Tuning fork

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Tuning fork on resonance box, by Max Kohl, Chemnitz, Germany

A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it against a surface or with an object, and emits a pure musical tone once the high overtones fade 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.

The tuning fork was invented in 1711 by British musician John Shore, Sergeant Trumpeter and Lutenist to the court.[1]


Tuning fork by John Walker stamped with note (E) and frequency in hertz (659)
A needle on a tuning fork carves figures on carbon black.

A tuning fork is a fork-shaped 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, with most of the vibrational energy at the fundamental frequency. The reason for this is that the frequency of the first overtone is about 52/22 = 25/4 = ​6 14 times the fundamental (about ​2 12 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 be a mixture of 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, when it vibrates in its principal mode, the handle vibrates up and down as the prongs move apart and together. There is a node (point of no vibration) at the base of each prong. The handle motion is small, so the user can hold the fork by the handle without damping the vibration, but the handle can still transmit the vibration to a resonator, which amplifies the sound of the fork.[3] The user typically strikes the fork, and then presses the handle against a wooden box resonator, table top, edge of a musical instrument, or just behind their ear. If just held in open air, the sound of a tuning fork is very faint. The sound waves from each prong are 180° out of phase with the other, so at a distance from the fork they 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 actually increases, due to a reduction of this cancellation.

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.[citation needed]

Currently, the most common tuning fork sounds the note of A = 440 Hz since this is the standard concert pitch which many orchestras use. That A is the pitch of the violin's second string, the first string of the viola, and an octave above the first string of the cello. Orchestras between 1750 and 1820 mostly used a frequency of A = 423.5 Hz, though there were many forks and many slightly different pitches.[4] Standard tuning forks are available that vibrate at all the pitches within the central octave of the piano, and also other pitches. Well-known tuning fork manufacturers include Ragg and John Walker, both of Sheffield, England.

Tuning fork pitch varies slightly with temperature, due mainly to a slight decrease in the 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) with increasing temperature.[5] Tuning forks are manufactured to have their correct pitch at a standard temperature. The standard temperature 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[edit]

The frequency of a tuning fork depends on its dimensions and what it's made from:[6]


  • f is the frequency the fork vibrates at in hertz.
  • 1.875 is the smallest positive solution of cos(x)cosh(x) = −1.[7]
  • l is the length of the prongs in metres.
  • E is the Young's modulus (elastic modulus or stiffness) of the material the fork is made from in pascals.
  • I is the second moment of area of the cross-section in metres to the fourth power.
  • ρ is the density of the material the fork is made from in kilograms per cubic metre.
  • A is the cross-sectional area of the prongs (tines) in square metres.

The ratio I/A in the equation above can be rewritten as r2/4 if the prongs are cylindrical with radius r, and a2/12 if the prongs have rectangular cross-section of width a along the direction of motion.


Tuning forks have traditionally been used to tune musical instruments, although electronic tuners are replacing them in many applications. Forks can be driven electrically by placing electromagnets close to the prongs that are attached to an electronic oscillator circuit so their sound does not die out.

In musical instruments[edit]

A number of 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.

In clocks and watches[edit]

Quartz crystal resonator from a modern quartz watch, formed in the shape of a tuning fork. It vibrates at 32,768 Hz in the ultrasonic range.
A Bulova Accutron watch from the 1960s, which uses a steel tuning fork (visible in center) vibrating at 360 Hz.

The quartz crystal that serves as the timekeeping element in modern quartz clocks and watches is in the form of a tiny tuning fork. It usually vibrates at a frequency of 32,768 Hz in the 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 tines to bend rapidly back and forth.

The Accutron, an 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.

Medical and scientific uses[edit]

1 kHz tuning fork vacuum tube oscillator used by the U.S. National Bureau of Standards (now NIST) in 1927 as a frequency standard.

An alternative to the usual A440 diatonic scale is that of philosophical or scientific pitch with standard pitch of C512. According to Rayleigh, the scale was used by physicists and acoustic instrument makers.[8] The tuning fork John Shore gave to George Frideric Handel gives a pitch of C512.[9]

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 and 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.[10]

Within Orthopedic surgery, physicians have explored using a tuning fork (lowest frequency C128) to help assess injuries where bone fracture is suspected. They tone the tuning fork on the bone with the suspected fracture, progressively closer to suspected area of fracture. If there is a fracture, the periosteum of the bone vibrates and fire nociceptors (pain receptors) causing a local sharp pain.[citation needed] This can indicate a fracture, which the practitioner refers for medical X-ray. Note that 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 in BMJ Open suggests that this technique is not sufficiently reliable or accurate for widespread clinical use.[11]

Tuning forks also play a role in several alternative therapy modalities, such as sonopuncture and polarity therapy.[12]

Radar gun calibration[edit]

A radar gun that measures the speed of cars or a ball in sports is usually calibrated with a tuning fork.[13][14] 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-grade Vibrating Structure Gyroscopes and various types of microelectromechanical systems.[15]

See also[edit]


  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. ^ Fletcher, Neville H.; Rossing, Thomas (2008). The Physics of Musical Instruments (2nd ed.). Springer. ISBN 978-0387983745. [page needed]
  5. ^ Ellis, Alexander J. (1880). "On the History of Musical Pitch". Journal of the Society of Arts. 28: 293–336. 
  6. ^ 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. doi:10.1006/jsvi.1999.2257. 
  7. ^ Whitney, Scott (1999-04-23). "Vibrations of Cantilever Beams: Deflection, Frequency, and Research Uses". University of Nebraska–Lincoln. Retrieved 2011-11-09. 
  8. ^ Rayleigh, J. W. S. (1945). The Theory of Sound. New York: Dover. p. 9. ISBN 0-486-60292-3. 
  9. ^ Bickerton, RC; Barr, GS (December 1987). "The origin of the tuning fork" (PDF). Journal of the Royal Society of Medicine. 80 (12): 771–773. PMC 1291142Freely accessible. PMID 3323515. 
  10. ^ 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. 
  11. ^ 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.  open access publication – free to read
  12. ^ Hawkins, Heidi (Aug 1995). "SONOPUNCTURE: Acupuncture Without Needles". Holistic Health News. 
  13. ^ "Calibration of Police Radar Instruments" (PDF). National Bureau of Standards. 1976. 
  14. ^ "A detailed explanation of how police radars work". Radars.com.au. Perth, Australia: TCG Industrial. 2009. Retrieved 2010-04-08. 
  15. ^ 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. 

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