Tuning fork

Atuning forkis anacoustic resonatorin the form of a two-prongedforkwith the prongs (tines) formed from a U-shaped bar ofelasticmetal (usuallysteel). Itresonatesat a specific constantpitchwhen set vibrating by striking it against a surface or with an object, and emits a pure musical tone once the highovertonesfade out. A tuning fork's pitch depends on the length and mass of the two prongs. They are traditional sources of standard pitch fortuningmusical instruments.

The tuning fork was invented in 1711 by British musicianJohn Shore,sergeanttrumpeterandlutenistto the royal court.^[1]

Description[edit]

A tuning fork is a fork-shapedacoustic resonatorused in many applications to produce a fixed tone. The main reason for using the fork shape is that, unlike many other types of resonators, it produces a verypure tone,with most of the vibrational energy at thefundamental frequency.The reason for this is that the frequency of the first overtone is about⁠5²/2²⁠=⁠25/4⁠=6+1⁄4times the fundamental (about2+1⁄2octaves above it).^[2]By comparison, the first overtone of a vibrating string or metal bar is one octave above (twice) the fundamental, so when the string is plucked or the bar is struck, its vibrations tend to mix the fundamental and overtone frequencies. When the tuning fork is struck, little of the energy goes into the overtone modes; they also die out correspondingly faster, leaving a pure sine wave at the fundamental frequency. It is easier to tune other instruments with this pure tone.

Another reason for using the fork shape is that it can then be held at the base withoutdampingthe oscillation. That is because its principalmodeof vibration is symmetric, with the two prongs always moving in opposite directions, so that at the base where the two prongs meet there is anode(point of no vibratory motion) which can therefore be handled without removing energy from the oscillation (damping). However, there is still a tiny motion induced in the handle in its longitudinal direction (thus at right angles to the oscillation of the prongs) which can be made audible using any sort ofsound board.Thus by pressing the tuning fork's base against a sound board such as a wooden box, table top, or bridge of a musical instrument, this small motion, but which is at a highacoustic pressure(thus a very highacoustic impedance), is partly converted into audible sound in air which involves a much greater motion (particle velocity) at a relatively low pressure (thus low acoustic impedance).^[3]The pitch of a tuning fork can also be heard directly throughbone conduction,by pressing the tuning fork against the bone just behind the ear, or even by holding the stem of the fork in one's teeth, conveniently leaving both hands free.^[4]Bone conduction using a tuning fork is specifically used in theWeberandRinne testsfor hearing in order to bypass themiddle ear.If just held in open air, the sound of a tuning fork is very faint due to the acousticimpedance mismatchbetween the steel and air. Moreover, since the feeble sound waves emanating from each prong are 180° out ofphase,those two opposite wavesinterfere,largely cancelling each other. Thus when a solid sheet is slid in between the prongs of a vibrating fork, the apparent volume actuallyincreases,as this cancellation is reduced, just as a loudspeaker requires abafflein order to radiate efficiently.

Commercial tuning forks are tuned to the correct pitch at the factory, and the pitch and frequency in hertz is stamped on them. 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.

Currently, the most common tuning fork sounds the note ofA = 440 Hz,the standardconcert pitchthat many orchestras use. That A is the pitch of the violin's second-highest string, the highest string of the viola, and an octave above the highest string of the cello. Orchestras between 1750 and 1820 mostly used A = 423.5 Hz, though there were many forks and many slightly different pitches.^[5]Standard tuning forks are available that vibrate at all the pitches within the central octave of the piano, and also other pitches.

Tuning fork pitch varies slightly with temperature, due mainly to a slight decrease in themodulus of elasticityof steel with increasing temperature. A change in frequency of 48 parts per million per °F (86 ppm per °C) is typical for a steel tuning fork. The frequency decreases (becomesflat) with increasing temperature.^[6]Tuning forks are manufactured to have their correct pitch at a standard temperature. Thestandard temperatureis now 20 °C (68 °F), but 15 °C (59 °F) is an older standard. The pitch of other instruments is also subject to variation with temperature change.

