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| [[Image:Tuning fork on resonator.jpg|thumb|right|250px|Tuning fork on resonance box, by Max Kohl, Chemnitz, Germany]]
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| A '''tuning fork''' is an [[Musical acoustics|acoustic]] [[resonator]] in the form of a two-pronged [[fork]] with the prongs ([[Tine (structural)|tines]]) formed from a U-shaped bar of [[Elastic deformation|elastic]] metal (usually [[steel]]). It [[resonance|resonates]] at a specific constant [[pitch (music)|pitch]] when set vibrating by striking it against a surface or with an object, and emits a pure musical tone after waiting a moment to allow some high [[overtones]] to die out. The pitch that a particular tuning fork generates depends on the length and mass of the two prongs. It is frequently used as a standard of pitch to tune musical instruments.
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| The tuning fork was invented in 1711 by British musician [[John Shore (trumpeter)|John Shore]], Sergeant [[Trumpet]]er and [[Lute]]nist to the court.<ref>{{cite journal |pmid=9172630 |year=1997 |last1=Feldmann |first1=H |title=History of the tuning fork. I: Invention of the tuning fork, its course in music and natural sciences. Pictures from the history of otorhinolaryngology, presented by instruments from the collection of the Ingolstadt German Medical History Museum |volume=76 |issue=2 |pages=116–22 |doi=10.1055/s-2007-997398 |journal=Laryngo- rhino- otologie}}</ref>
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| ==Description==
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| [[Image:TuningFork659Hz.jpg|thumb|Tuning fork by John Walker stamped with note (E) and frequency in hertz (659)]]
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| [[Image:Tuning fork on carbon black.jpg|thumb|A needle on a tuning fork carves figures on carbon black.]]
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| The main reason for using the fork shape is that, unlike many other types of resonators, it produces a very [[pure tone]], with most of the vibrational energy at the [[fundamental frequency]], and little at the [[overtone]]s ([[harmonic]]s). The reason for this is that the frequency of the first overtone is about 5<sup>2</sup>/2<sup>2</sup> = 25/4 = 6¼ times the fundamental (about 2½ octaves above it).<ref>{{cite book
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| | last = Tyndall
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| | first = John
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| | authorlink =
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| | coauthors =
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| | title = Sound
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| | publisher = D. Appleton & Co.
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| | year = 1915
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| | location = New York
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| | page = 156
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| | url = http://books.google.com/books?id=hCgZAAAAYAAJ&pg=PA156
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| | doi =
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| | id =
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| | isbn = }}</ref> By comparison, the first overtone of a vibrating string or metal bar is only one octave above the fundamental. So when the fork is struck, little of the energy goes into the overtone modes; they also die out correspondingly faster, leaving the fundamental. It is easier to tune other instruments with this pure tone.
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| Another reason for using the fork shape is that, when it vibrates in its principal mode, the handle vibrates up and down as the prongs move apart and together. There is a [[node (physics)|node]] (point of no vibration) at the base of each prong. The handle motion is small, allowing the fork to be held by the handle without damping the vibration, but it allows the handle to transmit the vibration to a [[resonator]], which amplifies the sound of the fork.<ref>The Science of Sound, 3rd ed., Rossing, Moore, and Wheeler</ref> The fork is usually struck, and then the handle is pressed against a wooden box resonator, or a table top. Without the resonator the sound is very faint. The reason for this is that the sound waves produced by each fork prong are 180° out of [[phase (waves)|phase]] with the other, so at a distance from the fork they [[Interference (wave motion)|interfere]] and largely cancel each other out. If a sound absorbing sheet is slid in between the prongs of a vibrating fork, reducing the waves reaching the ear from one prong, the volume heard will actually increase, due to a reduction of this cancellation.
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| Although commercial tuning forks are normally tuned to the correct pitch at the factory, they can be retuned by filing material off the prongs. Filing the ends of the prongs raises the pitch, while filing the inside of the base of the prongs lowers it.
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| Currently, the most common tuning fork sounds the note of [[A440 (pitch standard)|A = 440 Hz]], because this is the standard [[concert pitch]], which is used as tuning note by some orchestras, it being the pitch of the violin's second string, the first string of the viola, and an octave above the first string of the cello, all played open. Tuning forks used by orchestras between 1750 and 1820 mostly had a frequency of A = 423.5 Hz, although there were many forks and many slightly different pitches.<ref>The Physics of Musical Instruments [http://www.amazon.com/dp/0387983740/ amazon.com]{{Page needed|date=January 2012}}</ref> Standard tuning forks are available that vibrate at all the musical pitches within the central octave of the piano, and other pitches. Well-known manufacturers of tuning forks include Ragg and John Walker, both of [[Sheffield]], [[England]].
