Didgeritubes
 

Welcome to my page on Didgeritubes!  It is designed for middle and high school science students who are interested in studying the physics of brass instruments and Australian didgeridoos!  On this page, you will find a short introduction on didgeritubes; a description on how they produce sound; and a demonstration on how to apply physics principles to this instrument this section is particularly relevant for Science Olympiad participants in the Sounds of Music event.

Introduction

Brass instruments in a modern symphony orchestra include trumpets, trombones, french horns, and tubas.  However, many ancient cultures also developed similar instruments, which were made from a variety of materials such as animal horns, elephant tusks, sea shells, and wood [15, pg. 105-110].  One of the most widely used of these ancient instruments, is the Austrailian didgeridoo, which is made from a hollowed out branch from a Eucalyptus tree.   Didgeritubes are essentially tubes that are played like didgeridoos.  They are constructed from 3/4-inch class-200 PVC, with a section of electrical tape serving as the mouthpiece.  The electrical tape provides a soft surface on the mouthpiece end, in the same way that didgeridoos have a soft rim of beeswax.   In terms of classification, didgeritubes are considered aerophones according to the Sachs-Hornbostel system, or in orchestral terminology, are considered part of the brass family of instruments. 

 

How It Works

What actually happens inside of the horn, when a bugler plays taps?  How does the sound vibrate? 

Didgeritubes, like all other brass instruments, produce their sound by vibrating a column of air inside of a tube.  Stated another way, what you hear is not the tube, but a vibrating column of air inside of the tube. 

In this section, we are going to look at this vibrating column of air: how it starts with something called an lip reed, how it is shaped by the open and closed ends of the tube, and how it is stabilized into a constant pitch that is recognizable to our ears.

If you are a middle school student, the animations and videos below will probably be sufficient.  For high school students, I've also included additional text that is consistent with a high school physics textbook.  Lastly, for college-level physics students, it is important to note that sound waves are the result of both acoustic pressure and acoustic flow, which are 90 degrees out of phase with each other.  However, for the purposes of this web site, I will simply address the acoustic flow or the amplitude of motion of the air [5].  This will provide an approach that is consistent with current high school science curriculum.

Lip reed:

The sound of a brass instrument begins with buzzing the lips into the mouthpiece in effect, the lips vibrate like a reed.  Although it might seem a bit erratic, this buzzing movement, when slowed down, is actually a smooth fluid motion of the lips.  As shown below, when pressure inside the mouth increases, it pushes the lips outwards in a rolling motion.  As the lips roll open, a compression forms.  As a result, the pressure inside the of mouth is reduced, and the muscle tension closes the lips again [6, pg. 264].  This rolling motion (opening and

How Didgeritubes Work

closing) creates a longitudinal wave of compressions and rarefactions traveling down the tube [7, pg. 136 Fig. 9.9].  In order to reach and maintain the desired frequency, the player must constantly adjust the speed at which the lips vibrate, thereby approximating the frequency of the note being played.   

 Reflection and oscillation:

As the longitudinal wave is traveling down the tube, it forms an alternating pattern of compressions and rarefactions.  Because the bottom of the tube is an open end, the waves reflect back without inverting.  As such, compressions reflect back as compressions, and rarefactions reflect back as rarefactions.  As the reflected waves travel up the tube they interfere with the incident waves traveling down the tube.  This creates both constructive and destructive interference. 

A note on interference: The two major types of interference that occur are constructive and destructive. When compressions meet rarefactions, destructive interference occurs.  However, when reflected compressions meet incident compressions, constructive interference occurs [17].

When the reflected compression reaches the top of the tube it undergoes a fixed-end reflection, and reflects back as a rarefaction.  It reaches the top of the tube exactly at the time when the lips are at their most closed point of the cycle. Therefore, when the reflected compression reaches the top and reflects, it also integrates into the incident wave traveling down the pipe, thereby strengthening and stabilizing the wave pattern.

Standing wave:

Once the wave pattern is stabilized it is known as a standing wave pattern. The areas of constructive interference become the antinodes of the wave, while the areas of destructive interference become the nodes [7, pg. 110-111].  As shown above, the didgeritube is vibrating with a standing wave pattern of three antinodes and two nodes.  This indicates that it is vibrating at the 5th harmonic.  Because it has a closed or stopped end, it can only vibrate at odd harmonics, such as the 1st harmonic or fundamental, the 3rd harmonic, or the 5th harmonic.  To see and hear a demonstration on harmonics and many other topics, please continue down the page.

 

Demonstrating What You Know

Now that we understand how didgeritubes produce sound, let's continue by exploring four more areas: frequency, amplitude, wavelength, and harmonics.

