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Resonance and Musical Instruments

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

Summary: 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 first, and its vibrations can be called sympathetic vibrations. Resonance is very important in the physics of music. In fact, in many musical instruments, the part of the instrument that first produces vibrations is often a rather small, insignificant-looking part of the instrument - a thin string, or a sliver of reed. (In the case of brass 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 violin, for example, or the many brass loops of the French horn 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, timbre, and dynamic capabilities.

Resonance in Winds

If you ever get a chance to hear a brass or woodwind mouthpiece 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 frequency 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 frequency 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 pitch by changing the effective length of the instrument, so that a different frequency will resonate inside the instrument.

Unlike a swing, more than one frequency can be successful at each length, but it is a very specific set of frequencies that are allowed. This set of possible frequencies is called a harmonic series, and the sounds coming out of a wind instrument are actually a combination of harmonic series pitches. Please see Timbre and Standing Waves and Wind Instruments for more on this subject.

Voices and Formants

Like the pushed swing, a wind instrument is an example of a specifically tuned resonator. Other resonators are more broadly tuned to resonate over a larger range 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 affects the sound of the note. Formants are a basic part of the timbre of every person's speaking and singing voice, and trained singers also spend much effort learning to control formant effects.

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 effect, 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 efficiently 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 amplification before they are released through sound holes in the body of the instrument into the air outside.

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