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| The pitch of a tuning fork can vary slightly with weathering and temperature. A change in frequency of one vibration in 21,000 for each °F (86 ppm per °C) change is typical for a steel tuning fork, flattened by heat and sharpened by cold.<ref>[http://books.google.com/books?id=xqU9AQAAIAAJ&pg=PA297#v=onepage&q&f=false Journal of the Society of Arts, Vol. 28], p. 297</ref> The [[Standard conditions for temperature and pressure|standard temperature]] is now 68 °F (20 °C) but 59 °F (15 °C) is an older standard. The pitches of a musical instrument such as an organ are also subject to variation with temperature change.
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| ==Calculation of frequency==
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| The frequency of a tuning fork depends on its dimensions and the material from which it is made:<ref>{{cite journal |doi=10.1006/jsvi.1999.2257 |title=Dynamics of Transversely Vibrating Beams Using Four Engineering Theories |year=1999 |last1=Han |first1=Seon M. |last2=Benaroya |first2=Haym |last3=Wei |first3=Timothy |journal=Journal of Sound and Vibration |volume=225 |issue=5 |pages=935}}</ref>
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| :<math>f = \frac{1.875^2}{2\pi l^2} \sqrt\frac{EI}{\rho A}</math> | |
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| Where:
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| * ''f'' is the [[frequency]] the fork vibrates at in [[Hertz]].
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| * 1.875 the smallest positive solution of cos(''x'')cosh(''x'') = -1.<ref>{{cite web
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| | url=http://emweb.unl.edu/Mechanics-Pages/Scott-Whitney/325hweb/Beams.htm
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| | title=Vibrations of Cantilever Beams: Deflection, Frequency, and Research Uses
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| | last=Whitney
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| | first=Scott
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| | publisher=University of Nebraska–Lincoln
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| | date=1999-04-23
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| | accessdate=2011-11-09 }}</ref>
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| * ''l'' is the length of the prongs in metres.
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| * ''E'' is the [[Young's modulus]] of the material the fork is made from in [[Pascal (unit)|pascal]]s.
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| * ''I'' is the [[second moment of area]] of the cross-section in metres to the fourth power.
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| * ''ρ'' is the [[density]] of the material the fork is made from in [[kilogramme]]s per cubic metre.
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| * ''A'' is the cross-sectional [[area]] of the prongs (tines) in square metres.
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| The ratio <math>\frac{I}{A}</math> in the equation above can be rewritten as
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| <math>r^2/4</math> if the prongs are cylindrical of radius ''r'', and
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| <math>a^2/12</math> if the prongs have rectangular cross-section of width ''a'' along the direction of motion.
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| ==Uses==
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| [[Image:Accutron.jpg|thumb|A [[Bulova]] Accutron watch from the 1960s, which uses a steel tuning fork ''(visible in center)'' vibrating at 360 Hz.]]
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| Forks have traditionally been used to [[Musical tuning|tune]] [[musical instrument]]s, although [[electronic tuner]]s are replacing them in many applications. Tuning forks can be driven electrically, by placing [[electromagnet]]s close to the prongs that are attached to an [[electronic oscillator]] circuit, so that their sound does not die out.
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| ===In musical instruments===
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| A number of [[keyboard instrument|keyboard]] musical instruments using constructions similar to tuning forks have been made, the most popular of them being the [[Rhodes piano]], which has hammers hitting constructions working on the same principle as tuning forks and uses electric amplification of the generated sound. The earlier, unamplified [[dulcitone]] used tuning forks directly; it suffered from faintness of volume.
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| [[File:Inside QuartzCrystal-Tuningfork.jpg|thumb|right|Quartz crystal resonator from a modern [[quartz watch]], formed in the shape of a tuning fork. It vibrates at 32,768 Hz in the [[ultrasound|ultrasonic]] range.]]
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| ===In clocks and watches===
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| The [[crystal oscillator|quartz crystal]] that serves as the timekeeping element in modern [[quartz clock]]s and [[watch]]es ''(right)'' is in the form of a tiny tuning fork. It usually vibrates at a frequency of 32,768 Hz in the [[ultrasound|ultrasonic]] range, above the range of human hearing. It is made to vibrate by small oscillating voltages applied to metal electrodes plated on the surface of the crystal, by an [[electronic oscillator]] circuit. Quartz is [[piezoelectric]], so the voltage causes the fork tines to bend rapidly back and forth.
