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Sound, Physics, and Music

Module by: Catherine Schmidt-Jones. E-mail the author

Summary: For middle school to adult, an overview of the relationship between musical instruments and the physics of sound.

Note: You are viewing an old version of this document. The latest version is available here.

Talking about Sound

Music is the art of sound, so let's start by talking about sound. Sound is invisible waves moving through the air around us. In the same way that ocean waves are made of ocean water, sound waves are made of the air (or water or whatever) they are moving through. When something vibrates, it moves the air around it. The vibrations move through the air in waves, spreading out from the thing that made the sound the way water waves spread out from a stone that's been dropped into a pond. When scientists or engineers or musicians talk about sounds, they are usually describing these invisible waves. They might want to talk about how big the waves are or how far apart they are. Engineers and musicians use different words to talk about sound, but they are often talking about the same things.

There are some things that all kinds of waves - light waves, sound waves, water waves - have in common, but there are differences between them, too. One big difference between sound waves and waves on water is that water waves are transverse. In transverse waves, the waves are moving in a certain direction, call it the forward direction. But the distance between the high point of the wave (where the water is piled up) and the low point (where there is less water) is in a different direction, the up-and-down direction.

Sound waves are longitudinal waves. This means that the distance between the high point of the wave (where the air molecules are "piled up")and the low point (where there are fewer molecules) is also in the forward direction. There is no "up-and-down" to the waving.

Figure 1: In water waves and other transverse waves, the ups and downs are in a different direction from their forward movement. The highs and lows of sound waves and other longitudinal waves are arranged in the "forward" direction. This can be harder to show on paper, so the rest of the figures in this module will show sound waves as if they are transverse waves.
Transverse and Longitudinal Waves
Transverse and Longitudinal Waves (wavetypes.png)

Any sound that we hear as a tone is made of regular, evenly spaced waves that move through the air at the speed of sound. The main differences between these sound waves are how big they are and how far apart they are spaced. Their spacing - the distance from the high point of one wave to the next one - is the wavelength.

Since the waves are all travelling at about the same speed, the sounds with a longer wavelength don't arrive (at your ear, for example) as frequently as the shorter waves. This aspect of a sound - how often a wave goes by, is called frequency by scientists and engineers. They measure it in hertz, which is how many waves go by per second. People can hear sounds that range from about 20 to about 17,000 hertz.

The word that musicians use for frequency is pitch. The shorter the wavelength, the higher the frequency, and the higher the pitch, of the sound. In other words, short waves sound high; long waves sound low. Instead of measuring frequencies, musicians name the pitches that they use most often. They might call a note "middle C" or "the F sharp in the bass clef". These notes have definite frequencies (Have you heard of the "A 440" that is used as a tuning note?), but musicians usually find it easier just to use the note names.

Figure 2: Since the sounds are travelling at about the same speed, the one with the shorter wavelength will go by more frequently; it has a higher frequency, or pitch. In other words, it sounds higher.
Wavelength, Frequency, and Pitch
Wavelength, Frequency, and Pitch (frequency.png)

The other way that evenly spaced sound waves can be different from each other is in how big a difference there is between the high and low points of the waves. Engineers and scientists call how big a wave is its amplitude. They measure the amplitude of sound waves in decibels. Leaves rustling in the wind are about 10 decibels; a jet engine is about 120 decibels.

Musicians call the loudness of a note its dynamic level. Forte (pronounced "FOR-tay") is a loud dynamic level; piano is soft. Dynamic levels don't correspond to a measured decibel level. An orchestra playing "fortissimo" (which basically means "even louder than forte") is going to be quite a bit louder than a string quartet playing "fortissimo".

Figure 3: The size of a wave (how much it is piled up at the high points) is its amplitude. For sound waves, the bigger the amplitude, the louder the sound.
Amplitude is Loudness
Amplitude is Loudness (physics1c.png)

Music is Organized Sound

Surf rolling down a beach, leaves rustling in the wind, a book thudding on a desk, or a plate crashing on the floor all make sounds, but these sounds are not music. Music is sound that's organized by people on purpose, to dance to, to tell a story, to make other people feel a certain way, or just to sound pretty or be entertaining.

Music is organized on many different levels. Beats can be arranged in measures, notes can be arranged into melodies and melodies can be organized into simple songs or complex symphonies. One of the most basic ways that music is organized, though, is simply organizing the sound waves so that the sounds are pretty and go well together.

A rhythmic, organized set of thuds and crashes is perfectly good music - think of your favorite drum solo - but many musical instruments are designed specifically to produce those regular, evenly spaced waves that we hear as particular pitches (musical notes). Crashes, thuds, and bangs are loud, short jumbles of lots of different wavelengths. The sound of surf, rustling leaves, or bubbles in a fish tank are also white noise, the term that scientists and engineers use for sounds that are mixtures of all the different wavelengths (just as white light is made of all the different wavelengths, or colors, of light).

