Tuning fork: Difference between revisions

Revision as of 22:39, 22 March 2007

Latest revision as of 17:43, 22 July 2025

(539 intermediate revisions by more than 100 users not shown)

Line 1:

{{Short description|Device that generates sounds of constant pitch when struck}}

{{unreferenced|date=December 2006}}

{{Use dmy dates|date=June 2020}}

[[Image:Tuning_fork_on_resonator.jpg|thumb|right|250px|Tuning fork on resonance box, by Max Kohl, Chemnitz, Germany]]

[[Image:TuningFork659Hz.jpg|thumb|Tuning fork by John Walker stamped with note (E) and frequency in hertz (659)]]

A '''tuning fork''' is aan simple[[Musical metalacoustics|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]] materialmetal (usually [[steel]]). A tuning forkIt [[acoustic resonance|resonates ]] at a specific constant [[pitch (music)|pitch]] when set vibrating by striking it against a surface or with an object, and after waitingemits a momentpure to[[Musical allowtone|musical sometone]] once the high [[overtonesovertone]]s to diefade out. The pitch that a particularA tuning fork's generatespitch depends on the length and mass of the two prongs,. withThey twoare nodestraditional nearsources theof bendstandard ofpitch thefor U.[[musical tuning|tuning]] musical instruments.

The tuning fork was invented in 1711 by British musician [[John Shore (trumpeter)|John Shore]], sergeant [[trumpet]]er and [[lute]]nist to the royal 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>

==Explanation==

Currently, the most common tuning fork used by musicians sounds the note of [[A440|A (440 Hz, international "concert pitch")]], which has long been used as a standard tuning note by orchestras, it being the pitch of the violin's third string played open, the fourth string of the viola played open, and an octave above the fourth string of the cello, again played open. However, they are also commercially made to vibrate at frequencies corresponding to all musical pitches within the central octave of the piano, and other pitches.

==Description==

[[Image:TuningFork659Hz.jpg|thumb|Tuning fork by John Walker showing note (E) and frequency in hertz (659)]]

[[Image:Mode Shape of a Tuning Fork at Eigenfrequency 440.09 Hz.gif|thumb|Motion of an A-440 tuning fork (greatly exaggerated) vibrating in its principal [[Normal mode|mode]]]]

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 {{sfrac|5²|2²}} = {{sfrac|25|4}} = {{frac|6|1|4}} times the fundamental (about {{frac|2|1|2}} octaves above it).<ref>{{cite book | last = Tyndall | first = John | title = Sound | publisher = D. Appleton & Co. | year = 1915 | ___location = New York | page = 156 | url = https://books.google.com/books?id=hCgZAAAAYAAJ&pg=PA156}}</ref> 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.

The tuning fork was invented in [[1711]] by [[John Shore]], Sergeant [[Trumpet]]er to the court, who had parts specifically written for him by both [[George Friderich Handel]] and [[Henry Purcell]].

Another reason for using the fork shape is that it can then be held at the base without [[Damping ratio|damping]] the oscillation. That is because its principal [[Normal mode|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 (physics)|node]] (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 (music)|sound 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 high [[Sound pressure|acoustic pressure]] (thus a very high [[acoustic 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).<ref>{{cite book|title=The Science of Sound|edition=3rd|first1=Thomas D.|last1=Rossing|first2=F. Richard|last2=Moore|first3=Paul A.|last3=Wheeler|publisher=Pearson|year=2001|isbn=978-0805385656}}{{page needed|date=January 2017}}</ref> The pitch of a tuning fork can also be heard directly through [[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.<ref>{{cite book|title=Teach Yourself to Play Mandolin|url=https://books.google.com/books?id=1jFWy2qR4U4C&q=bone+conduction|publisher=Alfred Music Publishing|access-date=3 July 2015|author=Dan Fox|date=1996|isbn=9780739002865}}</ref> Bone conduction using a tuning fork is specifically used in the [[Weber test|Weber]] and [[Rinne test]]s for hearing in order to bypass the [[middle ear]]. If just held in open air, the sound of a tuning fork is very faint due to the acoustic [[impedance mismatch]] between the steel and air. Moreover, since the feeble sound waves emanating from each prong are 180° out of [[phase (waves)|phase]], those two opposite waves [[Interference (wave motion)|interfere]], 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 [[Loudspeaker enclosure|baffle]] in order to radiate efficiently.

When struck, it gives out a very faint note which is barely audible unless held close to the [[ear]]. For this reason, it is sometimes struck and then pressed down on a solid surface such as a desk which acts as a [[sounding board]] and greatly amplifies the note.

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.

