Resonance

:This article is about resonance in physics. For other senses of this term, see resonance (disambiguation).

Acoustics

Resonance is an important consideration for instrument builders as most acoustic instruments use resonators, such as the strings and body of a violin, the length of tube in a flute, and the shape of a drum membrane.

Related Topics:
Violin - Flute

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• Resonance of a string.

Violin (or harp, guitar, piano, etc.) strings have a fundamental resonant frequency directly related to the length and tension of the string. The wavelength that will create the first resonance on the string is equal to twice the length of the string. This frequency is related to the speed v of a wave traveling down the string by the equation

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:f = {v over 2L}

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where L is the length of the string (for a string fixed at both ends). The speed of a wave through a string or wire is related to its tension T and the mass per unit length ρ:

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:v = sqrt {T over ho}

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So the frequency is related to the properties of the string by the equation

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:f = {sqrt {T over ho} over 2 L} = {sqrt {T over m / L} over 2 L}

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where T is the tension, ρ is the mass per unit length, and m is the total mass.

Related Topics:
Tension - Mass

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Higher tension and shorter lengths increase the resonant frequency, and vice versa. The string also has a resonance at integer multiples of the fundamental frequency f. It will then also resonate at 2f, 3f, 4f, and so on. When the string is excited with an impulsive function (a finger pluck or a strike by a hammer), the string vibrates at all the frequencies present in the impulse (an impulsive function theoretically contains 'all' frequencies). Those frequencies that are not one of the resonances are quickly filtered out—they are attenuated—and all that is left is the harmonic vibrations that we hear as a musical note.

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• Resonance of a tube of air.

The resonance of a tube of air is related to the length of the tube and whether it has closed or open ends. When a wave reaches the end of the tube, part of it will be reflected back into the tube, and part will be transmitted to the outside air. An open end will reflect a wave with no inversion; in other words, a compression wave will be reflected as a compression wave. A closed end will invert the wave that is reflected; in other words, a compression wave will be reflected as a rarefaction wave. Examples of instruments that have both ends open are the flute, saxophone, oboe, and trombone. An example of an instrument that has one closed end and one open end is the clarinet. Vibrating air columns also have resonances at harmonics, like strings. Tubes with both ends open resonate at the frequency

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:f = {v over 2L}

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This is similar to the string formula, except v now becomes the speed of sound in air (which is approximately 340 meters per second at sea level).

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Note however that in practise the exact point at which a sound wave is reflecting at an open end is not perfectly at the end section of the tube. The wave in fact progresses over a small distance outside the tube and the reflection ratio is also not perfectly equal to one. This phenomena is caused by the fact that the open end does not behave like an infinite acoustical impedance. It has a finite value, called radiation impedance, which is dependent on the diameter of the tube, the wavelength and the type of reflection board possibly present around the opening of the tube.

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A tube with one end closed will have a resonance of

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:f = {v over 4L}

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This type of tube can only produce odd harmonics, f, 3f, 5f, and so on.

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Composers have begun to make resonance the subject of compositions. Alvin Lucier has used acoustic instruments and sine wave generators to explore the resonance of objects large and small in many of his compositions. The complex inharmonic partials of a swell shaped crescendo and decrescendo on a tam tam or other percussion instrument interact with room resonances in James Tenney's Koan: Having Never Written A Note For Percussion. Pauline Oliveros and Stuart Dempster regularly perform in large reverberant spaces such as the two million gallon cistern at Fort Warden, WA, which has a reverb with a 45 second decay.

Related Topics:
Alvin Lucier - Inharmonic - Partial - Crescendo - Tam tam - James Tenney - Pauline Oliveros - Stuart Dempster - Reverberant - Reverb

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