But a string that's held tightly, or the air inside a long, thin, tube, can only vibrate at particular wavelengths. You can start the string or air vibrating at any wavelength you like, but the only wavelengths that will "survive" long enough for you to hear them coming from the string or the tube of air are those that are just the right length to bounce back and forth in the string or tube, setting up a standing wave that can keep vibrating without going anywhere.

Figure 4: A string that's held very tightly at both ends can only vibrate at very particular wavelengths. The whole string can vibrate back and forth. It can vibrate in halves, with the very middle of the string as well as each end holding still, or in thirds, fourths, and so on. But there are many wavelengths that don't "fit" the string; all the wavelengths that would need one end of it to move. To get any of those wavelengths, you need to change the length of the vibrating string, which is what the player does when she holds the string down with a finger.
Standing Waves on a String
Standing Waves on a String (phys2a.png)

Exercise 1

When the string player puts a finger down tightly on the string,

  1. How has the part of the string that vibrates changed?
  2. How does this change the sound waves that the string makes?
  3. How does this change the sound that is heard?

Solution

  1. The part of the string that can vibrate is shorter. The finger becomes the new "end" of the string.
  2. The new sound wave is shorter, so its frequency is higher.
  3. It sounds higher; it has a higher pitch.
Figure 5: When a finger holds the string down, the finger becomes the new end of the vibrating part of the string. The vibrating part of the string is shorter, and the whole set of sound waves it makes is shorter.
Figure 5 (physsolu.png)

The wave that we hear giving the pitch of the string is from the whole string vibrating back and forth. But the string is actually making all those other possible vibrations, too, all at the same time, so that the actual vibration of the string is pretty complicated. The other vibrations (the ones that basically divide the string into halves, thirds and so on) produce a whole series of harmonics. We don't hear the harmonics as separate notes, but we do hear them. They are what gives the string its rich, musical, string-like sound. To find out more about harmonics and how they affect a musical sound, see the module on The Harmonic Series.

Strings aren't the only instruments that are designed to make sounds of particular wavelengths. Although percussion specializes in white-noise "crash"-type sounds, even instruments like snare drums follow the basic physics rule of "bigger instrument makes longer wavelengths and lower sounds".

Note:

If you can, listen to a percussion player or section that is using snares, bongos, cymbals, or other drums of the same type but different sizes to see if you can hear the differences.

Exercise 2

There are also many percussion instruments, like the xylophone, that are designed to ring at specific pitches when they are hit. Can you think of some others?

Solution

There are many, but here are some of the most familiar:
  • Other xylophone-style instruments, such as marimba and glockenspiel
  • Handbells and other tuned bells
  • Chimes
  • Steel drums

Just as the string of a certain length would only vibrate at particular frequencies, these "tuned" percussion instruments are shaped so that when they are struck, they will only vibrate at certain frequencies. But the other big family of instruments that produces pitched sounds is the wind instruments.

They are called wind instruments because, although the instrument itself does vibrate a little, what you are really hearing when they play is vibrations in the column of air inside the instrument. Because of the shape of the instruments, the columns of air inside them act a lot like a vibrating string.

Note:

If it is possible, have a reed player and a brass player demonstrate to you the sounds that their mouthpieces make without the instrument. This will be a sound much more like "white noise", with lots of extra frequencies in it that don't sound very musical. But, just as with the string, these extra waves don't get picked up by the instrument, because they are the wrong length. The only waves that get picked up are the ones that are just the right length to become standing waves inside the instrument.

Figure 6: Standing waves are waves that can keep on vibrating in the same place or in an object, because they are just exactly the right size for that space or object. The only sounds you hear coming from a wind instrument are the ones that could set up standing waves in the instrument.
Waves in Wind Instruments
Waves in Wind Instruments (phys2b.png)

The standing waves in a wind instrument are a little different from a vibrating string, but they also end up being related to each other by fractions (halves, thirds, fourths, and so on, of a particular length). So the set of harmonics is the same for winds as it is for strings, or any other instrument that produces particular pitches. Wind players can actually use these harmonics to get different notes from the same length of tube (see The Harmonic Series), but they can also use the finger holes, keys, or valves on their instrument to make the vibrating column of air longer or shorter. As always, a shorter instrument means a shorter wavelength, higher frequency, and higher sound.

Suggestions for presenting this module to a class

  • Present most of the text above as a classroom lecture.
  • Use the exercises for class participation and discussion.
  • Try to arrange for some demonstrations: by a string player to demonstrate open and held strings; by a brass and/or woodwind player to demonstrate mouthpiece sound vs. whole-instrument sound; by a percussionist to demonstrate how size affects the sound of percussion instruments, too.
  • Download and copy these PDF files as handouts for your class: Sound Waves handout; Strings and Winds handout; Waves Worksheet; Worksheet Answer Key. In case you have any trouble with the PDF files, these handouts are also included at the end of this module, but they will look better if you print out the PDF files.
  • For younger students, consider arranging some of the demonstrations suggested in the module Sound and Music.
Figure 7
Figure 7 (waves.png)
Figure 8
Figure 8 (stringswinds.png)
Figure 9
Figure 9 (wavesworksheet.png)
Figure 10
Figure 10 (wavesworksheetanswers.png)

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