Tuning-fork
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A tuning fork is an acoustic
resonator A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a reso ...
in the form of a two-pronged
fork In cutlery or kitchenware, a fork (from 'pitchfork') is a utensil, now usually made of metal, whose long handle terminates in a head that branches into several narrow and often slightly curved tines with which one can spear foods either to h ...
with the prongs ( ''tines'') formed from a U-shaped bar of
elastic Elastic is a word often used to describe or identify certain types of elastomer, Elastic (notion), elastic used in garments or stretch fabric, stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rub ...
metal (usually
steel Steel is an alloy of iron and carbon that demonstrates improved mechanical properties compared to the pure form of iron. Due to steel's high Young's modulus, elastic modulus, Yield (engineering), yield strength, Fracture, fracture strength a ...
). 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
overtone An overtone is any resonant frequency above the fundamental frequency of a sound. (An overtone may or may not be a harmonic) In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental i ...
s 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 musical instruments. The tuning fork was invented in 1711 by British musician John Shore, sergeant
trumpet The trumpet is a brass instrument commonly used in classical and jazz musical ensemble, ensembles. The trumpet group ranges from the piccolo trumpet—with the highest Register (music), register in the brass family—to the bass trumpet, pitche ...
er and
lute A lute ( or ) is any plucked string instrument with a neck (music), neck and a deep round back enclosing a hollow cavity, usually with a sound hole or opening in the body. It may be either fretted or unfretted. More specifically, the term "lu ...
nist to the royal court.


Description

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 In psychoacoustics, a pure tone is a sound with a sinusoidal waveform; that is, a sine wave of constant frequency, phase-shift, and amplitude. By extension, in signal processing a single-frequency tone or pure tone is a purely sinusoidal signal ...
, with most of the vibrational energy at the
fundamental frequency The fundamental frequency, often referred to simply as the ''fundamental'' (abbreviated as 0 or 1 ), is defined as the lowest frequency of a Periodic signal, periodic waveform. In music, the fundamental is the musical pitch (music), pitch of a n ...
. The reason for this is that the frequency of the first overtone is about = = times the fundamental (about octaves above it). 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 In physical systems, damping is the loss of energy of an oscillating system by dissipation. Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. Examples of damping include ...
the oscillation. That is because its principal
mode Mode ( meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * MO''D''E (magazine), a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is the setting fo ...
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 In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics * Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two or more curves, lines ...
(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. 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 Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by a sound wave. In air, sound pressure can be measured using a microphone, and in water with a hydrophone ...
(thus a very high
acoustic impedance Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The International System of Units, SI unit of acoustic impeda ...
), is partly converted into audible sound in air which involves a much greater motion (
particle velocity Particle velocity (denoted or ) is the velocity of a particle (real or imagined) in a medium as it transmits a wave. The SI unit of particle velocity is the metre per second (m/s). In many cases this is a longitudinal wave of pressure as with ...
) at a relatively low pressure (thus low acoustic impedance). The pitch of a tuning fork can also be heard directly through
bone conduction Bone conduction is the conduction of sound to the inner ear primarily through the bones of the skull, allowing the hearer to perceive audio content even if the ear canal is blocked. Bone conduction transmission occurs constantly as sound waves vi ...
, 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. Bone conduction using a tuning fork is specifically used in the
Weber Weber may refer to: Places United States * Weber, Missouri, an unincorporated community * Weber City, Virginia, a town * Weber City, Fluvanna County, Virginia, an unincorporated community * Weber County, Utah * Weber Canyon, Utah * Weber R ...
and
Rinne test The Rinne test ( ) is used primarily to evaluate loss of hearing in one ear. It compares perception of sounds transmitted by air conduction to those transmitted by bone conduction through the mastoid. Thus, one can quickly screen for the presence ...
s for hearing in order to bypass the
middle ear The middle ear is the portion of the ear medial to the eardrum, and distal to the oval window of the cochlea (of the inner ear). The mammalian middle ear contains three ossicles (malleus, incus, and stapes), which transfer the vibrations ...
. If just held in open air, the sound of a tuning fork is very faint due to the acoustic
impedance mismatch In electrical engineering, impedance matching is the practice of designing or adjusting the input impedance or output impedance of an electrical device for a desired value. Often, the desired value is selected to maximize power transfer or mi ...
between the steel and air. Moreover, since the feeble sound waves emanating from each prong are 180° out of
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematica ...
, those two opposite waves 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 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 A = 440 Hz, the standard
concert pitch Concert pitch is the pitch reference to which a group of musical instruments are tuned for a performance. Concert pitch may vary from ensemble to ensemble, and has varied widely over time. The ISO defines international standard pitch as A440, ...
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. 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 An elastic modulus (also known as modulus of elasticity (MOE)) is a quantity that describes an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. Definition The elastic modu ...
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. Tuning forks are manufactured to have their correct pitch at a standard temperature. The
standard temperature Standard temperature and pressure (STP) or standard conditions for temperature and pressure are various standard sets of conditions for experimental measurements used to allow comparisons to be made between different sets of data. The most used ...
is now , but 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: : f = \frac \sqrt\frac, where : is the
frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
the fork vibrates at, (
SI units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...
: 1/s) :  ≈ 3.516015 is the square of the smallest positive solution to , which arises from the boundary conditions of the prong’s cantilevered structure. : is the length of the prongs, (m) : is the
Young's modulus Young's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Youn ...
(elastic modulus or stiffness) of the material the fork is made from, (Pa or N/m2 or kg/(ms2)) : is the
second moment of area The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. Th ...
of the cross-section, (m4) : is the
density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
of the fork's material (kg/m3), and : is the cross-sectional
area Area is the measure of a region's size on a surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an open surface or the boundary of a three-di ...
of the prongs (tines) (m2). The ratio in the equation above can be rewritten as if the prongs are cylindrical with radius , and if the prongs have rectangular cross-section of width along the direction of motion.