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| The [[Accutron]] ''(right)'', an [[Electromechanical watches|electromechanical watch]] developed by Max Hetzel and manufactured by [[Bulova]] beginning in 1960, used a 360 [[hertz]] steel tuning fork as its timekeeper, powered by electromagnets attached to a battery-powered transistor oscillator circuit. The fork allowed it to achieve greater accuracy than conventional balance wheel watches. The humming sound of the tuning fork could be heard when the watch was held to the ear.
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| ===Medical and scientific uses===
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| [[Image:Tuning fork oscillator frequency standard.jpg|thumb|1 kHz tuning fork [[vacuum tube]] [[electronic oscillator|oscillator]] used by the U.S. National Bureau of Standards (now [[National Institute of Standards and Technology|NIST]]) in 1927 as a frequency standard.]]
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| An alternative to the usual A440 diatonic scale is that of [[Concert pitch#19th and 20th century standards|philosophical or scientific pitch]] with standard pitch of C512. According to [[John William Strutt, 3rd Baron Rayleigh|Rayleigh]], the scale was used by physicists and acoustic instrument makers.<ref>{{cite book|last=Rayleigh|first=J.W.S.|title=The Theory of Sound|year=1945|publisher=Dover|location=New York|isbn=0-486-60292-3|page=9}}</ref> The tuning fork that John Shore gave to Handel gives a pitch of C512.<ref>[http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1291142/pdf/jrsocmed00168-0057.pdf The origin of the tuning fork - nih]</ref>
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| Tuning forks, usually C512, are used by medical practitioners to assess a patient's hearing. Lower-pitched ones (usually C128) are also used to check vibration sense as part of the examination of the peripheral nervous system. For the Weber and Rinne test, the C128 ''with weight ''(emphasis added) is the absolute gold standard and only workable one for a realistic W and R test in the clinical setting. This is true despite Youtube videos erroneously showing the use of other tuning forks. This frequency is also used by EMT's and Paramedics to locate fractures in bone.
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| Tuning forks also play a role in several [[alternative medicine]] modalities, such as [[sonopuncture]] and [[polarity therapy]].
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| === Radar gun calibration ===
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| A [[radar gun]], typically used for measuring the speed of cars or balls in sports, is usually calibrated with tuning forks.<ref>[http://tf.nist.gov/timefreq/general/pdf/87.pdf Calibration of Police Radar Instruments, National Bureau of Standards, 1976]</ref><ref>{{cite web
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| | last =
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| | first =
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| | authorlink =
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| | coauthors =
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| | title = A detailed explanation of how police radars work
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| | work = Radars.com.au
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| | publisher = TCG Industrial, Perth, Australia
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| | year = 2009
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| | url = http://radars.com.au/police-radar.php
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| | format =
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| | doi =
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| | accessdate = 2010-04-08}}</ref>
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| Instead of the frequency, these forks are labeled with the calibration speed and radar band (e.g. X-Band or K-Band) for which they are calibrated.
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| ===In gyroscopes===
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| Doubled and H-type of tuning forks are used for tactical-grade [[Vibrating structure gyroscope#Tuning fork gyroscope|Vibrating Structure Gyroscopes]] like QuapasonTM and different types of MEMS.<ref>Proceedings of Anniversary Workshop on Solid-State Gyroscopy (19–21 May 2008. Yalta, Ukraine). - Kyiv-Kharkiv. ATS of Ukraine. 2009. - ISBN 978-976-0-25248-6 {{Please check ISBN|reason=Check digit (6) does not correspond to calculated figure.}}.</ref>
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| == See also ==
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| * [[Electronic tuner]]
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| * [[Pitch pipe]]
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| * [[Weber test]]
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| * [[Rinne test]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| {{Commons category|Tuning forks}}
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| *[http://www.onlinetuningfork.com/ Onlinetuningfork.com], an online tuning fork using [[Macromedia]] [[Flash Player]].
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| *[http://www.usneurologicals.com/ Usneurologicals.com], numerous examples of medical uses of tuning forks.
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| {{Use dmy dates|date=March 2011}}
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| {{DEFAULTSORT:Tuning Fork}}
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| [[Category:1711 introductions]]
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| [[Category:Musical instrument parts and accessories]]
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| [[Category:Idiophones]]
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