Tuning fork

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 after waiting a moment to allow some high overtones to die out. The pitch that a particular tuning fork generates depends on the length of the two prongs. Its main use is as a standard of pitch to tune other musical instruments.

Explanation

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

The tuning fork was invented in 1711 by British musician John Shore, Sergeant Trumpeter to the court, who had parts specifically written for him by both George Frideric Handel and Henry Purcell.

The main reason for using the fork shape is that it produces a very pure tone, with most of the vibrational energy at the fundamental frequency, and little at the overtones (harmonics), as is the case with other resonators. 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). By comparison, the first overtone of a vibrating string is only one octave above the fundamental. So when the fork is struck, little of the energy goes into the overtone modes; they also die out correspondingly faster, leaving the fundamental. 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, allowing the fork to be held by the handle without damping the vibration, but it allows the handle to transmit the vibration to a resonator (like the hollow rectangular box often used), which amplifies the sound of the fork. Without the resonator (which may be as simple as a table top to which the handle is pressed), the sound is very faint. The reason for this is that the sound waves produced by each fork 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 heard will actually increase, due to a reduction of this cancellation.

Currently, the most common tuning fork used by musicians sounds the note of A (440 Hz, international "concert pitch"), which is used as a standard tuning note by orchestras, it being the pitch of the violin's second string played open, the first string of the viola played open, and an octave above the first 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. Well-known manufacturers of tuning forks include Ragg and John Walker, both of Sheffield, England.

Calculation of frequency

The frequency of a tuning fork depends on its dimensions and the material from which is made:

$f\propto {\frac {1}{l^{2}}}{\sqrt {\frac {AE}{\rho }}}$, and, if the prongs are cylindrical, $f={\frac {R}{\pi l^{2}}}{\sqrt {\frac {E}{\rho }}}$

Where:

• f is the frequency the fork vibrates at in Hertz.
• A is the cross-sectional area of the prongs (tines) in square metres.
• l is the length of the prongs in metres.
• E is the Young's modulus of the material the fork is made from in pascals.
• ρ is the density of the material the fork is made from in kilogrammes per cubic metre.
• R is the radius of the prongs in metres

Uses

They are commonly used to tune musical instruments, although electronic tuners also exist, and some musicians have perfect pitch. Tuning forks can be tuned by removing material off the prongs (filing the ends to raise it or inside the base of the prongs to lower it) or by sliding weights attached to them. 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. Tuning forks can be driven electrically, by placing electromagnets close to the prongs that are attached to an electronic oscillator circuit, so that their sound does not die out.

In musical instruments

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.

In watches

The Accutron, an electromechanical watch developed by Max Hetzel for Bulova used a 360 Hertz steel tuning fork powered by a battery to make a mechanical watch keep time with great accuracy. The humming sound of the tuning fork could be heard when the watch was held to the ear.

The tiny quartz crystal used to keep time in modern quartz watches is also in the shape of a tuning fork. The piezoelectric properties of quartz cause the 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 $2^{15}=32,768$ Hz.

Medical uses

Main article: Hearing test

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.

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

Radar gun calibration

A radar gun, typically used for measuring the speed of cars or balls in sports, is usually calibrated with tuning forks. Instead of the frequency, these forks are labeled with the calibration speed and radar band (e.g. X-Band or K-Band) for which they are calibrated.

See also

• Pitch pipe
• Electronic tuner

External links

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