Frequency:

Frequency is simply a mathematical representation of how low or high a pitch is, and is based on the rate at which waves vibrate [15, pg. 8].  It is measured in Hertz, or number of complete wave cycles per second, and is commonly abbreviated as Hz [18].  Since sound is produced on panpipes by a vibrating column of air, the amount of time it takes for one compression to travel down and up the tube will determine its frequency.  To see how frequency can be demonstrated on a set of panpipes, start the video below.

Changing Frequency and Harmonics on Didgeritubes

 

Fundamental Principle:
frequency and tube length are inversely proportional

If we change the length of a tube, we also change the length of the air column inside of that tube.  Simply put: shorter is higher, and longer is lower.  But it's actually more precise than that.  The Fundamental Principal states that each time we cut the length in half, we double the frequency.  Stated another way: tube length and frequency are inversely proportional [15, pg. 10]. 

This Fundamental Principle is demonstrated with the animation on the right.  One didgeritube has a length that is equal to 1 unit, while the other tube is 1/2 of that length.  Imagine that sound, as represented by the arrow, is the motion of a longitudinal wave traveling down the tube and then reflecting back.  Notice how sound waves travel the length of the shorter tube twice as fast as the longer tube.  Sound waves complete two cycles with the shorter tube in the time it takes to complete one cycle with the longer tube.  As a result, when tube length is halved, frequency is doubled [15, pg. 10]. 

 

Amplitude:

Amplitude is the variation or displacement of a wave from its mean value.  With sound waves, it is the extent to which air particles are displaced, and is experienced as the intensity or loudness of a sound.   As shown below,  when a tuning fork vibrates to a greater degree, it displaces more air particles in each compression.  When the tuning fork vibrates to a lesser degree, it displaces fewer air particles in each compression. 

Amplitude can be changed on panpipes by simply varying the amount of air in your playing technique.  Playing softly, with less air, will produce less amplitude.  Taking a deep breath and playing with more air, will produce greater amplitude.

 

Varying Amplitude

 

Wavelength:

Wavelengths for a Closed-end Tube

In determining the wavelength of a tube, it is important to know if the tube has two open ends, or one open end and one closed end.  With didgeritubes, the tubes all have one open end, and one closed end.  

Since one end is closed, the wavelength of the fundamental frequency is four times the length of the tube [6, pg. 250]. This is because the closed end always serves as a node when the tube resonates in a standing wave pattern.  The opposite effect occurs at the open end, which always serves as an antinode [7, pg. 111].

Therefore, if we superimpose a transverse wave over the tube (as shown in the adjacent figure) one complete wave cycle extends four times the length of the tube.  This represents the fundamental frequency for the tube, or the lowest resonant frequency that the tube can produce.   Again, notice the relationship between the tube's closed and open ends, and the wave's nodes and antinodes.  We can see the same relationship with the third and fifth harmonics.  Also, notice how wavelengths are shorter with higher frequencies.   To see more on the topic of wavelength for open and closed-end tubes, please also see my Harmonics Activity.

 

Harmonics:

When the air vibrates inside of a didgeritube, it resonates in fractional vibrations called Harmonics.  Because of this phenomenon, there is an interesting relationship between wavelength and frequency one that relates to the Fundamental Principal [15, pg. 10]

Let's start with the first harmonic.  It's also called the fundamental and it has a wavelength as shown above.  Now when we look at the third harmonic, we see that its wavelength is only 1/3 of the fundamental, while its frequency is tripled.  Similarly, the wavelength of the fifth harmonic is 1/5 of the fundamental, and its frequency is multiplied by five.  This shows an important characteristic of panpipes: because they vibrate in fractions, the harmonics they produce are all multiples of the fundamental frequency.  And as we learned in the previous section, since didgeritubes are closed at one end, they can only play odd harmonics [3]. 

However, when looking at a modern brass instrument like the trumpet, the mystery of harmonics becomes very intriguing.  A regular trumpet can play all harmonics, both even and odd; and yet, a cylindrical tube, such as a didgeritube, can only play odd harmonics.  The differences are due to the flaring bell of the trumpet, and its cup-shaped mouthpiece.  These two improvements in trumpet design change the way that standing waves vibrate inside of instrument.  In short, modes of vibration are shifted so that trumpet's normal resonant frequencies are re-tuned to a different fundamental.  The lowest modes respond more quickly to the flared bell, creating higher frequencies based on a shorter effective length.  In terms of the mouthpiece, it  serves the opposite effect for the higher modes.  It causes the length of the tube to be slightly longer, thereby shifting the resonant frequencies lower [6, pg. 265].   Since didgeritubes do not have a mouthpiece or a flared bell, the blown end of the tube acts as a closed end, rendering only odd harmonics.

