Put theory into action by building instruments that demonstrate how sound waves make music!

To really understand the connection between science and music, it helps to watch what happens when an instrument starts to shake, rattle, and roll. On some chordophones (string instruments), you can actually see the strings vibrate back and forth as they create sound waves, which is why it’s so useful to use chordophones to study how music works.

Aerophones (wind instruments) are also good for demonstrating sound waves in action—even though you can’t see air molecules vibrating. You can even change the length of some aerophones as you play, sliding between long and short sound waves and high and low notes.

In this chapter you make a variety of chordophones and aerophones and learn a little bit more about the science of sound waves. Try the projects and then use what you discover to invent some instruments of your own!

Playing Around with Notes

Instruments use different methods to change the pitch of the notes they play, and some use more than one method. To help you understand the science behind musical instrument design, here’s a quick recap of what you learned in the Introduction.

• Every wave, including sound waves, can be described by three measurements:
  • Its wavelength (the distance from one point on the wave to the same point on the next wave)
  • Its frequency (how many complete waves pass by in one second)
  • Its speed (how fast the wave travels away from the point where the sound started)
• Frequency and wavelength are related—if the wavelength is shorter, more waves can pass by your ear in one second, so the frequency goes up.
• Frequency and speed are also related. The faster a wave is traveling, the more waves will pass by in one second, which also makes the frequency go up.
• The frequency of a sound wave is translated by your brain into a pitch (how high or low a note sounds). Every note has its own frequency, so changing the length or the speed of a sound wave (or both) will also change the pitch. On any instrument, the way to do this is by changing the part that’s vibrating.
• Every instrument (or part of any instrument, like a guitar string) tends to vibrate at a particular frequency or frequencies, which are called its harmonics. The lowest note an instrument (or part of an instrument) can produce is its fundamental frequency, also called its first harmonic. Sometimes you will also hear higher frequencies, which are the instrument’s overtones.

  

One interesting thing about instruments is that the sound you hear is actually made up of multiple sound waves blended together. Here’s how it works: when a traveling wave hits a boundary between one kind of material and another, it bounces back. For example, when a sound wave moving down a vibrating string hits the end of the string is attached to, it turns around and heads back up the string. Soon you have sound waves with the same frequency traveling back and forth along the string in both directions at the same time. As the waves on the string overlap, they get added together. In scientific terms, when two or more waves cross over each other, that’s called interference.

Where two high points or low points meet, you get points that move twice as high or low as the original waves.

Where a high point on one wave meets a low point on another wave, they cancel each other out, and you end up with a point that doesn’t move at all. When the interference between two waves creates a wave that looks like it is no longer moving forward and back, you have a standing wave pattern.

The points that don’t move on a standing wave pattern are called nodes. If you picture two people holding a jump rope, the jump rope represents a standing wave, and the two people holding the ends of the rope are the nodes. (The part that seems to go up and down on a standing wave pattern is called the antinode.) On any instrument, the first harmonic is the note produced by a standing wave pattern with two nodes.

The second harmonic is produced by a standing wave pattern with three nodes. In our jump rope model, it’s as if you add a third person who holds the jump rope right in the middle, while the people at the end keep turning it. The two loose parts of the jump rope still go up and down, but each section is only half as long as before. For the third harmonic, you have four nodes that divide the vibrating part into three equal parts.

In Figures 1-3, 1-4, and 1-5, you may have noticed that the wavelength of a harmonic is related to the length of the string (that is, the part of the string that is free to vibrate). Figure 1-6 shows all three harmonics at the same time. The wavelength of the first harmonic is twice as long as the string. The wavelength of the second harmonic is the same length as the string. If you look closely, you can also see that the frequency of the second harmonic is twice the frequency of the first harmonic.

Remember the ratios you read about in the Introduction? This is where they come in. In math terms, we say the frequencies of the second harmonic and the first harmonic are in a ratio of 2:1. In musical terms, we say the second harmonic is an octave higher than the first harmonic. The ratio of the frequencies of the third harmonic compared to the second harmonic is 3:2. (In musical terms, the notes are a fifth apart.) So the reason why notes with frequencies in simple ratios like 2:1 and 3:2 sound good together is because they are created by the same vibration! (As you will see in Chapter 2, you can also have overtones that are nonharmonic.)

How to Change Notes on a Chordophone

Chordophones include all kinds of instruments with strings, from violins to guitars to ukuleles to harps. Even pianos and harpsichords (which have strings hidden inside them) are types of chordophones. On a chordophone, there are three main ways to control the frequency of the vibration produced by the strings, and they can be used separately or in combination:

When you pull a string tighter, it will play a higher note. Loosen it and the note goes down. The measurement of how tight a string is stretched is its tension. Most chordophones let you tune the strings to the correct pitch with tuning pegs. When you wrap the end of the string around a tuning peg and turn it, you can increase or decrease the tension in the string.

