# Tuning fork

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Device that generates sounds of constant pitch when struck

Tuning fork by John Walker stamped with note (E) and frequency in hertz (659)

A **tuning fork** is an [acoustic](/source/Musical_acoustics) [resonator](/source/Resonator) in the form of a two-pronged [fork](/source/Fork) with the prongs ([*tines*](/source/Tine_(structural))) formed from a U-shaped bar of [elastic](/source/Elastic_deformation) metal (usually [steel](/source/Steel)). It [resonates](/source/Acoustic_resonance) at a specific constant [pitch](/source/Pitch_(music)) when set vibrating by striking it against a surface or with an object, and emits a pure [musical tone](/source/Musical_tone) once the high [overtones](/source/Overtone) fade out. A tuning fork's pitch depends on the length and mass of the two prongs. They are traditional sources of standard pitch for [tuning](/source/Musical_tuning) musical instruments.

The tuning fork was invented in 1711 by British musician [John Shore](/source/John_Shore_(trumpeter)), sergeant [trumpeter](/source/Trumpet) and [lutenist](/source/Lute) to the royal court.[1]

## Description

Motion of an A-440 tuning fork (greatly exaggerated) vibrating in its principal [mode](/source/Normal_mode)

A tuning fork is a fork-shaped [acoustic resonator](/source/Acoustic_resonator) used 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 very [pure tone](/source/Pure_tone), with most of the vibrational energy at the [fundamental frequency](/source/Fundamental_frequency). The reason for this is that the frequency of the first overtone is about ⁠52/22⁠ = ⁠25/4⁠ = 6+1⁄4 times the fundamental (about 2+1⁄2 octaves 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 without [damping](/source/Damping_ratio) the oscillation. That is because its principal [mode](/source/Normal_mode) of vibration is symmetric, with the two prongs always moving in opposite directions, so that at the base where the two prongs meet there is a [node](/source/Node_(physics)) (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 of [sound board](/source/Sound_board_(music)). 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 high [acoustic pressure](/source/Sound_pressure) (thus a very high [acoustic impedance](/source/Acoustic_impedance)), is partly converted into audible sound in air which involves a much greater motion ([particle velocity](/source/Particle_velocity)) at a relatively low pressure (thus low acoustic impedance).[3] The pitch of a tuning fork can also be heard directly through [bone conduction](/source/Bone_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 the [Weber](/source/Weber_test) and [Rinne tests](/source/Rinne_test) for hearing in order to bypass the [middle ear](/source/Middle_ear). If just held in open air, the sound of a tuning fork is very faint due to the acoustic [impedance mismatch](/source/Impedance_mismatch) between the steel and air. Moreover, since the feeble sound waves emanating from each prong are 180° out of [phase](/source/Phase_(waves)), those two opposite waves [interfere](/source/Interference_(wave_motion)), largely cancelling each other. Thus when a solid sheet is slid in between the prongs of a vibrating fork, the apparent volume actually *increases*, as this cancellation is reduced, just as a loudspeaker requires a [baffle](/source/Loudspeaker_enclosure) in 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 of [A = 440 Hz](/source/A440_(pitch_standard)), the standard [concert pitch](/source/Concert_pitch) that 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 the [modulus of elasticity](/source/Modulus_of_elasticity) of 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 (becomes [flat](/source/Flat_(music))) with increasing temperature.[6] Tuning forks are manufactured to have their correct pitch at a standard temperature. The [standard temperature](/source/Standard_temperature_and_pressure) is 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

The frequency of a tuning fork depends on its dimensions and what it is made from. Using the [Euler-Bernoulli beam model](/source/Euler%E2%80%93Bernoulli_beam_theory#Example:_Cantilevered_beam), the [fundamental frequency](/source/Fundamental_frequency) of the tuning fork is:[7][8]

- f = α 2 2 π L 2 E I ρ A , {\displaystyle f={\frac {\alpha ^{2}}{2\pi L^{2}}}{\sqrt {\frac {EI}{\rho A}}},}

where

- f is the [frequency](/source/Frequency) the fork vibrates at, ([SI units](/source/SI_units): Hz or 1/s)

- *α* ≈ 1.875 is the smallest positive real solution to [cos](/source/Cosine)(*α*)[cosh](/source/Hyperbolic_cosine)(*α*) = −1,[7] which arises from the boundary conditions of the prong's cantilevered structure.

- L is the length of the prongs, (m)

- E is the [Young's modulus](/source/Young's_modulus) (elastic modulus or stiffness) of the material the fork is made from, (Pa or N/m2 or kg/(ms2))

- I is the [second moment of area](/source/Second_moment_of_area) of the cross-section, (m4)

- ρ is the [density](/source/Density) of the fork's material (kg/m3), and

- A is the cross-sectional area of the prongs (tines), (m2).