Well-known manufacturers of tuning forks include Ragg and John Walker, both of [[Sheffield]], [[England]].

Currently, the most common tuning fork sounds the note of [[A440 (pitch standard)|A&nbsp;= 440&nbsp;Hz]], the standard [[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&nbsp;= 423.5&nbsp;Hz, though there were many forks and many slightly different pitches.<ref>{{cite book |title= The Physics of Musical Instruments |edition= 2nd |first1= Neville H. |last1= Fletcher |first2= Thomas | last2= Rossing |publisher= Springer |year= 2008 |isbn= 978-0387983745 }}{{Page needed|date=January 2012}}</ref> 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]] of steel with increasing temperature. A change in frequency of 48&nbsp;parts per million per&nbsp;°F (86&nbsp;ppm per&nbsp;°C) is typical for a steel tuning fork. The frequency decreases (becomes [[flat (music)|flat]]) with increasing temperature.<ref>{{cite journal|url=https://books.google.com/books?id=xqU9AQAAIAAJ&pg=PA297 |journal=Journal of the Society of Arts |volume=28 |issue=545 |year= 1880 |pages=293–336 |title= On the History of Musical Pitch |first= Alexander J. |last= Ellis|bibcode=1880Natur..21..550E |doi=10.1038/021550a0 |doi-access=free }}</ref> Tuning forks are manufactured to have their correct pitch at a standard temperature. The [[Standard temperature and pressure|standard temperature]] is now {{convert|20|°C}}, but {{convert|15|°C}} 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_theory#Example:_Cantilevered_beam|Euler-Bernoulli beam model]], the [[Fundamental frequency|fundamental frequency]] of the tuning fork is:<ref name="HanSeonM">{{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=935–988|bibcode=1999JSV...225..935H |s2cid=121014931 }}</ref><ref>{{cite web | url=http://emweb.unl.edu/Mechanics-Pages/Scott-Whitney/325hweb/Beams.htm | title=Vibrations of Cantilever Beams: Deflection, Frequency, and Research Uses | last=Whitney | first=Scott | publisher=University of Nebraska–Lincoln | date=1999-04-23 | access-date=2011-11-09 }}</ref>

: <math>f = \frac{\alpha^2}{2\pi L^2} \sqrt\frac{EI}{\rho A},</math>

where

: {{mvar|f}} is the [[frequency]] the fork vibrates at, ([[SI units]]: Hz or 1/s)

: {{mvar|''&alpha;'' &asymp; }}{{math|1.875}} is the smallest positive real solution to {{math|[[cosine|cos]](''&alpha;'')[[hyperbolic cosine|cosh]](''&alpha;'') {{=}} −1}},<ref name="HanSeonM"></ref> which arises from the boundary conditions of the prong’s cantilevered structure.

: {{mvar|L}} is the length of the prongs, (m)

: {{mvar|E}} is the [[Young's modulus]] (elastic modulus or stiffness) of the material the fork is made from, (Pa or N/m² or kg/(ms²))

: {{mvar|I}} is the [[second moment of area]] of the cross-section, (m⁴)

: {{mvar|ρ}} is the [[density]] of the fork's material (kg/m³), and

: {{mvar|A}} is the cross-sectional area of the prongs (tines), (m²).

The ratio {{math|''k''{{sup|2}} {{=}} ''I''/''A''}} in the equation above, where {{mvar|k}} is the [[Radius of gyration|radius of gyration]] for the prongs, can be rewritten as {{math|''r''²/4}} if the prongs are cylindrical with radius {{mvar|r}}, and {{math|''b''²/12}} if the prongs have rectangular cross-section of width {{mvar|b}} along the direction of motion.<ref>{{cite book|last1=Gentle|first1=Richard|last2=Edwards|first2=Peter|last3=Bolton|first3=Bill|title=Mechanical Engineering Systems|publisher=[[Butterworth-Heinemann]]|series=IIE Core Textbooks Series|date=2001|page=262-264|doi=10.1016/B978-0-7506-5213-1.X5000-4|isbn=978-0-7506-5213-1}}</ref>

==Uses==

Tuning forks have traditionally been used to [[Musical tuning|tune]] [[musical instrument]]s, though [[electronic tuner]]s have largely replaced them. Forks can be driven electrically by placing [[electronic oscillator]]-driven [[electromagnet]]s close to the prongs.