If you have two strings that are the same length and tension but different thicknesses, the thicker string will play a lower note, and the thinner string will play a higher note. The thickness of a string on a chordophone is called its gauge. Most instruments have a standard length for the strings they use, so a string with a higher gauge will also have a higher mass. The mass is the amount of material in an object.

How do tension and mass affect the pitch of a string? By changing the speed of the sound wave that is traveling along it. A sound wave will move faster along a string that’s tighter or thinner than it will on a string that’s looser or thicker. Since the speed is related to the frequency of the sound wave, that means that tighter or thinner strings have a higher fundamental frequency and play a higher note. The opposite is also true—that’s why a string bass, which can play very deep low notes, uses strings that are thicker and looser than those on a violin or a guitar.

Some chordophones only have one string, so it’s easy to test the different ways of changing the pitch of a string instrument. Make this Compact Washtub Bass and try it out for yourself!

Project:
Compact Washtub Bass

A washtub bass is one of the homemade instruments that make up the jug band, a type of country music group popular in the early 1900s. It is usually made by connecting a piece of cord from the top of a wooden stick to the middle of a metal tub that has been turned upside down. The tub serves as a sound box, deepening and amplifying the sound. To play this instrument, you tilt the stick to make the string tighter or looser, creating higher and lower notes. Some players also use the stick as a fingerboard, pressing down on the string the same way you would with a guitar or violin. This Compact Washtub Bass has a great sound and doesn’t take up a lot of room. It’s also just the right size for kids.

1. Turn the pail upside down, and use a hammer and nail to make a small starter hole in the center of the pail bottom.
2. Screw one of the nuts onto the eyebolt. Slide on one of the washers. Insert the eyebolt into the hole you made with your hammer and nail, loop side up. Inside the pail, slide the other washer onto the bolt. Fasten it on with the other nut.

   

   

3. Tie one end of the cord tightly to the loop in the eyebolt.

   

4. Put the rubber cane tip on the smooth end of the stick to keep it from slipping. Set the pail on the floor, and place the end of the stick with the rubber tip next to the eyebolt. Tie the other end of the string to the top of the stick, wrapping it around the threads so it doesn’t slide down. The string should be tight.

   

   

5. Time to give the washtub bass a test! Put one foot on the edge of the pail to hold it in place. Move the bottom of the stick to the rim of the pail. The string should get a little tighter. Try plucking the string—do you hear a note? Now tilt the top of the stick away from the pail, keeping the bottom of the stick resting on the rim. The pitch of the string should get higher and higher.

   

6. To see how many notes you can play with your one-string bass, start with the stick as close to straight up and down as it can go and still play a loud, clear note. Tilt the stick a little bit to get the next note in the scale. (Think “do, re, mi” to get the notes of the scale.) Repeat this action to get the next few notes. At some point, you may have to tilt the stick a lot to get the next few notes. But stop if the string starts to pull the bottom of the pail up—you don’t want to break the string or rip the eyebolt out of the pail. If you don’t quite get a full octave, try loosening the string a little bit and starting over.
7. To get more volume, try propping up one side of the pail with a flat pencil eraser. This lets the vibrating air out from under the pail and makes it easier for the sound waves to reach your ears.

Project:
Stick-on-Top 3-String Strummer

There aren’t a lot of parts to this primitive guitar-like instrument: a neck to hold the strings, a body to act as a sound box to amplify the vibrations, screws to let you tighten the strings to the notes you want, and a nut and a bridge to hold the strings a little away from the neck at either end. Depending on how many strings you add and how you tune them, your strummer can be used like a traditional cigar box guitar (or CBG for short), a slide guitar, a ukulele, a dulcimer, or another type of chordophone. Or just invent your own kind of stringed instrument!

1. If the wooden strip you plan to use for the neck feels rough, use sandpaper to smooth it on all surfaces. If you want to finish it, you can paint the wood or seal it with linseed oil or a stain.
2. Next, attach the neck to the body of the instrument. If you are using a cigar box, open the lid and hold it straight up. On the inside of the lid, measure and mark the center along the top edge. Stand the neck up against the outside the lid. Trace a line on the neck and measure and mark the center. Make sure the two center marks are lined up. Use masking tape to attach the neck temporarily.

