Acoustic resonance - Citizendia

Acoustic resonance is the tendency of an acoustic system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency) than it does at other frequencies. Acoustics is the interdisciplinary science that deals with the study of Sound, Ultrasound and Infrasound (all mechanical waves in gases liquids and solids Frequency is a measure of the number of occurrences of a repeating event per unit Time. In Physics, resonance is the tendency of a system to Oscillate at maximum Amplitude at certain frequencies, known as the system's

A resonant object will probably have more than one resonance frequency, especially at harmonics of the strongest resonance. It will easily vibrate at those frequencies, and vibrate less strongly at other frequencies. It will "pick out" its resonance frequency from a complex excitation, such as an impulse or a wideband noise excitation. In effect, it is filtering out all frequencies other than its resonance.

Acoustic 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. A musical instrument is a device constructed or modified for the purpose of making Music. A resonator is a device or system that exhibits Resonance or resonant behavior that is it naturally oscillates at some frequencies, called its resonance The violin is a bowed String instrument with four strings usually tuned in Perfect fifths It is the smallest and highest-pitched member The flute is a Musical instrument of the Woodwind family Unlike other woodwind instruments a flute is a Reedless wind instrument that produces its

1 Resonance of a string
- 1.1 String resonance in music instruments
2 Resonance of a tube of air
- 2.1 Cylinders
3 Open
4 Closed
- 4.1 Cones
- 4.2 Rectangular box
5 Resonance in musical composition
6 References
7 See also

Resonance of a string

Strings under tension, as in instruments such as lutes, harps, guitars, pianos, violins and so forth, have resonant frequencies directly related to the mass, length, and tension of the string. Lute can refer generally to any plucked string instrument with a neck (either Fretted or unfretted and a deep round back or more specifically to an instrument from The harp is a Stringed instrument which has the plane of its strings positioned perpendicular to the soundboard. The guitar is a Musical instrument with ancient roots that is used in a wide variety of musical styles The piano is a Musical instrument played by means of a keyboard that produces sound by striking steel strings with Felt covered hammers The violin is a bowed String instrument with four strings usually tuned in Perfect fifths It is the smallest and highest-pitched member In Physics, resonance is the tendency of a system to Oscillate at maximum Amplitude at certain frequencies, known as the system's The wavelength that will create the first resonance on the string is equal to twice the length of the string. Higher resonances correspond to wavelengths that are integer divisions of the fundamental wavelength. The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. The corresponding frequencies are related to the speed v of a wave traveling down the string by the equation

$f = {nv \over 2L}$

where L is the length of the string (for a string fixed at both ends) and n = 1, 2, 3. . . The speed of a wave through a string or wire is related to its tension T and the mass per unit length ρ:

$v = \sqrt {T \over \rho}$

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

$f = {n\sqrt {T \over \rho} \over 2 L} = {n\sqrt {T \over m / L} \over 2 L}$

where T is the tension, ρ is the mass per unit length, and m is the total mass. In Physics String Tension is the magnitude of the pulling force exerted by a string cable chain or similar object on another object Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object

Higher tension and shorter lengths increase the resonant frequencies. 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.

String resonance in music instruments

Main article: String resonance (music)

String resonance occurs on string instruments. String resonance occurs on String instruments. Strings or parts of strings may resonate at their Fundamental or Overtone frequencies when other strings String resonance occurs on String instruments. Strings or parts of strings may resonate at their Fundamental or Overtone frequencies when other strings A string instrument (or stringed instrument) is a Musical instrument that produces Sound by means of Vibrating strings In the Hornbostel-Sachs Strings or parts of strings may resonate at their fundamental or overtone frequencies when other strings are sounded. An overtone is a natural resonance or vibration frequency of a system For example, an A string at 440 Hz will cause an E string at 330 Hz to resonate, because they share an overtone of 1320 Hz (3rd overtone of A and 4th overtone of E).

Resonance of a tube of air

The resonance of a tube of air is related to the length of the tube, its shape, and whether it has closed or open ends. Musically useful tube shapes are conical and cylindrical (see bore). The bore of a Wind instrument is its interior chamber that defines a flow path through which air travels and is set into vibration to produce sounds A pipe that is closed at one end is said to be stopped while an open pipe is open at both ends. Modern orchestral flutes behave as open cylindrical pipes; clarinets and lip-reed instruments (brass instruments) behave as closed cylindrical pipes; and saxophones, oboes, and bassoons as closed conical pipes. The flute is a Musical instrument of the Woodwind family Unlike other woodwind instruments a flute is a Reedless wind instrument that produces its The clarinet is a Musical instrument in the Woodwind family The name derives from adding the suffix -et meaning little to the Italian word A brass instrument is a Musical instrument whose tone is produced by vibration of the lips as the player blows into a tubular Resonator. The saxophone (commonly referred to simply as sax) is a conical- bored transposing Musical instrument considered a member of the Woodwind "Hautbois" redirects here for the strawberry variety see Hautbois strawberry. The bassoon is a Woodwind instrument in the Double reed family that typically plays music written in the bass and Tenor registers and occasionally Vibrating air columns also have resonances at harmonics, like strings.

