Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Tuning Fork

Tuning Fork

Gist

A Tuning fork is a narrow, two-pronged steel bar that when tuned to a specific musical pitch retains its tuning almost indefinitely. It was apparently invented by George Frideric Handel’s trumpeter John Shore shortly before Shore’s death in 1752.

Because it produces a nearly pure tone (without overtones), it is useful in experimental study of the physics of sound. It has also been used in musical instruments—e.g., the dulcitone, or typophone, a set of graduated tuning forks struck by felt hammers by means of a keyboard mechanism.

Summary

Tuning forks, typically aluminum, consist of a stem (handle) and two prongs that form a U-shaped fork. The tuning fork vibrates at a set frequency after being struck on the heel of the hand and is used to assess vibratory sensation and hearing (air conduction and bone conduction). Hold the tuning fork by the stem, not the prongs. Tuning forks are available in a wide range of frequencies (64 Hz to 4096 Hz); 128 Hz is a commonly used frequency for screening.

Rinne test

After setting the tuning fork (usually C2 = 512 Hz) in vibration, its stem is placed on the mastoid process. The patient is asked to report when s/he can no longer hear the tone. Then, the fork is placed close to the concha on the same side, while ensuring that the prongs are parallel to the axis of the ear canal. The patient is asked whether the tone can still be heard. If so, the result of the test is “positive,” indicating that either the patient's hearing on this side is normal, or that the patient has a sensorineural hearing loss. In the latter case both bone conduction and air conduction times are shortened, and the result of the test is described as “small positive.” If the patient does not hear the tone, the test should be repeated in reverse order – first, the tuning fork should be placed close to the concha, and once the patient can no longer hear the tone, its position has to be changed to the mastoid process on the same side. If the time of hearing the pure tone emitted by the tuning fork through the bone is longer than through the air, the result is “negative.” This indicates a conductive hearing loss in the ear on the tested side. The same procedure is repeated for the opposite ear.

Details

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. 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 trumpeter and lutenist 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, with most of the vibrational energy at the fundamental frequency. The reason for this is that the frequency of the first overtone is about

  times the fundamental (about 2+1⁄2 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 the oscillation. That is because its principal 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 (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 (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). 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. Bone conduction using a tuning fork is specifically used in the Weber and Rinne tests 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, 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 that 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 = 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 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 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.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.