The ratio *k*2 = *I*/*A* in the equation above, where k is the [radius of gyration](/source/Radius_of_gyration) for the prongs, can be rewritten as *r*2/4 if the prongs are cylindrical with radius r, and *b*2/12 if the prongs have rectangular cross-section of width b along the direction of motion.[9]

## Uses

Tuning forks have traditionally been used to [tune](/source/Musical_tuning) [musical instruments](/source/Musical_instrument), though [electronic tuners](/source/Electronic_tuner) have largely replaced them. Forks can be driven electrically by placing [electronic oscillator](/source/Electronic_oscillator)-driven [electromagnets](/source/Electromagnet) close to the prongs.

### In musical instruments

A number of [keyboard](/source/Keyboard_instrument) musical instruments use principles similar to tuning forks. The most popular of these is the [Rhodes piano](/source/Rhodes_piano), in which hammers hit metal tines that vibrate in the magnetic field of a [pickup](/source/Pickup_(music_technology)#Magnetic_pickups), creating a signal that drives electric amplification. The earlier, un-amplified [dulcitone](/source/Dulcitone), which used tuning forks directly, suffered from low volume.

### In clocks and watches

Quartz crystal resonator from a modern [quartz watch](/source/Quartz_watch), formed in the shape of a tuning fork. It vibrates at 32,768 Hz, in the [ultrasonic](/source/Ultrasound) range.

A [Bulova](/source/Bulova) Accutron watch from the 1960s, which uses a steel tuning fork *(visible in center)* vibrating at 360 Hz.

The [quartz crystal](/source/Crystal_oscillator) that serves as the timekeeping element in modern [quartz clocks](/source/Quartz_clock) and [watches](/source/Watch) is in the form of a tiny tuning fork. It usually vibrates at a frequency of 32,768 Hz in the [ultrasonic](/source/Ultrasound) range (above the range of human hearing). It is made to vibrate by small oscillating voltages applied by an [electronic oscillator](/source/Electronic_oscillator) circuit to metal electrodes plated on the surface of the crystal. Quartz is [piezoelectric](/source/Piezoelectric), so the voltage causes the tines to bend rapidly back and forth.

The [Accutron](/source/Accutron), an [electromechanical watch](/source/Electromechanical_watches) developed by Max Hetzel[10] and manufactured by [Bulova](/source/Bulova) beginning in 1960, used a 360-[hertz](/source/Hertz) steel 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

1 kHz tuning fork [vacuum tube](/source/Vacuum_tube) [oscillator](/source/Electronic_oscillator) used by the U.S. National Bureau of Standards (now [NIST](/source/National_Institute_of_Standards_and_Technology)) in 1927 as a frequency standard.

Alternatives to the common A=440 standard include [philosophical or scientific pitch](/source/Scientific_pitch) with standard pitch of C=512. According to [Rayleigh](/source/John_William_Strutt%2C_3rd_Baron_Rayleigh), physicists and acoustic instrument makers used this pitch.[11] The tuning fork [John Shore](/source/John_Shore_(trumpeter)) gave to [George Frideric Handel](/source/George_Frideric_Handel) produces C=512.[12]

Tuning forks, usually C512, are used by medical practitioners to assess a patient's hearing. This is most commonly done with two exams called the [Weber test](/source/Weber_test) and [Rinne test](/source/Rinne_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.[13]

[Orthopedic surgeons](/source/Orthopedic_surgery) have 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, the [periosteum](/source/Periosteum) of the bone vibrates and fires [nociceptors](/source/Nociceptor) (pain receptors), causing a local sharp pain.[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia: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](https://en.wikipedia.org/wiki/Wikipedia: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 in [BMJ Open](/source/BMJ_Open) suggests that this technique is not reliable or accurate enough for clinical use.[14]

### Non-medical and non-scientific uses

Tuning forks also play a role in several [alternative therapy](/source/Alternative_medicine) practices, such as [sonopuncture](/source/Sonopuncture) and [polarity therapy](/source/Polarity_therapy).[15]

### Radar gun calibration

A [radar gun](/source/Radar_gun) that measures the speed of cars or a ball in sports is usually calibrated with a tuning fork.[16][17] 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

Doubled and H-type tuning forks are used for tactical-grade [Vibrating Structure Gyroscopes](/source/Vibrating_structure_gyroscope#Tuning_fork_gyroscope) and various types of [microelectromechanical systems](/source/Microelectromechanical_systems).[18]

### Level sensors

Tuning fork forms the sensing part of vibrating [point level sensors](/source/Level_sensor#Point_level_detection_of_liquids). 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.[19] For liquids, the resonant frequency of tuning fork changes upon coming in contact with the liquids, change in frequency is used to detect level.