Uses

Tuning forks have traditionally been used to tune
musical instrument A musical instrument is a device created or adapted to make Music, musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that the object becomes a musical instrument. A person ...
s, though
electronic tuner In music, an electronic tuner is a device that detects and displays the pitch of musical notes played on a musical instrument. "Pitch" is the perceived fundamental frequency of a musical note, which is typically measured in hertz. Simple tune ...
s have largely replaced them. Forks can be driven electrically by placing
electronic oscillator An electronic oscillator is an electronic circuit that produces a periodic, oscillating or alternating current (AC) signal, usually a sine wave, square wave or a triangle wave, powered by a direct current (DC) source. Oscillators are found ...
-driven
electromagnet An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire (likely copper) wound into a electromagnetic coil, coil. A current through the wire creates a magnetic ...
s close to the prongs.


In musical instruments

A number of
keyboard Keyboard may refer to: Text input * Keyboard, part of a typewriter * Computer keyboard ** Keyboard layout, the software control of computer keyboards and their mapping ** Keyboard technology, computer keyboard hardware and firmware Music * Mus ...
musical instruments use principles similar to tuning forks. The most popular of these is the
Rhodes piano The Rhodes piano (also known as the Fender Rhodes piano) is an electric piano invented by Harold Rhodes, which became popular in the 1970s. Like a conventional piano, the Rhodes generates sound with keys and hammers, but instead of strings, th ...
, in which hammers hit metal tines that vibrate in the magnetic field of a pickup, creating a signal that drives electric amplification. The earlier, un-amplified
dulcitone A dulcitone is a keyboard instrument in which sound is produced by a range of tuning forks, which vibrate when struck by felt-covered hammers activated by the keyboard. The instrument was designed by Thomas Machell of Glasgow in the 1860s, at the ...
, which used tuning forks directly, suffered from low volume.


In clocks and watches

The
quartz crystal Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical fo ...
that serves as the timekeeping element in modern
quartz clock Quartz clocks and quartz watches are timepieces that use an electronic oscillator regulated by a quartz crystal to keep time. The crystal oscillator, controlled by the resonant mechanical vibrations of the quartz crystal, creates a signal with ...
s and
watch A watch is a timepiece carried or worn by a person. It is designed to maintain a consistent movement despite the motions caused by the person's activities. A wristwatch is worn around the wrist, attached by a watch strap or another type of ...
es is in the form of a tiny tuning fork. It usually vibrates at a frequency of 32,768 Hz in the
ultrasonic Ultrasound is sound with frequencies greater than 20 kilohertz. This frequency is the approximate upper audible limit of human hearing in healthy young adults. The physical principles of acoustic waves apply to any frequency range, includi ...
range (above the range of human hearing). It is made to vibrate by small oscillating voltages applied by an
electronic oscillator An electronic oscillator is an electronic circuit that produces a periodic, oscillating or alternating current (AC) signal, usually a sine wave, square wave or a triangle wave, powered by a direct current (DC) source. Oscillators are found ...
circuit to metal electrodes plated on the surface of the crystal. Quartz is
piezoelectric Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied stress (mechanics), mechanical s ...
, 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 Bulova is an American luxury timepiece manufacturing company that was founded in 1875 in New York City. Formally the Bulova Watch Company, it makes watches, clocks and accessories. History Founding Bulova was founded and incorporated as the J ...
beginning in 1960, used a 360-
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in ter ...
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