They are commonly used to [[tuning|tune]] [[musical instrument]]s, although [[electronic tuner]]s also exist, and some musicians have [[Absolute pitch|perfect pitch]]. Tuning forks can be tuned by removing material off the tines (filing the ends of the tines to raise it or filing inside the base of the tines to lower it) or by sliding weights attached to the prongs. Once tuned, a tuning fork's frequency varies only with changes in the [[elastic modulus]] of the material; for precise work, a tuning fork should be kept in a thermostatically controlled enclosure. Large forks are often made to be driven electrically, like an electric bell or buzzer, and can vibrate for an indefinite time.

===In musical instruments===

A number of [[keyboard instrument|keyboard]] musical instruments usinguse constructionsprinciples similar to tuning forks. have been made, theThe most popular of themthese beingis the [[Rhodes piano]], in which has hammers hittinghit constructionsmetal workingtines onthat vibrate in the samemagnetic principlefield asof a [[Pickup (music technology)#Magnetic pickups|pickup]], creating a signal that drives electric amplification. The earlier, un-amplified [[dulcitone]], which used tuning forks directly, suffered from low volume.

===In clocks and watches===

[[File:Inside QuartzCrystal-Tuningfork.jpg|thumb|upright|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.]]

[[Image:Accutron.jpg|thumb|upright|A [[Bulova]] Accutron watch from the 1960s, which uses a steel tuning fork ''(visible in center)'' vibrating at 360&nbsp;Hz.]]

The [[crystal oscillator|quartz crystal]] that serves as the timekeeping element in modern [[quartz clock]]s and [[watch]]es is in the form of a tiny tuning fork. It usually vibrates at a frequency of 32,768&nbsp;Hz in the [[ultrasound|ultrasonic]] range (above the range of human hearing). It is made to vibrate by small oscillating voltages applied by an [[electronic oscillator]] circuit to metal electrodes plated on the surface of the crystal. Quartz is [[piezoelectric]], so the voltage causes the tines to bend rapidly back and forth.

The [[Accutron]], an [[Electromechanical watches|electromechanical watch]] developed by Max Hetzel<ref>{{Patent|ch|312290}}</ref> 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 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===

[[Image:Tuning fork oscillator frequency standard.jpg|thumb|upright|1&nbsp;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.]]

Alternatives to the common A=440 standard include [[Scientific pitch|philosophical or scientific pitch]] with standard pitch of C=512. According to [[John William Strutt, 3rd Baron Rayleigh|Rayleigh]], physicists and acoustic instrument makers used this pitch.<ref>{{cite book|last=Rayleigh|first=J. W. S.|title=The Theory of Sound|url=https://archive.org/details/theoryofsoundvol000709mbp|url-access=limited|year=1945|publisher=Dover|___location=New York|isbn=0-486-60292-3|page=[https://archive.org/details/theoryofsoundvol000709mbp/page/n54 9]}}</ref> The tuning fork [[John Shore (trumpeter)|John Shore]] gave to [[George Frideric Handel]] produces C=512.<ref>{{cite journal |pmc=1291142 |title=The origin of the tuning fork |first1=RC |last1=Bickerton |first2=GS |last2=Barr |journal=[[Journal of the Royal Society of Medicine]] |volume=80 |issue=12 |pages=771–773 |date=December 1987 |pmid=3323515|doi = 10.1177/014107688708001215}}</ref>

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.<ref>{{cite book |last1=Bickley |first1=Lynn |last2=Szilagyi |first2=Peter |date=2009 |title=Bates' guide to the physical examination and history taking |edition=10th |___location=Philadelphia, PA |publisher=Lippincott Williams & Wilkins |isbn=978-0-7817-8058-2}}</ref>

[[orthopedic surgery|Orthopedic surgeons]] 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]] of the bone vibrates and fires [[nociceptor]]s (pain receptors), causing a local sharp pain.{{citation needed|date=April 2016}} 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|date=April 2016}} 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 reliable or accurate enough for clinical use.<ref>{{cite journal |url= |title=Is there sufficient evidence for tuning fork tests in diagnosing fractures? A systematic review |first1=Kayalvili |last1=Mugunthan |first2=Jenny |last2=Doust |first3=Bodo |last3=Kurz |first4=Paul |last4=Glasziou |date=4 August 2014 |journal=[[BMJ Open]] |volume=4 |issue=8 |pages=e005238 |doi=10.1136/bmjopen-2014-005238|pmid=25091014 |pmc=4127942 }} {{open access}}</ref>

=== Non-medical and non-scientific uses ===

Tuning forks also play a role in several [[alternative medicine|alternative therapy]] practices, such as [[sonopuncture]] and [[polarity therapy]].<ref>{{Cite news|title=SONOPUNCTURE: Acupuncture Without Needles|last=Hawkins|first=Heidi|date=Aug 1995|work=Holistic Health News}}</ref>