Calculation of frequency[edit]

The frequency of a tuning fork depends on its dimensions and what it is made from:^[7]

f={\frac {N}{2\pi L^{2}}}{\sqrt {\frac {EI}{\rho A}}},

where

f

is thefrequencythe fork vibrates at, (SI units:1/s)

N

≈ 3.516015 is the square of the smallest positive solution to

cos (x) cosh (x) = -1

,^[8]which arises from the boundary conditions of the prong’s cantilevered structure.

L

is the length of the prongs, (m)

E

is theYoung's modulus(elastic modulus or stiffness) of the material the fork is made from, (Pa or N/m²or kg/(ms²))

I

is thesecond moment of areaof the cross-section, (m⁴)

ρ

is thedensityof the fork's material (kg/m³), and

A

is the cross-sectionalareaof the prongs (tines) (m²).

The ratio $I / A$ in the equation above can be rewritten as $r 2 /4$ if the prongs are cylindrical with radius $r$ ,and $a 2 /12$ if the prongs have rectangular cross-section of width $a$ along the direction of motion.

Uses[edit]

Tuning forks have traditionally been used totune musical instruments,thoughelectronic tunershave largely replaced them. Forks can be driven electrically by placingelectronic oscillator-drivenelectromagnetsclose to the prongs.

In musical instruments[edit]

A number ofkeyboardmusical instruments use principles similar to tuning forks. The most popular of these is theRhodes piano,in which hammers hit metal tines that vibrate in the magnetic field of apickup,creating a signal that drives electric amplification. The earlier, un-amplifieddulcitone,which used tuning forks directly, suffered from low volume.

In clocks and watches[edit]

ABulovaAccutron watch from the 1960s, which uses a steel tuning fork(visible in center)vibrating at 360 Hz.

Thequartz crystalthat serves as the timekeeping element in modernquartz clocksandwatchesis in the form of a tiny tuning fork. It usually vibrates at a frequency of 32,768 Hz in theultrasonicrange (above the range of human hearing). It is made to vibrate by small oscillating voltages applied by anelectronic oscillatorcircuit to metal electrodes plated on the surface of the crystal. Quartz ispiezoelectric,so the voltage causes the tines to bend rapidly back and forth.

TheAccutron,anelectromechanical watchdeveloped by Max Hetzel^[9]and manufactured byBulovabeginning in 1960, used a 360-hertzsteel tuning fork as its timekeeper, powered by electromagnets attached to a battery-powered transistor oscillator circuit. The fork provided greater accuracy than conventional balance wheel watches. The humming sound of the tuning fork was audible when the watch was held to the ear.

Medical and scientific uses[edit]

Alternatives to the common A=440 standard includephilosophical or scientific pitchwith standard pitch of C=512. According toRayleigh,physicists and acoustic instrument makers used this pitch.^[10]The tuning forkJohn Shoregave toGeorge Frideric Handelproduces C=512.^[11]

Tuning forks, usually C512, are used by medical practitioners to assess a patient's hearing. This is most commonly done with two exams called theWeber testandRinne test,respectively. Lower-pitched ones, usually at C128, are also used to check vibration sense as part of the examination of the peripheral nervous system.^[12]

Orthopedic surgeonshave explored using a tuning fork (lowest frequency C=128) to assess injuries where bone fracture is suspected. They hold the end of the vibrating fork on the skin above the suspected fracture, progressively closer to the suspected fracture. If there is a fracture, theperiosteumof the bone vibrates and firesnociceptors(pain receptors), causing a local sharp pain.^{[citation needed]}This can indicate a fracture, which the practitioner refers for medical X-ray. The sharp pain of a local sprain can give a false positive.^{[citation needed]}Established practice, however, requires an X-ray regardless, because it's better than missing a real fracture while wondering if a response means a sprain. A systematic review published in 2014 inBMJ Opensuggests that this technique is not reliable or accurate enough for clinical use.^[13]

Non-medical and non-scientific uses[edit]

Tuning forks also play a role in severalalternative therapypractices, such assonopunctureandpolarity therapy.^[14]

Radar gun calibration[edit]

Aradar gunthat measures the speed of cars or a ball in sports is usually calibrated with a tuning fork.^[15]^[16]Instead of the frequency, these forks are labeled with the calibration speed and radar band (e.g., X-band or K-band) they are calibrated for.