Alternatives to the common A=440 standard include philosophical or scientific pitch with standard pitch of C=512. According to
Rayleigh Rayleigh may refer to: Science *Rayleigh scattering *Rayleigh–Jeans law *Rayleigh waves *Rayleigh (unit), a unit of photon flux named after the 4th Baron Rayleigh *Rayl, rayl or Rayleigh, two units of specific acoustic impedance and characte ...
, physicists and acoustic instrument makers used this pitch. The tuning fork John Shore gave to
George Frideric Handel George Frideric (or Frederick) Handel ( ; baptised , ; 23 February 1685 – 14 April 1759) was a German-British Baroque composer well-known for his operas, oratorios, anthems, concerti grossi, and organ concerti. Born in Halle, Germany, H ...
produces C=512. 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 The Weber test is a screening test for hearing performed with a tuning fork. It can detect Unilateral hearing loss, unilateral (one-sided) conductive hearing loss (middle ear hearing loss) and unilateral sensorineural hearing loss (inner ear he ...
and
Rinne test The Rinne test ( ) is used primarily to evaluate loss of hearing in one ear. It compares perception of sounds transmitted by air conduction to those transmitted by bone conduction through the mastoid. Thus, one can quickly screen for the presence ...
, respectively. Lower-pitched ones, usually at C128, are also used to check vibration sense as part of the examination of the peripheral nervous system.
Orthopedic surgeons Orthopedic surgery or orthopedics ( alternative spelling orthopaedics) is the branch of surgery concerned with conditions involving the musculoskeletal system. Orthopedic surgeons use both surgical and nonsurgical means to treat musculoskeletal ...
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 The periosteum is a membrane that covers the outer surface of all bones, except at the articular surfaces (i.e. the parts within a joint space) of long bones. (At the joints of long bones the bone's outer surface is lined with "articular cartila ...
of the bone vibrates and fires
nociceptor A nociceptor (; ) is a sensory neuron that responds to damaging or potentially damaging stimuli by sending "possible threat" signals to the spinal cord and the brain. The brain creates the sensation of pain to direct attention to the body part, ...
s (pain receptors), causing a local sharp pain. 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. 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 ''BMJ Open'' is a peer-reviewed open access medical journal that is dedicated to publishing medical research from all disciplines and therapeutic areas. It is published by BMJ and considers all research study types, from protocols through phase I ...
suggests that this technique is not reliable or accurate enough for clinical use.


Non-medical and non-scientific uses

Tuning forks also play a role in several alternative therapy practices, such as sonopuncture and polarity therapy.


Radar gun calibration

A
radar gun A radar speed gun, also known as a radar gun, speed gun, or speed trap gun, is a device used to measure the speed of moving objects. It is commonly used by police to check the speed of moving vehicles while conducting Traffic police, traffic enf ...
that measures the speed of cars or a ball in sports is usually calibrated with a tuning fork. 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 and various types of
microelectromechanical systems MEMS (micro-electromechanical systems) is the technology of microscopic devices incorporating both electronic and moving parts. MEMS are made up of components between 1 and 100 micrometres in size (i.e., 0.001 to 0.1 mm), and MEMS devices ...
.


Level sensors

Tuning fork forms the sensing part of vibrating 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. 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 In music, an electronic tuner is a device that detects and displays the pitch of musical notes played on a musical instrument. "Pitch" is the perceived fundamental frequency of a musical note, which is typically measured in hertz. Simple tune ...
*
Pitch pipe A pitch pipe is a small device (type of tuning Harmonica) used to provide a pitch reference for musicians. Although it may be described as a musical instrument, it is not typically used to play music as such. Origins The earliest pitch pipes ...
*
Savart wheel The Savart wheel is an acoustical device named after the French physicist Félix Savart (1791–1841), which was originally conceived and developed by the English scientist Robert Hooke (1635–1703). A card held to the edge of a spinning toot ...
*
Tonometer Tonometry is the procedure that eye care professionals perform to determine the intraocular pressure (IOP), the fluid pressure inside the eye. It is an important test in the evaluation of patients at risk from glaucoma. Most tonometers are calib ...


References


External links


Onlinetuningfork.com
an online tuning fork using
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. * * {{DEFAULTSORT:Tuning Fork 1711 introductions Musical instrument parts and accessories Idiophones Acoustics Sound