipes may be as long as 19.5 m which makes an 8 Hz pitch.

A final class of instruments that use reeds but not tubes are called free reed aerophones. These include harmonicas, accordions, bandoleóns and similar instruments. In these instruments a reed vibrates as air is forced over it, so they are blown open reeds, unlike clarinet or saxophone reeds. There is a reed with different tension to produce each note. The mouth and cupped hands form the resonating bodies for harmonicas. In accordions and similar instruments a set of bellows are used to force air over the reed and the air box forms the resonating cavity.

Video/audio examples:

Wikipedia on free reed aerophones.
A web site about harmonicas and other mouth blown, free reed instruments with sound samples.
Performance of the Wanamaker Organ.
Slow motion of harmonica reeds.
One of many YouTube video of a didgeridoo. The didgeridoo is an instrument used by the aboriginal peoples of Australia and consists of a long tube of wood. The lips are buzzed to make a sound but the voice is also used. Because of the large diameter and length there are many interesting resonances that can be excited while playing the instrument.

Summary

As is the case for all instruments, tube instruments start with a vibrating sound source and use resonance to amplify the desired frequencies. For woodwind instruments a single or double reed vibrates. For flutes a fipple turns a smooth air flow into an oscillating flow which becomes the initial vibration. Woodwind instruments use holes to change the effective length of the tube to get different fundamental frequencies. Keys activated by springs and levers extend the reach of the human hand in opening and closing holes in the instrument. The cross sectional shape of the tube changes the overtone frequencies, giving the particular instrument its timbre. Brass instruments start with a pair of buzzing lips. The length of the tube is changed by either a sliding tube arrangement or a valve that shunts the air through tubes of different lengths. The impedance matching provided by the bell of a brass instruments enables them to produce more sound and also shift their overtone frequencies to give them their unique timbre.

End of chapter exercises: Tube Instruments.