In gyroscopes[edit]

Doubled and H-type tuning forks are used for tactical-gradeVibrating Structure Gyroscopesand various types ofmicroelectromechanical systems.^[17]

Level sensors[edit]

Tuning fork forms the sensing part of vibratingpoint level sensors.The tuning fork is kept vibrating at its resonant frequency by a piezoelectric device. Upon coming in contact with solids, amplitude of oscillation goes down, the same is used as a switching parameter for detecting point level for solids.^[18]For liquids, the resonant frequency of tuning fork changes upon coming in contact with the liquids, change in frequency is used to detect level.

References[edit]

^Feldmann, H. (1997). "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".Laryngo-rhino-otologie.76(2): 116–22.doi:10.1055/s-2007-997398.PMID 9172630.
^Tyndall, John (1915).Sound.New York: D. Appleton & Co. p. 156.
^Rossing, Thomas D.; Moore, F. Richard; Wheeler, Paul A. (2001).The Science of Sound(3rd ed.). Pearson.ISBN 978-0805385656.^{[page needed]}
^Dan Fox (1996).Teach Yourself to Play Mandolin.Alfred Music Publishing.ISBN 9780739002865.Retrieved3 July2015.
^Fletcher, Neville H.; Rossing, Thomas (2008).The Physics of Musical Instruments(2nd ed.). Springer.ISBN 978-0387983745.^{[page needed]}
^Ellis, Alexander J. (1880)."On the History of Musical Pitch".Journal of the Society of Arts.28(545): 293–336.Bibcode:1880Natur..21..550E.doi:10.1038/021550a0.
^Han, Seon M.; Benaroya, Haym; Wei, Timothy (1999). "Dynamics of Transversely Vibrating Beams Using Four Engineering Theories".Journal of Sound and Vibration.225(5): 935–988.Bibcode:1999JSV...225..935H.doi:10.1006/jsvi.1999.2257.S2CID 121014931.
^Whitney, Scott (23 April 1999)."Vibrations of Cantilever Beams: Deflection, Frequency, and Research Uses".University of Nebraska–Lincoln.Retrieved9 November2011.
^ch 312290
^Rayleigh, J. W. S. (1945).The Theory of Sound.New York: Dover. p.9.ISBN 0-486-60292-3.
^Bickerton, RC; Barr, GS (December 1987)."The origin of the tuning fork".Journal of the Royal Society of Medicine.80(12): 771–773.doi:10.1177/014107688708001215.PMC1291142.PMID 3323515.
^Bickley, Lynn; Szilagyi, Peter (2009).Bates' guide to the physical examination and history taking(10th ed.). Philadelphia, PA: Lippincott Williams & Wilkins.ISBN 978-0-7817-8058-2.
^Mugunthan, Kayalvili; Doust, Jenny; Kurz, Bodo; Glasziou, Paul (4 August 2014)."Is there sufficient evidence for tuning fork tests in diagnosing fractures? A systematic review".BMJ Open.4(8): e005238.doi:10.1136/bmjopen-2014-005238.PMC4127942.PMID 25091014.
^Hawkins, Heidi (August 1995). "SONOPUNCTURE: Acupuncture Without Needles".Holistic Health News.
^"Calibration of Police Radar Instruments"(PDF).National Bureau of Standards. 1976. Archived fromthe original(PDF)on 22 February 2012.Retrieved29 October2008.
^"A detailed explanation of how police radars work".Radars.au.Perth, Australia: TCG Industrial. 2009.Retrieved8 April2010.
^Proceedings of Anniversary Workshop on Solid-State Gyroscopy (19–21 May 2008. Yalta, Ukraine).Kyiv/Kharkiv: ATS of Ukraine. 2009.ISBN 978-976-0-25248-5.
^"Vital- Vibrating Fork Level Switch for Solids".Sapcon Instruments.Retrieved28 May2023.

