Do-Re-Mi with Straws

Abstract

Objective

In this science fair project you will make musical instruments using drinking straws. One end of a straw will be fashioned into a "reed." When you place the "reed" end in your mouth and blow, the straw will play a single note, with the pitch determined by the length of the straw. The goal of the experiment is to make a series of straw instruments that correspond to the eight notes of a one-octave major scale.

Credits

Andrew Olson, PhD, Science Buddies

Sources

• Henderson, T. (2004). Lesson 5: Musical Instruments: Resonance. Retrieved March 27, 2006 from http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/sound/u11l5a.html
• Kelly, J.P. with E.R., J.H. Schwartz and T.M. Jessel, (eds.) (1991). Principles of Neural Science, Third Edition. Norwalk, CT: Appleton & Lange.
• McREL. (2006). Whelmer #11: Straw Oboes. Retrieved March 27, 2006 from http://www.mcrel.org/whelmers/whelm11.asp#

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Introduction

In this science fair project, you'll be making simple "oboes" using drinking straws. You'll find that the pitch of the note that your straw "oboe" can play depends on the length of the straw. By learning about sound waves and how they are produced in the straw, you should be able to figure out what lengths to use in order to create a series of eight straws that play a musical scale (do-re-mi-fa-so-la-ti-do). If you want to see a picture of what one of the straw instruments will look like when it's finished, visit DragonflyTV's "do it" section.

Click here to watch a video of this investigation, produced by DragonflyTV and presented by pbskidsgo.org

You will also explore the science of musical sounds and find out how sound is produced and how sound is perceived. This will help you understand what makes a sound musical. If you’d like an introduction to the science of musical sounds, check out the DragonflyTV video on the right and join Maxine and Hannah as they create musical instruments and play scales on different types of tubing.

Once you understand the basics of musical sounds, this is a fairly simple science fair project that explores the science of musical sounds. What exactly do we mean by musical sounds? It will help if you think about it step by step. First you need to understand the basics of sound: how it is produced and how it is perceived. Then you can consider what makes a sound musical.

You'll also need to understand some basic properties of waves to get the most out of this project. You can read a quick introduction here, but for a more complete understanding, we recommend some background research on your own. The Bibliography section, below, has some good starting points for research before you begin this science fair project.

What is sound? Sound is a wave, a pattern—simple or complex, depending on the sound—of changing air pressure. Sound is produced by vibrations of objects. The vibrations push and pull on air molecules. The pushes cause a local compression of the air (increase in pressure), and the pulls cause a local rarefaction of the air (decrease in pressure). Since the air molecules are already in constant motion, the compressions and rarefactions starting at the original source are rapidly transmitted through the air as an expanding wave. When you throw a stone into a still pond, you see a pattern of waves rippling out in circles on the surface of the water, centered at about the place where the stone went in. Sound waves travel through the air in a similar manner, but in all three dimensions. If you could see them, the pattern of sound waves from the stone hitting the water would resemble an expanding hemisphere. The sound waves from the stone also travel much faster than the rippling water waves from the stone (you hear the sound long before the ripples reach you). The exact speed depends on the number of air molecules and their intrinsic (existing) motion, which are reflected in the air pressure and temperature. At sea level (one atmosphere of pressure) and room temperature (20°C), the speed of sound is about 344 m/s.

Perception of a sound begins when sound pressure waves reach the tympanic membrane (eardrum), a thin, flexible membrane in the middle ear. The pressure waves cause the tympanic membrane to vibrate. The vibrations are amplified by a series of three tiny bones and transmitted to the cochlea. Curled up inside the fluid-filled, snail-shaped cochlea is the organ of corti, where the vibrations are transduced into nerve impulses by cells called hair cells. Moving along the length of the organ of corti, each region is sensitive to vibrations of decreasing frequency (i.e., higher pitch). The nerve impulses from the hair cells are conducted to the brain, where they are further processed, leading ultimately to the perception of sound. (Chudler, 2006; Kelly, J.P., 1991)

You've seen that one way to describe a wave is by its speed. In addition to wave speed, you will also find it useful to describe waves by their frequency, period, and wavelength. Let's start with frequency (f). The top part of Figure 1, below, represents the compressions (darker areas) and rarefactions (lighter areas) of a pure-tone (i.e., single-frequency) sound wave traveling in air (Henderson, 2004). If you were to measure the changes in pressure with a detector and graph the results, you could see how the pressure changes over time, as shown in the bottom part of Figure 1. The peaks in the graph correspond to the compressions (increase in pressure) and the troughs in the graph correspond to the rarefactions (decrease in pressure).

Figure 1. Illustration of a sound wave as compression and rarefaction of air, and as a graph of pressure vs. time (Henderson, 2004).

Notice how the pressure rises and falls in a regular cycle. The frequency of a wave describes how many cycles of the wave occur per unit time. Frequency is measured in hertz (Hz), which is the number of cycles per second. Figure 2, below, shows examples of sound waves of two different frequencies (Henderson, 2004).