 

Timbre:

Timbre (pronounced tam-ber) refers to the quality or tonal color of a sound, and it is determined by which harmonics are simultaneously present in the sound. Timbre in brass instruments is usually changed in one of four ways.  These include the shape of the tube, the use of mutes, varying amplitude, and incorporating vocal sounds.

1. Changes in bore type, whether conical or cylindrical, have an effect on the timbre of a brass instrument.  Conical tubing, as used in a cornet or flugelhorn, has a mellow timbre that emphasizes the fundamental frequencies.  Cylindrical tubing, which is used in a didgeridoo or trumpet, causes the timbre to be brassier by accentuating more of the higher harmonics. 

2. Mutes also change the timbre of the tone produced.  Different mutes for brass instruments include straight mutes, Harmon mutes, plungers, and cup mutes.  When a mute is inserted into the bell of a brass instrument, it changes what is called the radiating efficiency of most frequencies, and therefore makes the sound less brassy [20].  By definition, a mute is simply anything that, "occludes a substantial fraction of the bell" and in some cases can cause the, "pitch [to be] altered by a semitone" [20].

3. Changes in amplitude also affect the timbre of brass instruments.  When a note is played softly on a brass instrument, the player's lips move slower than normal, and never completely cycle to a closed position.  As a result, a nearly sinusoidal wave is produced in which the fundamental frequency is predominant, with very few higher frequencies in the overall sound [20].  The opposite is therefore true in playing loudly with greater amplitude.  Loud notes have what is called clipping and nonlinear behavior, because the player's lips vibrate at such a high rate they often close abruptly.   In addition, this timbral change actually seems louder to our ears, simply because our ear drums are more sensitive to these higher frequencies [4]. 

4. The vocal track is commonly used by didgeridoo players in order to produce wide variances in timbre. The process begins when the vibrating lips transmit waves into the didgeridoo and into the vocal tract [19].  The waves in the vocal track are then mixed with vocal resonances, resulting in a composite sound with much greater frequency range [19].  Didgeridoo players develop this potential further by creating unique renditions of natural sounds, such as singing and speaking effects, as well as various animal noises like barking dogs.  Although these techniques have very little application to orchestral brass instruments, they are of great importance to didgeridoo players in their effort to produce musical expressiveness through changes in timbre [19].  

 

Works Cited

[1] Neville H. Flectcher, Thomas D. Rossing, The Physics of Musical Instruments (Springer- Verlag, New York, 1991) 

[2]  Murray Campbell, Clive Greated, The Musicians Guide to Acoustics (Schirmer Books, New York, 1988)

[3] http://www.physicsclassroom.com/Class/sound/u11l3d.cfm

[4] http://www.phys.unsw.edu.au/jw/fluteacoustics.html

[5] http://www.phys.unsw.edu.au/jw/pipes.html - interaction between acoustic pressure and acoustic flow

[6] Donald E. Hall, Musical Acoustics (Brookes Cole, 2001)

[7] Alexander Wood M.A., D.  Sc., The Physics of Music (Methuen & Co. Ltd., London) 

[8] John R. Pierce, The Science of Musical Sound (W.H. Freeman and Company, New York NY, 1992)

[9] Thomas D. Rossing, The Science of Percussion Instruments (World Scientific Publishing Co., Singapore, 2000)

[10] http://www.phy.mtu.edu/~suits/windchime.html

[11] http://www.phy.mtu.edu/~suits/scales.html

[12] http://www.exo.net/~pauld/summer_institute/summer_day11sound/ringing%20_Al_rod.html

[13] http://wordnetweb.princeton.edu/perl/webwn?s=wavelength

[14]  Robert Erickson, Sound Structure in Music (University of California Press, 1975)

[15]  Willi Apel, The Harvard Dictionary of Music, Second Edition (The Belknap Press of Harvard University Press, Massachusetts, 1972)

[16] http://www.physicsclassroom.com/Class/sound/U11L3c.html

[17] http://www.windows.ucar.edu/tour/link=/earth/Atmosphere/tornado/beat.html

[18] http://science.education.nih.gov/supplements/nih3/Hearing/other/glossary.htm

[19] http://www.phys.unsw.edu.au/jw/didjeridu.html#work

[20] http://www.phys.unsw.edu.au/jw/brassacoustics.html

[21] http://www.panflutejedi.com/pan-flute-history-main.html

 

Copyright 2009 Sarah Tulga