Editing Tuning fork (section)

==Description==
[[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|5<sup>2</sup>|2<sup>2</sup>}} = {{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.

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.

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 [[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.