Melodic Tube Drums
 

Welcome to my page on Melodic Tube Drums!  It's designed for middle and high school science students who are interested in studying the physics of drums!  On this page, you will find a short introduction on tube drums; 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

Drums are among the oldest and most widespread of all musical instruments, and can be found in all cultures.  In a traditional sense, drums  usually consist of a frame or a vessel that is covered with skin, and struck with a stick or the hands [15, pg. 247].   As a result, most of the tuning on a traditional drum is accomplished by varying the tension of the drum head a process that needs to be repeated frequently to maintain a given pitch.  To address this, I will be demonstrating tube drums that have a rigid drum head, which will allow us to determine the pitch or frequency of a drum simply by its length.  The melodic tube drums on this page are constructed from 2-inch diameter ABS pipe, with plastic heads glued onto the ends.  In terms of classification, tube drums are considered membranophones according to the Sachs-Hornbostel system, or in orchestral terminology, are considered part of the percussion family of instruments. 

 

How It Works

When a stick hits a drum head, what happens?  How is the sound produced?

Melodic tube drums produce their sound by vibrating a column of air inside of a tube.  In this section, we are going to look at this vibrating column of air: how it starts with the striking of a drum head, 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.

Drum Head:

A drum head can vibrate in a number of different modes many of them resembling geometric-shaped patterns.  Which mode is excited is determined by the point at which the drum head is struck.  For our purposes, let's assume that the drum head is struck in the center, and as a result it begins to vibrate in its fundamental mode, as shown in the animation below.  The fundamental mode pushes the adjacent air in one forceful direction [6, box 9.1]. This creates one uniform motion,

How Melodic Tube Drums Work

rather than a variety of smaller bidirectional motions that would be characteristic of higher modes. As the drum head pushes downward on the air, it forms a compression.  When the drum head becomes convex and moves upward, it forms a rarefaction.  In this manner, a longitudinal wave is formed and begins to travel down the tube.

 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, since the drum head is closed at the top.  It reaches the top of the tube exactly at the time when the drum head is at the most convex point of its 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.  The areas of constructive interference become the antinodes of the wave, and the areas of destructive interference become the nodes [7, pg. 110-111].  As shown above, the melodic tube drum is vibrating with a standing wave pattern of three antinodes and three 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.   Also, notice that because the drum head it struck once with a given amount of force, the energy dissipates over time as the longitudinal waves dissipate.  Therefore, the drum head will lose the amplitude it achieved on the first compression and slowly decrease thereafter.  As such, the standing wave pattern is only sustained for a fraction of a second. This is unlike panpipes or didgeritubes, since their standing wave patterns are sustained by a constant flow of air.

 

Demonstrating What You Know

Now that we understand how melodic tube drums 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 melodic tube drums 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 melodic tube drums, start the video below.

Changing Frequency on Melodic Tube Drums

 

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 melodic tube drum 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 melodic tube drums by varying the amount of striking force on the membrane or drum head.  If the membrane has less force applied to it, just like the tuning fork example, fewer air particles are displaced.  However, if the membrane has more force applied to it, more air particles are displaced.  This is true because the drum head moves up and down with lesser or greater deformation depending on the force that is applied to it.  Striking softly, with less force, will produce less amplitude.  Striking harder, with more force, will produce greater amplitude.

Varying Amplitude

 

 

 

Wavelength:

Wavelengths on a Closed-end Tube:
Fundamental or 1st harmonic, 3rd harmonic, and 5th harmonic

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 melodic tube drums, 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 or stopped 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 and Timbre:

Changing Harmonics and Timbre on Melodic Tube Drums

Melodic tube drums vibrate in fractional vibrations called Harmonics.  Unlike most percussion instruments that produce non-harmonic overtones, melodic tube drums produce their pitch by vibrating a column of air inside of a tube.  Because of this distinction, they are very much like panpipes, in that they produce a mixture of odd harmonics.  There is also an interesting relationship that arises 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 melodic tube drums: they vibrate in fractions and produce harmonics multiples of the fundamental frequency.  And as we learned in the previous section, since melodic tube drums are closed or stopped at one end, they can only play odd harmonics [3].  To hear how to obtain these harmonics, please play the video on the right.

After we understand harmonics, we can apply it to the musical concept of timbre or tone.  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.  In order to produce a change in timbre, one can vary the striking point on the drum head, and use different mallets. To achieve a sound that accentuates the lowest resonant frequency of a tube, use a large soft mallet and strike the center-most point of the membrane.  In so doing, the drum head moves up and down in a uniform manner, causing the air in the tube to accentuate its fundamental frequency.  To blend in the third or fifth harmonics, strike the drum head slightly off center and switch to a harder thinner mallet.  As a result, the drum head will vibrate in higher modes, which will excite the air in the tube to move in fractional vibrations or harmonics.  By mixing harmonics into the sound of the fundamental frequency, drummers can produce composite sounds in which timbre becomes a controllable variable for musical effect [6, pg. 249]. 

 

 

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