Download Resonance and Musical Instruments

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Resonance and Musical Instruments
Catherine Schmidt-Jones
This work is produced by OpenStax-CNX and licensed under the
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Creative Commons Attribution License 3.0
Abstract
An introduction to the concept of resonance as it applies to musical instruments.
Whenever the vibrations of one object cause a second object to start vibrating, the second object is said
to be resonating with the rst, and its vibrations can be called sympathetic vibrations. Resonance is
very important in the physics of music1 . In fact, in many musical instruments, the part of the instrument
that rst produces vibrations is often a rather small, insignicant-looking part of the instrument - a thin
string, or a sliver of reed. (In the case of brass2 instruments, it is not a part of the instrument at all, but
the players lips, that produce the original vibrations.) The largest, most obvious part of the instrument the delicately curved body of the violin3 , for example, or the many brass loops of the French horn4 is just
the main resonator, and this resonating part of the instrument (often called the body of the instrument)
determines, or helps to determine, many important apsects of the instrument's sound, including tone quality,
timbre5 , and dynamic6 capabilities.
1 Resonance in Winds
If you ever get a chance to hear a brass7 or woodwind8 mouthpiece9 played without the rest of the instrument,
you might be surprised at the unmusical buzzes and squawks you hear. The feedback from the body of the
instrument is very important in producing a musical tone.
To understand why this is so, picture someone pushing a child's swing. Like any pendulum, the natural
frequency10 of the swing depends on the swing's length. A swing on a short chain will change direction more
often than one on a long chain. Pushes that are timed with the swing's natural frequency give a nice, strong,
high, smooth, swinging motion. Pushes that are badly timed give a jerky motion that slows or even stops
the swing. If you really want it to swing faster or slower, you have to change the length of the swing's chain.
In a wind instrument, the mouthpiece vibrations are the "push". The column of air inside the instrument's
body is the "swing". A "push" that gives the right frequency11 causes the air to vibrate very strongly, like
the well-timed swing. Wrong frequencies cause the sound to sputter or fail. The player changes the pitch12
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1.6: Jan 18, 2013 7:08 pm -0600
† http://creativecommons.org/licenses/by/3.0/
1 "Acoustics for Music Theory" <http://cnx.org/content/m13246/latest/>
2 "Orchestral Instruments": Section Brass <http://cnx.org/content/m11897/latest/#s13>
3 "Introduction to the Violin and FAQ" <http://cnx.org/content/m13437/latest/>
4 "The French Horn" <http://cnx.org/content/m11617/latest/>
5 "Timbre: The Color of Music" <http://cnx.org/content/m11059/latest/>
6 "Dynamics and Accents in Music" <http://cnx.org/content/m11649/latest/>
7 "Orchestral Instruments": Section Brass <http://cnx.org/content/m11897/latest/#s13>
8 "Orchestral Instruments": Section Woodwinds <http://cnx.org/content/m11897/latest/#s12>
9 "Wind Instruments: Some Basics" <http://cnx.org/content/m12364/latest/#p1b>
10 "Frequency, Wavelength, and Pitch" <http://cnx.org/content/m11060/latest/>
11 "Frequency, Wavelength, and Pitch" <http://cnx.org/content/m11060/latest/>
12 "Pitch: Sharp, Flat, and Natural Notes" <http://cnx.org/content/m10943/latest/>
http://cnx.org/content/m13537/1.6/
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by changing the eective length of the instrument, so that a dierent frequency will resonate inside the
instrument.
Unlike a swing, more than one frequency can be successful at each length, but it is a very specic set of
frequencies that are allowed. This set of possible frequencies is called a harmonic series13 , and the sounds
coming out of a wind instrument are actually a combination of harmonic series pitches. Please see Timbre14
and Standing Waves and Wind Instruments15 for more on this subject.
2 Voices and Formants
Like the pushed swing, a wind instrument is an example of a specically tuned resonator. Other resonators
are more broadly tuned to resonate over a larger range16 of pitches. The voice is the most well-known
instrument of this type. The vocal chords produce the vibrations, which then resonate in the throat, mouth,
and nasal cavities. The vocal chords are only capable of a certain range of sounds, of course, although a
trained vocalist can extend this range considerably.
The resonating space of the voice, however, also has a pitch range, called the formant, in which it
naturally resonates, so that any vibration in this range will naturally be louder than other vibrations. Like
instrument sounds, a sung tone consists of a combination of vibrations, so the relationship between a sung
pitch and the vocal formant greatly aects the sound of the note. Formants are a basic part of the timbre17
of every person's speaking and singing voice, and trained singers also spend much eort learning to control
formant eects.
3 Resonance in Strings
The sound of a string without an instrument body is a musical tone, but a very, very quiet one. The main
job of the body of a string instrument is to amplify the original sound, so string instruments resonate over
a wide range of pitches. Like voices, they will have formants, and also as in voices, the smoother and less
noticeable the formant eect, the better the instrument.
In most string intruments, one end of each string is held tight against a piece of of the instrument (often
called a bridge) that rests on the body of the instrument. The contact is important, because vibrations travel
through some solids (wood, for example) much more eciently than they do through air. The vibrations
travel from the end of the string through the bridge to the body, which is often hollow. The sounds can then
resonate in the body of the instrument and in the air inside the instrument, for amplication before they
are released through sound holes in the body of the instrument into the air outside.
13 "Harmonic Series" <http://cnx.org/content/m11118/latest/>
14 "Timbre: The Color of Music" <http://cnx.org/content/m11059/latest/>
15 "Standing Waves and Wind Instruments" <http://cnx.org/content/m12589/latest/>
16 "Range" <http://cnx.org/content/m12381/latest/>
17 "Timbre: The Color of Music" <http://cnx.org/content/m11059/latest/>
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