   

   

3. Next, lay the neck down on a sturdy work surface with the cigar box lid on top of it. Put pencil marks where you want the screws to go. It’s best to zigzag them rather than line them up one above the other. Use a drill (or a hammer and nail) to make starter holes for the screws. Then screw in the screws through the box lid and into the stick.

   

4. Close the box so the neck is now on top of the lid. Near the end of the stick closest to the box, draw a line straight across. This is where the bottom screws will be attached. Mark one spot for each eye screw—one for each string. They should be evenly spaced and far enough apart that you can twist the loops without them bumping into each other. Do the same thing near the other end of the neck, at the top of the fingerboard, furthest from the box. Screw in the eye screws. If you have trouble turning the screws, you can insert a thin screwdriver into the eyehole as a handle.

   

   

   

5. Take the drawer pull and place it over the stick. This will be the bridge that holds the strings above the body. With the pencil, mark where the ends attach to the box. Measure the distance between them to be sure it is accurate. Also measure the distance from each mark to the bottom of the box to make sure they are even. Then place the lid over a piece of scrap wood and carefully make a starter hole straight through the lid at each mark. (The scrap wood supports the thin lid and protects the surface below it as you drive in a nail or a drill bit.) Then from the inside of the lid, screw in the screws to attach the ends of the drawer pull securely.

   

6. Now attach the strings one at a time. The lowest note usually goes on the left, so start on the left with the thickest string. (If you are left-handed, you can string it the opposite way.) Tie one end to the bottom eye screw furthest left with a double knot. Tie the other end to the top. Twist the screw at the top until you get a good sound. Repeat with the next thickest string. Tune it to an interval that sounds good when you play the two open strings together. An open string is one that you play without pressing it down to shorten it. Continue with the remaining strings until you have them all attached. (See the sidebar titled “Tuning Your Strummer” later in this chapter for some suggestions on tuning your instrument.)

   

   

7. To reduce buzzing when you play the strings, add a smaller version of a bridge at the top of the neck to hold the strings a little above the fingerboard. This piece is known as a nut. You can make a nut using a small wooden dowel or two mini craft sticks glued together. Slide the nut under the strings across the neck, near the eye screw tuners. Adjust it until it gives you the best possible sound, and mark the spot. Be careful to place the nut close to the screws, to prevent it from getting in the way of your fingering when you play. To glue the nut on without removing the strings, loosen the strings slightly and slide a pencil under the strings to hold them away from the neck. Squeeze a very thin line of glue onto the nut, and then carefully slide it into place. Wipe up any excess glue. Remove the pencil. Use clamps, large binder clips, or crisscrossed rubber bands to hold the nut tight against the neck until the glue is dry.

Adaptations, variations, and extensions:

• For a narrower neck (good for smaller hands), use only two strings instead of three.
• If your instrument’s neck is wide enough, use larger eye screws to make them easier to turn and to tune. You can also zigzag them rather than place them in a straight line.
• Use four strings instead of three to turn your instrument into a ukulele.
• Frets are small ridges that make it easier to press down the strings to get different notes. Some CBG makers simply draw on frets with permanent markers to show where your fingers should go. You can also make frets by gluing wooden toothpicks or pieces of bamboo skewers at the fret marks. (Doing this may be easier if you temporarily remove the strings.) You can make a sound hole (about the size of a quarter) in the lid next to the string to release more of the sound from inside.
• Make a slide that lets you press down all the strings at once. A traditional slide is made from the neck of a glass bottle, cut off and smoothed. You put your finger inside the slide and rub it up and down the strings to create different types of sound. You can make your own slide from an old glue stick cap or other small sturdy plastic tube. If it’s too small to slip over your finger easily, just hold it against the strings.

How to Change Notes on an Aerophone

Aerophones include all kinds of instruments where the part that vibrates is the air in or around them. They include wind instruments that you blow into, like recorders. On some, like flutes and panpipes, you start the air vibrating by blowing across an opening. Other aerophones, such as the trumpet, tuba, and didgeridoo (a very long pipe from Australia, usually made from a hollow eucalyptus tree) require you to buzz your lips while you blow. Many wind instruments use a reed, a thin piece of material you hold in your mouth to create the vibration. These include the saxophone and clarinet, which use a single reed, and the oboe and the bassoon, which use a double reed. But some aerophones don’t need you to blow into them at all. Accordions and pipe organs use a bellows that is squeezed or pumped up and down, and calliopes use steam!

On a chordophone, it’s easy to see the part that’s vibrating—the string. With an aerophone, the part that’s vibrating, the air, is invisible. But just like with string instruments, the length of a wind instrument tells you what the wavelength of its sound waves will be. For tube-shaped instruments, such as the flute, the ends of the tube act like the ends of the string. Even if the tube is open at one or both ends, the change in air pressure between the inside and the outside of the tube is enough of a barrier to cause the sound wave to reflect back and create a standing wave pattern.