External links[edit]

Onlinetuningfork,an online tuning fork usingMacromedia Flash Player.
"Tuning Fork".Collier's New Encyclopedia.1921.
"Tuning Fork".Encyclopædia Britannica.Vol. 27 (11th ed.). 1911. p. 392.

[1] Feldmann, H. (1997). "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".Laryngo-rhino-otologie.76(2): 116–22.doi:10.1055/s-2007-997398.PMID 9172630.

[2] Tyndall, John (1915).Sound.New York: D. Appleton & Co. p. 156.

[3] Rossing, Thomas D.; Moore, F. Richard; Wheeler, Paul A. (2001).The Science of Sound(3rd ed.). Pearson.ISBN 978-0805385656.^{[page needed]}

[4] Dan Fox (1996).Teach Yourself to Play Mandolin.Alfred Music Publishing.ISBN 9780739002865.Retrieved3 July2015.

[5] Fletcher, Neville H.; Rossing, Thomas (2008).The Physics of Musical Instruments(2nd ed.). Springer.ISBN 978-0387983745.^{[page needed]}

[6] Ellis, Alexander J. (1880)."On the History of Musical Pitch".Journal of the Society of Arts.28(545): 293–336.Bibcode:1880Natur..21..550E.doi:10.1038/021550a0.

[7] Han, Seon M.; Benaroya, Haym; Wei, Timothy (1999). "Dynamics of Transversely Vibrating Beams Using Four Engineering Theories".Journal of Sound and Vibration.225(5): 935–988.Bibcode:1999JSV...225..935H.doi:10.1006/jsvi.1999.2257.S2CID 121014931.

[8] Whitney, Scott (23 April 1999)."Vibrations of Cantilever Beams: Deflection, Frequency, and Research Uses".University of Nebraska–Lincoln.Retrieved9 November2011.

[9] 312290

[10] Rayleigh, J. W. S. (1945).The Theory of Sound.New York: Dover. p.9.ISBN 0-486-60292-3.

[11] Bickerton, RC; Barr, GS (December 1987)."The origin of the tuning fork".Journal of the Royal Society of Medicine.80(12): 771–773.doi:10.1177/014107688708001215.PMC1291142.PMID 3323515.

[12] Bickley, Lynn; Szilagyi, Peter (2009).Bates' guide to the physical examination and history taking(10th ed.). Philadelphia, PA: Lippincott Williams & Wilkins.ISBN 978-0-7817-8058-2.

[13] Mugunthan, Kayalvili; Doust, Jenny; Kurz, Bodo; Glasziou, Paul (4 August 2014)."Is there sufficient evidence for tuning fork tests in diagnosing fractures? A systematic review".BMJ Open.4(8): e005238.doi:10.1136/bmjopen-2014-005238.PMC4127942.PMID 25091014.

[14] Hawkins, Heidi (August 1995). "SONOPUNCTURE: Acupuncture Without Needles".Holistic Health News.

[15] "Calibration of Police Radar Instruments"(PDF).National Bureau of Standards. 1976. Archived fromthe original(PDF)on 22 February 2012.Retrieved29 October2008.

[16] "A detailed explanation of how police radars work".Radars.au.Perth, Australia: TCG Industrial. 2009.Retrieved8 April2010.

[17] Proceedings of Anniversary Workshop on Solid-State Gyroscopy (19–21 May 2008. Yalta, Ukraine).Kyiv/Kharkiv: ATS of Ukraine. 2009.ISBN 978-976-0-25248-5.

[18] "Vital- Vibrating Fork Level Switch for Solids".Sapcon Instruments.Retrieved28 May2023.

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v t e Frequencyandpitch
Notation	Concert pitch A440 Enharmonic Helmholtz pitch notation Letter notation Piano key frequencies Pitch class Scientific pitch notation
Perception	Absolute pitch Ear training Pitch circularity Relative pitch Tonal memory Tone deafness Virtual pitch
See also	Electronic tuner Mersenne's laws Microtuner Musical tuning Beating Pitch pipe Savart wheel Tuning fork