## See also

- [Electronic tuner](/source/Electronic_tuner)

- [Pitch pipe](/source/Pitch_pipe)

- [Savart wheel](/source/Savart_wheel)

- [Tonometer](/source/Tonometer_(music))

## References

1. **[^](#cite_ref-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](/source/Doi_(identifier)):[10.1055/s-2007-997398](https://doi.org/10.1055%2Fs-2007-997398). [PMID](/source/PMID_(identifier)) [9172630](https://pubmed.ncbi.nlm.nih.gov/9172630).

1. **[^](#cite_ref-2)** Tyndall, John (1915). [*Sound*](https://books.google.com/books?id=hCgZAAAAYAAJ&pg=PA156). New York: D. Appleton & Co. p. 156.

1. **[^](#cite_ref-3)** Rossing, Thomas D.; Moore, F. Richard; Wheeler, Paul A. (2001). *The Science of Sound* (3rd ed.). Pearson. [ISBN](/source/ISBN_(identifier)) [978-0-8053-8565-6](https://en.wikipedia.org/wiki/Special:BookSources/978-0-8053-8565-6).[*[page needed](https://en.wikipedia.org/wiki/Wikipedia:Citing_sources)*]

1. **[^](#cite_ref-4)** Dan Fox (1996). [*Teach Yourself to Play Mandolin*](https://books.google.com/books?id=1jFWy2qR4U4C&q=bone+conduction). Alfred Music Publishing. [ISBN](/source/ISBN_(identifier)) [978-0-7390-0286-5](https://en.wikipedia.org/wiki/Special:BookSources/978-0-7390-0286-5). Retrieved 3 July 2015.

1. **[^](#cite_ref-5)** Fletcher, Neville H.; Rossing, Thomas (2008). *The Physics of Musical Instruments* (2nd ed.). Springer. [ISBN](/source/ISBN_(identifier)) [978-0-387-98374-5](https://en.wikipedia.org/wiki/Special:BookSources/978-0-387-98374-5).[*[page needed](https://en.wikipedia.org/wiki/Wikipedia:Citing_sources)*]

1. **[^](#cite_ref-6)** Ellis, Alexander J. (1880). ["On the History of Musical Pitch"](https://books.google.com/books?id=xqU9AQAAIAAJ&pg=PA297). *Journal of the Society of Arts*. **28** (545): 293–336. [Bibcode](/source/Bibcode_(identifier)):[1880Natur..21..550E](https://ui.adsabs.harvard.edu/abs/1880Natur..21..550E). [doi](/source/Doi_(identifier)):[10.1038/021550a0](https://doi.org/10.1038%2F021550a0).

1. ^ [***a***](#cite_ref-HanSeonM_7-0) [***b***](#cite_ref-HanSeonM_7-1) 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](/source/Bibcode_(identifier)):[1999JSV...225..935H](https://ui.adsabs.harvard.edu/abs/1999JSV...225..935H). [doi](/source/Doi_(identifier)):[10.1006/jsvi.1999.2257](https://doi.org/10.1006%2Fjsvi.1999.2257). [S2CID](/source/S2CID_(identifier)) [121014931](https://api.semanticscholar.org/CorpusID:121014931).

1. **[^](#cite_ref-8)** Whitney, Scott (23 April 1999). ["Vibrations of Cantilever Beams: Deflection, Frequency, and Research Uses"](http://emweb.unl.edu/Mechanics-Pages/Scott-Whitney/325hweb/Beams.htm). University of Nebraska–Lincoln. Retrieved 9 November 2011.

1. **[^](#cite_ref-9)** Gentle, Richard; Edwards, Peter; Bolton, Bill (2001). *Mechanical Engineering Systems*. IIE Core Textbooks Series. [Butterworth-Heinemann](/source/Butterworth-Heinemann). p. 262-264. [doi](/source/Doi_(identifier)):[10.1016/B978-0-7506-5213-1.X5000-4](https://doi.org/10.1016%2FB978-0-7506-5213-1.X5000-4). [ISBN](/source/ISBN_(identifier)) [978-0-7506-5213-1](https://en.wikipedia.org/wiki/Special:BookSources/978-0-7506-5213-1).