One way to play different notes on a tube-like aerophone is to add holes. When the holes are open, they act like the end of the tube to make the sound wave reflect back. When the holes are closed, the sound wave keeps going as if the hole isn’t there. Other aerophones, such as trombones, use extra pieces of tube that can slide in and out to make the tube longer or shorter. And changing the shape or position of your mouth can also change the sound wave the aerophone produces.

As you try these aerophone projects, see if you can find ways to change the notes they play. Some of the projects also let you hear the different harmonics an instrument can make. You may hear them created one at a time, or all together, as very faint overtones.

Project:
Drinking Straw Aerophones

Turn a drinking straw into an instrument by giving it a double reed like an oboe. Then use the science of standing waves to create drinking straw aerophones that can play a range of notes.

1. Bite down on one end of the straw to make it flat. Cut the flattened end to make a V shape. Open the flattened part of the straw a little.

   

   

   

2. To play, put the V in your mouth and blow.
3. Make another straw and blow on it the same way, but this time, snip off a piece while you’re blowing. You’ll hear the pitch get higher as the column of air inside the straw gets shorter. Keep cutting and you’ll hear the note go up and up. How short can your straw get and still produce a sound?

Variations:

• Add finger holes to create different notes without changing the length. Measure the length of the straw, and then use a permanent marker to put dots halfway from the end, one third of the way from the end, and so on. Pinch the straw and cut a small V-shaped opening at each mark. (You can also use a hole puncher to make the holes perfectly round. Now cover the holes with your fingers as you blow. As you uncover each one, the pitch should change to notes related to the pitch of the whole straw.
• Try making an extra-long straw oboe by connecting additional straws. Take a new straw or piece of straw and squish it enough to slide it inside the end of the oboe. Keep adding more pieces to see what notes you can produce. If you have bendy straws, you can bend the extra pieces into interesting shapes. Does bending the straw affect the sound?
• If you have two straws that are slightly different widths, try making them into a trombone. Slide the fatter straw over the thinner straw. Make a reed on the thinner straw, then slide the wider straw back and forth to change the pitch by making the instrument longer and shorter.

Project:
Giant Corrugated Singing Tube

You may have seen singing tubes in the toy store. When you swing them around, you force air to rush through them. The bumpy insides churn up the air and create sound waves. The faster you swing the tube around, the faster the speed of the sound waves and the higher the pitch.

One unique feature of the singing tube is that it can only play certain notes—those related to the fundamental frequency. You’ll never get a note that’s out of tune, because the note jumps directly from one to the next. If you want to play notes other than those that are harmonics of the fundamental frequency, you’ll have to get a tube with a different length or width.

1. If you need to cut the hose to the proper length, use heavy-duty scissors or a utility knife to make a neat cut. Use the bumps as a guide.

   

   

2. To play the tube, find an open space with plenty of room around you. If it’s long enough, hold one end of the tube pointing toward your ear. This is the end the sound comes out of. With your other hand, grab the middle of the tube. The loose end is what you will swing, so make it short enough to be comfortable.
3. Begin to swing the tube around. As you twirl it faster and slower, listen closely to find the speeds that produce the clearest, loudest sounds. You may also be able to hear multiple overtones playing at the same time. See how many different notes you can produce with one tube!

Variations:

• If you have extra tubing, try cutting different lengths to hear the different notes they play. Try lengths that are twice as long, or one-third as long, as your first tube. Count the corrugations (the bumps) as a guide.
• Keep an eye out for other widths of tubing at hardware stores and elsewhere and create a corrugated tube orchestra!

Project:
Bullroarer

The bullroarer is an ancient kind of instrument that you swing around on a string. As it twirls, it produces a low humming sound that can be kind of eerie. The bullroarer has been used in religious ceremonies in different parts of the world, including Europe, North America, and Australia. It is usually made of wood, clay, or bone.

You may think that having a string means a bullroarer is a type of chordophone. In fact, it is a free aerophone—an instrument that creates sound waves by cutting through the air around it. As you swing the bullroarer around, it twists around on its string. This twisting stirs up the air and creates the sound waves.

You can change the sound of a bullroarer by spinning it faster or slower. In fact, you may hear the note it plays go up and down with each swing as your arm speeds up and slows down. Different sized bullroarers will also create different sounds. Try making one yourself and then see what you can do to vary the notes it plays!