Cylinders

By convention a rigid cylinder that is open at both ends is referred to as an "open" cylinder; whereas, a rigid cylinder that is open at one end and has a rigid surface at the other end is referred to as a "closed" cylinder.

The first three resonances in an open cylindrical tube. The horizontal axis is pressure.

The first three resonances in a closed cylindrical tube. The horizontal axis is pressure.

Open

Open cylindrical tubes resonate at the approximate frequencies

$f = {nv \over 2L}$

where n is a positive integer (1, 2, 3. . . ) representing the resonance mode, L is th the length of the tube and v is the speed of sound in air (which is approximately 344 meters per second at 20 °C and at sea level). Sound is a vibration that travels through an elastic medium as a Wave.

A more accurate equation considering an end correction is given below:

$f = {nv \over 2(L+0.8d)}$

where d is the diameter of the resonance tube. A theoretical basis for computation of the end correction is the radiation Acoustic impedance of a circular Piston. This equation compensates for the fact that the exact point at which a sound wave is reflecting at an open end is not perfectly at the end section of the tube, but a small distance outside the tube.

The reflection ratio is slightly less than 1; the open end does not behave like an infinite acoustic impedance; rather, 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. The acoustic impedance Z (or sound impedance) is a frequency f dependent parameter and is very useful for example for describing the behaviour of musical

Closed

A closed cylinder will have approximate resonances of

$f = {nv \over 4L}$

where "n" here is an odd number (1, 3, 5. . . ). This type of tube produces only odd harmonics and has its fundamental frequency an octave lower than that of an open cylinder (that is, half the frequency).

A more accurate equation is given below:

$f = {nv \over 4(L+0.4d)}$ .

Cones

An open conical tube, that is, one in the shape of a frustum of a cone with both ends open, will have resonant frequencies approximately equal to those of an open cylindrical pipe of the same length. Elements special cases and related concepts Each plane section is a base of the frustum

The resonant frequencies of a stopped conical tube — a complete cone or frustum with one end closed — satisfy a more complicated condition:

k L = n π - tan - 1 k x

where the wavenumber k is

k = 2π f / v

and x is the distance from the small end of the frustum to the vertex. Wavenumber in most physical sciences is a Wave property inversely related to Wavelength, having SI units of reciprocal meters When x is small, that is, when the cone is nearly complete, this becomes

$k(L+x) \approx n\pi$

leading to resonant frequencies approximately equal to those of an open cylinder whose length equals L + x. In words, a complete conical pipe behaves approximately like an open cylindrical pipe of the same length, and to first order the behavior does not change if the complete cone is replaced by a closed frustum of that cone.

Rectangular box

For a rectangular box, the resonant frequencies are given by

$f = {v \over 2} \sqrt{\left({\ell \over L_x}\right)^2 + \left({m \over L_y}\right)^2 + \left({n \over L_z}\right)^2}$

where v is the speed of sound, L_x and L_y and L_z are the dimensions of the box, and $\scriptstyle\ell,$ n, and m are the nonnegative integers. However, $\scriptstyle\ell$ , n, and m cannot all be zero.

Resonance in musical composition

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. Alvin Lucier (born May 14, 1931) is an American Composer of Experimental music and Sound installations that explore acoustic phenomena 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. In music inharmonicity is the degree to which the frequencies of Overtones (known as partials partial tones or Harmonics depart from whole James Tenney ( August 10, 1934 - August 24, 2006) was an American Composer and influential music theorist. 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. Pauline Oliveros (born May 30, 1932 in Houston Texas) is an Accordionist and Composer who currently resides in Kingston New Stuart Dempster (born July 7, 1936 in Berkeley California) is a Trombonist, Didjeridu player improvisor Composer, author Reverberation is the persistence of Sound in a particular space after the original sound is removed Reverberation is the persistence of Sound in a particular space after the original sound is removed

References

Nederveen, Cornelis Johannes, Acoustical aspects of woodwind instruments. Amsterdam, Frits Knuf, 1969.
Rossing, Thomas D. , and Fletcher, Neville H. , Principles of Vibration and Sound. New York, Springer-Verlag, 1995.

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