1. **[^](#cite_ref-10)** [ch 312290](https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=ch312290)

1. **[^](#cite_ref-11)** Rayleigh, J. W. S. (1945). [*The Theory of Sound*](https://archive.org/details/theoryofsoundvol000709mbp). New York: Dover. p. [9](https://archive.org/details/theoryofsoundvol000709mbp/page/n54). [ISBN](/source/ISBN_(identifier)) [0-486-60292-3](https://en.wikipedia.org/wiki/Special:BookSources/0-486-60292-3). {{[cite book](https://en.wikipedia.org/wiki/Template:Cite_book)}}: ISBN / Date incompatibility ([help](https://en.wikipedia.org/wiki/Help:CS1_errors#invalid_isbn_date))

1. **[^](#cite_ref-12)** Bickerton, RC; Barr, GS (December 1987). ["The origin of the tuning fork"](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1291142). *[Journal of the Royal Society of Medicine](/source/Journal_of_the_Royal_Society_of_Medicine)*. **80** (12): 771–773. [doi](/source/Doi_(identifier)):[10.1177/014107688708001215](https://doi.org/10.1177%2F014107688708001215). [PMC](/source/PMC_(identifier)) [1291142](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1291142). [PMID](/source/PMID_(identifier)) [3323515](https://pubmed.ncbi.nlm.nih.gov/3323515).

1. **[^](#cite_ref-13)** Bickley, Lynn; Szilagyi, Peter (2009). *Bates' guide to the physical examination and history taking* (10th ed.). Philadelphia, PA: Lippincott Williams & Wilkins. [ISBN](/source/ISBN_(identifier)) [978-0-7817-8058-2](https://en.wikipedia.org/wiki/Special:BookSources/978-0-7817-8058-2).

1. **[^](#cite_ref-14)** 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"](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4127942). *[BMJ Open](/source/BMJ_Open)*. **4** (8) e005238. [doi](/source/Doi_(identifier)):[10.1136/bmjopen-2014-005238](https://doi.org/10.1136%2Fbmjopen-2014-005238). [PMC](/source/PMC_(identifier)) [4127942](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4127942). [PMID](/source/PMID_(identifier)) [25091014](https://pubmed.ncbi.nlm.nih.gov/25091014).

1. **[^](#cite_ref-15)** Hawkins, Heidi (August 1995). "SONOPUNCTURE: Acupuncture Without Needles". *Holistic Health News*.

1. **[^](#cite_ref-16)** ["Calibration of Police Radar Instruments"](https://web.archive.org/web/20120222143735/http://tf.nist.gov/timefreq/general/pdf/87.pdf) (PDF). National Bureau of Standards. 1976. Archived from [the original](http://tf.nist.gov/timefreq/general/pdf/87.pdf) (PDF) on 22 February 2012. Retrieved 29 October 2008.

1. **[^](#cite_ref-17)** ["A detailed explanation of how police radars work"](http://radars.com.au/police-radar.php). *Radars.com.au*. Perth, Australia: TCG Industrial. 2009. Retrieved 8 April 2010.

1. **[^](#cite_ref-18)** *Proceedings of Anniversary Workshop on Solid-State Gyroscopy (19–21 May 2008. Yalta, Ukraine)*. Kyiv/Kharkiv: ATS of Ukraine. 2009. [ISBN](/source/ISBN_(identifier)) [978-976-0-25248-5](https://en.wikipedia.org/wiki/Special:BookSources/978-976-0-25248-5).

1. **[^](#cite_ref-19)** ["Vital- Vibrating Fork Level Switch for Solids"](https://www.sapconinstruments.com/products/vital-vibrating-fork-level-switch). *Sapcon Instruments*. Retrieved 28 May 2023.

## External links

Wikimedia Commons has media related to [Tuning forks](https://commons.wikimedia.org/wiki/Category:Tuning_forks).

Look up ***[tuning fork](https://en.wiktionary.org/wiki/Special:Search/tuning_fork)*** in Wiktionary, the free dictionary.

- [Onlinetuningfork.com](http://www.onlinetuningfork.com/), an online tuning fork using [Macromedia](/source/Macromedia) [Flash Player](/source/Flash_Player).

- ["Tuning Fork"](https://en.wikisource.org/wiki/Collier%27s_New_Encyclopedia_(1921)/Tuning_Fork). *[Collier's New Encyclopedia](/source/Collier's_Encyclopedia)*. 1921.

- ["Tuning Fork"](https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Tuning_Fork). *[Encyclopædia Britannica](/source/Encyclop%C3%A6dia_Britannica_Eleventh_Edition)*. Vol. 27 (11th ed.). 1911. p. 392.

v t e Frequency and pitch 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

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