1. Most bullroarers are shaped like airplane wings, with rounded edges that are thinner than the center of the weight. Take the coarse sandpaper and sand down the edges of the paint stirrer to make them thinner and rounder. Use the medium sandpaper to make the surface smoother. Clean off any sawdust. If you want, you can decorate your bullroarer with markers, paint, or wood stain.

   

2. Attach the string by tying it tightly around the indent in the paint stirrer. Keep tying knots to make a little “neck” that will let the stick twist as you twirl it around on the string.

   

3. Take your bullroarer to a wide open spot to test it out. Make sure that no one is close enough to be hit when you start spinning it around (or if it goes flying off accidentally). Wrap the string around your hand until the string is a comfortable length. Let the bullroarer hang down. Then twist the bullroarer at the end of the string as many times as possible. The string should coil up slightly. Start to swing it around over your head, or next to you, like a cowboy lasso. You should hear a low humming or buzzing sound. If the bullroarer doesn’t twist well and doesn’t create a sound, try a thinner string, such as kite string.

Extensions:

• Try making bullroarers that are heavier or lighter to see if the different masses play different notes. For instance, you could glue two paint stirrers together, or tie wooden beads onto the string.
• What other ways can you change the weight of the bullroarer?

Project:
The Pickle-O, a Vegetable Ocarina

An ocarina is also called a vessel flute. Instead of an open-ended tube, it is more like a miniature clay jug with holes. Ancient versions were often made in the shape of animals or people.

The ocarina works like a whistle, but it has finger holes that let you play different notes. The modern ocarina was invented in the late 1800s by Giuseppe Donati. Legend has it that Donati was a brickmaker who saw an ocarina from South America in a concert and made his own by firing clay models in his oven. He standardized the holes so that the ocarina could play along with other modern instruments.

The most common type of ocarina is sometimes called a sweet potato ocarina because of its shape—but you can make actual ocarinas from many kinds of vegetables! Cucumbers are a good size and soft enough to carve easily. They’re juicier than other vegetables, though, so you’ll need to dry them off as you work.

Your vegetable ocarinas may not last long, but they are fun to make and to play. This project was inspired by YouTube videos by the Vegetable Orchestra of Vienna, musician Junji Koyama, and a video tutorial by Dave Hax.

1. Thoroughly wash the skin of your vegetable.
2. To make your vegetable into an instrument, you need to cut a cylinder-shaped tunnel into it. The opening inside an aerophone is called its bore. Start by slicing off the tip of the vegetable; make your slice about 1 inch (2–3 cm) long. The sliced end should be wider than the corer. Set it aside.

   

3. Twist the corer into the vegetable as far as you can without breaking through the other end. Be careful not to poke through the sides as you work.

   

4. Remove the “core” you just cut. Since it is still connected at the far end, you will have to work it out carefully. One method is to poke a knife into the end, like sticking a screwdriver into the slot of a screw. Hold on to the knife while you try to twist the core until the end breaks off. If that doesn’t work, slice through the center of the core all the way down and then work out each half. Use the knife or vegetable peeler to clean out any bits remaining and smooth the inside of the bore. Rinse the vegetable if it needs it.

   

   

5. Choose one side of the vegetable to be the top of the ocarina. Leaving enough room for your lips when you blow on the end, take the knife and slice straight down, but only until you reach the bore. Then make another cut at an angle a little way back from the first cut and toward it so that it connects with the bottom of the first cut, making a wedge. You should be able to remove this triangular-shaped piece to create a little window into the bore.

   

   

   

   

6. Next, you need to make a fipple—a plug that makes your instrument whistle. Take the leftover tip and trim it so it is roughly the width of the bore. If the vegetable is soft like a cucumber, you may be able to squish a wider piece into place. You want it to fit snugly and stay in place when you blow! The fipple should be long enough to reach from the end of the ocarina to the “window” at the top. Slice off the top of the fipple so it is flat. Then slide the fipple into the bore, with the narrower end pointing out and the flat side up.
7. Test your flute by blowing into the opening until you get a clear whistling sound. You may need to move the fipple in and out or higher or lower, or trim it a little more. Try different shapes and placements. Don’t get discouraged if your instrument doesn’t work the first (or second, or third) time. You may need to make a few models to get one that makes a clear whistling note.
8. Once you have a good sound, you may want to carefully slice off an angled piece from the bottom of the opening to make it easier to fit the instrument in your mouth.

   

9. Add finger holes that will let you play different notes. On an ocarina, where the air churns around, it doesn’t matter where the holes are. To make different notes, make them different sizes.
10. Try different vegetables to see what different sounds you get. You can even start your own band! But don’t forget that your instruments are perishable. Just keep some extra veggies on hand so you can quickly carve up a replacement as needed!