Figure 2. Graphs of high (top) and low (bottom) frequency waves (Henderson, 2004).

Figure 2 also shows the period (T) of the wave, which is the time that elapses during a single cycle of the wave. The period is simply the reciprocal of the frequency (T = 1/f). For a sound wave, the frequency corresponds to the perception of the pitch of the sound. The higher the frequency, the higher the perceived pitch. On average, the frequency range for human hearing is from 20 Hz at the low end to 20,000 Hz at the high end.

The wavelength is the distance (in space) between corresponding points on a single cycle of a wave (e.g., the distance from one compression maximum (crest) to the next). The wavelength (λ), frequency (f), and speed (v) of a wave are related by a simple equation: v = fλ. So if you know any two of these variables (wavelength, frequency, or speed), you can calculate the third.

So far, the sound waves you've looked at graphically have been pure tones (i.e., single-frequency sound waves). What happens when you start combining tones of different frequencies? What happens is that the sound waves interfere, which basically means that they add together. When waves add together, they add algebraically. A "trough" (or rarefaction, in the case of a sound wave), will cancel out a "crest" (or compression, in the case of a sound wave) of the same magnitude. Figure 3, below, shows the sound pressure wave (green) that results when two pure tones are played with one tone (red) at twice the frequency of the other (blue) (Henderson, 2004). This 2:1 ratio of tone frequencies corresponds to notes that are one octave apart.

Figure 3. Interference pattern (green) for two tones one octave apart. The frequency of the wave in red is twice the frequency of the wave in blue. (Henderson, 2004).

Our perception of whether the interference sounds pleasant (the musical term is consonant) or jarring (dissonant) depends on the ratio of the frequencies of the tones. Within an octave, the intervals that are generally considered to be consonant end up having frequency ratios with numerator and denominator being small whole numbers. Figure 4, below, shows an octave of piano keys (starting at C and continuing to C'), and Table 1 gives the perfect whole-number ratios for the frequencies of the notes. (For details on the subtleties of how pianos are actually tuned, see the Einevoldsen reference in the Bibliography.)

Figure 4. An octave on the piano, from one C to the next (C to C'). (Einevoldsen, n.d.).

In the last part of this brief introduction to sound waves, you'll learn how sound is produced by musical instruments. First consider a stringed instrument, like a guitar or a piano. The strings in these instruments are attached at each end. One end wraps around a tuning peg, which can be twisted to change the tension on the string. The other end is attached to a fixed point. In between the two attachment points, the string passes over a bridge, which is attached to the soundboard. When the string is plucked (guitar) or struck (piano), it vibrates. The vibrations are transmitted by the bridge to the soundboard of the instrument, which amplifies the sound (in the case of the guitar, the entire body is the soundboard).

The string vibrates between two fixed points: where it touches the bridge and where it touches the tuning peg. In the case of the guitar, if your finger is pressing down on a string, that point becomes the new fixed point, effectively shortening the string. The vibration results in a standing wave on the string. The fixed points of the string don't move (nodes), while other points on the string oscillate back and forth maximally (antinodes). Figure 5, below, shows some of the standing wave patterns that can occur on a vibrating string (Nave, 2006a).

Figure 5. Standing waves on a vibrating string, showing the fundamental (top), first harmonic (middle), and second harmonic (bottom) vibrational modes. (Nave, 2006a)

The string can vibrate at several different natural modes (harmonics). Each of these vibrational modes has nodes at the fixed ends of the string. The fundamental mode (Figure 5, top) has a single antinode halfway along the string. Thus, the wavelength of the fundamental vibration is twice the length (L) of the string. The second harmonic has a node halfway along the string. Thus, the wavelength of the second harmonic is equal to the length of the string. Remember that the relationship between wavelength and frequency depends on the speed of the wave. You can rewrite the equation presented earlier as f = v/λ. If you take the ratio between the frequency, f₂, of the second harmonic and the frequency, f₁, of the first harmonic, the velocity term cancels out:

You can continue the calculations for the higher harmonics yourself. What is the frequency of the third harmonic, relative to the fundamental?

In an open-ended column of air, the situation is somewhat similar to the vibrating string; however, the standing wave in the air column has antinodes at the each end rather than nodes. This is because at the open ends, the air is free to move maximally (Henderson, 2004).

Figure 6. Standing waves in an open-ended column of air. Shown are the fundamental mode (top), second harmonic (middle) and third harmonic (bottom). (Henderson, 2004)

There is a reference in the Bibliography (Nave, 2006b) that has a calculator for determining the frequencies (fundamental and second through fifth harmonics) produced by a column of a given length. You might find this calculator useful as you work out the correct lengths for your straw "oboes." Now let's get started on those straws!