=== Radar gun calibration ===

A [[radar gun]] that measures the speed of cars or a ball in sports is usually calibrated with a tuning fork.<ref>{{cite web|url=http://tf.nist.gov/timefreq/general/pdf/87.pdf|title=Calibration of Police Radar Instruments|publisher=National Bureau of Standards|date=1976|access-date=29 October 2008|archive-date=22 February 2012|archive-url=https://web.archive.org/web/20120222143735/http://tf.nist.gov/timefreq/general/pdf/87.pdf|url-status=dead}}</ref><ref>{{cite web| title = A detailed explanation of how police radars work | work = Radars.com.au | publisher = TCG Industrial|___location= Perth, Australia | year = 2009 | url = http://radars.com.au/police-radar.php | access-date = 2010-04-08}}</ref> 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 gyroscope#Tuning fork gyroscope|Vibrating Structure Gyroscopes]] and various types of [[microelectromechanical systems]].<ref>{{cite book|title=Proceedings of Anniversary Workshop on Solid-State Gyroscopy (19–21 May 2008. Yalta, Ukraine) |___location=Kyiv/Kharkiv |publisher=ATS of Ukraine |date=2009 |isbn=978-976-0-25248-5}}</ref>

===Level sensors===

===In electromechanical watches===

Tuning fork forms the sensing part of vibrating [[Level sensor#Point level detection of liquids|point 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.<ref>{{Cite web|title=Vital- Vibrating Fork Level Switch for Solids|url=https://www.sapconinstruments.com/products/vital-vibrating-fork-level-switch|access-date=2023-05-28|website=Sapcon Instruments}}</ref> For liquids, the resonant frequency of tuning fork changes upon coming in contact with the liquids, change in frequency is used to detect level.

[[Electromechanical watches]] developed by Max Hetzel for [[Bulova]] used a 360 Hertz tuning fork with a battery to make a mechanical watch keep time with great accuracy. The production of the Bulova Accutron, as it was called, ceased in 1977.

== See also ==

A tiny [[quartz]] tuning fork is used in [[crystal oscillator]]s, the most notable use of which are quartz [[digital watch]]es. The [[piezoelectricity|piezoelectric]] properties of quartz [[crystal]]s cause a quartz tuning fork to generate a pulsed electrical current as it resonates, which is used by the [[computer chip]] in the watch to keep track of the passage of [[time]]. In today's watches, they generally resonate at <math>2^{15}=32,768</math> [[Hertz|Hz]]. (See [[quartz clock]].)

* [[Electronic tuner]]

* [[Pitch pipe]]

* [[Savart wheel]]

* [[Tonometer (music)|Tonometer]]

{{clear}}

==References==

♥♥♥♥♥♥♥===Medical uses===

{{Reflist}}

Tuning forks, usually C-512, are used by medical practitioners to assess a patient's hearing. Lower-pitched ones (usually C-128) are also used to check vibration sense as part of the examination of the peripheral nervous system. They are also used therapeutically in [[sonopuncture]]. [[John Beaulieu]], a researcher on the therapeutic benefits of tuning forks, has recorded an album of music made entirely with tuning forks, called ''Calendula''. Other researchers into the therapeutic benefits of tuning forks are [[Arden Wilken]] and Jack Wilken.

==External links==

{{Commons category|Tuning forks}}

*[http://www.onlinetuningfork.com/ http://www.onlinetuningfork.com], an online tuning fork using [[Macromedia]] [[Flash Player]].

{{wiktionary}}

*[http://www.onlinetuningfork.com/ Onlinetuningfork.com], an online tuning fork using [[Macromedia]] [[Flash Player]].

*{{Cite Collier's|wstitle=Tuning Fork|short=x}}

*{{Cite EB1911|wstitle=Tuning Fork |volume=27|page=392|short=x}}

{{Pitch (music)}}

[[Category:Musical instruments]]

{{Authority control}}

{{DEFAULTSORT:Tuning Fork}}

[[be:Камертон]]

[[Category:1711 introductions]]

[[ca:Diapasó]]

[[Category:Musical instrument parts and accessories]]

[[de:Stimmgabel]]

[[esCategory:DiapasónIdiophones]]

[[eoCategory:DiapazonoAcoustics]]

[[frCategory:DiapasonSound]]

[[id:Garpu tala]]

[[he:קולן]]

[[nl:Stemvork]]

[[ja:音叉]]

[[no:Stemmegaffel]]

[[pl:Kamerton]]

[[pt:Diapasão]]

[[ru:Камертон]]

[[sl:Glasbene vilice]]

[[fi:Äänirauta]]

[[sv:Stämgaffel]]