Terms and Concepts

To do this science fair project, you should do research that enables you to understand the following terms and concepts:

• Waves:
  • Wave speed (velocity)
  • Frequency
  • Period
  • Wavelength
  • Interference
  • Standing wave
  • Harmonics
  • Sound wave
• Musical scale
• Octave

Questions

• How are wavelength and frequency of a wave related?
• What is the wavelength of a 1000-Hz sound (at sea level, 20°C)?
• For a wind or woodwind instrument, what determines the pitch of the note played?
• Two notes, C₁ and C₂, are an octave apart. C₁ is the lower note. What is the ratio of their frequencies, f₂/f₁? What is the ratio of their wavelengths, λ₂/λ₁?

Bibliography

• TPT. (2006). Music and Sound by Maxine and Hannah. DragonflyTV, Twin Cities Public Television. Retrieved July 3, 2008 from http://pbskids.org/dragonflytv/show/musicandsound.html
• Waves: the first reference is a good general introduction, and those that follow cover the specific topics indicated by their titles:
  
  • Henderson, T. (2004). Sound Waves and Music. The Physics Classroom, Glenbrook South High School, Glenview, IL. Retrieved March 27, 2006 from http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/sound/u11l1a.html
  • (a) Nave, C.R. (2006). Standing Waves on a String. Retrieved March 27, 2006 from http://hyperphysics.phy-astr.gsu.edu/Hbase/waves/string.html#c1
  • (b) Nave, C.R. (2006). Resonances of Open Air Columns. Retrieved March 27, 2006 from http://hyperphysics.phy-astr.gsu.edu/Hbase/waves/opecol.html#c1
• Why does the musical scale have 12 notes (counting both the black and white keys on the piano)? Here is a good explanation:
  Enevoldsen, K. (n.d.). Twelve-Tone Musical Scale.Retrieved March 27, 2006 from http://thinkzone.wlonk.com/Music/12Tone.htm
• Chudler, E.H. (2006). Neuroscience for Kids: The Ear. Retrieved March 27, 2006 from http://staff.washington.edu/chudler/bigear.html

Materials and Equipment

To do this science fair project, you will need the following materials and equipment:

• Box of plastic or paper drinking straws (paper straws work best)
• Scissors
• Piano, electronic keyboard, or other musical instrument that can produce a scale of notes for comparison
• Lab notebook

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Experimental Procedure

1. Do your background research and make sure that you understand the terms, concepts and questions above.
2. To make and play a single straw "oboe," follow these steps:
   1. Flatten about 2 cm at one end of a drinking straw (the middle straw in Figure 7, below). You can use your teeth or pinch it between your fingers to flatten it.

      Figure 7. Forming the "reed" end of a straw oboe.

   2. Use scissors to make small, angular cuts, as shown in the rightmost straw in Figure 7, on each side of the flattened end.
   3. Insert the reed end of the straw into your mouth. Position the reed flaps just inside your lips and apply very light pressure with your lips.
   4. Blow through the straw. The reeds should vibrate and produce a tone. You may need to move the straw around slightly to locate the best position for creating your musical note.
   5. You can cut portions off the non-flattened end of the straw to create tones of different pitches.
3. Next, you will make a series of eight straw "oboes" to play the eight notes of a scale by varying their lengths. For a scale starting with C, these eight notes correspond to the white keys on the piano: C, D, E, F, G, A, B, C. Refer to Figure 4 in the Introduction for an illustration and to Table 1, also in the Introduction, for the correct ratios between the frequencies of these notes.
4. Start with the lowest and highest notes, which are one octave apart. From your background research, you should know how to make two straw "oboes" that will produce notes one octave apart. Note: it will help if you match your lowest note to a note on the piano. That way you can check your "oboe" scale with the piano when you are finished.
5. Calculate the straw lengths needed to build six more "oboes" to fill in the rest of the notes in the scale. There is a reference in the Bibliography ((b) Nave, 2006) that has a calculator for determining the frequencies (fundamental, and second through fifth harmonics) produced by a column of a given length. You may find this calculator useful as you work out the correct lengths for your straw "oboes."
6. Compare the scale you made with the scale on the piano. Do all your notes sound right?

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Variations

• Build a holder for your eight straws so that you can hold them all and play them in succession. You could even play a simple melody by playing them in the correct sequence.
• Other instruments you can construct a scale with include:
  • Soda bottles filled with different amounts of water, blow across the top
  • Goblets filled with different amounts of water, with a clean, slightly wet finger, stroke around the rim of the glass to excite vibrational modes. It makes an eerie sound.
  Both of these instruments are columns of air with a single open end. The twist with this type of instrument is that only odd harmonics of the fundamental are produced. There is a reference in the Bibliography ((b) Nave, 2006) that has a calculator for determining the frequencies (fundamental, third, and fifth harmonics) produced by a column of a given length with one end closed. You may find this calculator useful as you work out the correct amounts of water for filling your soda bottles or goblets.

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Related Links

• Science Fair Project Guide
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