A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs
formed from a U-shaped bar of elastic metal. 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 and mass of the two prongs.
It is frequently used as a standard of pitch to tune musical instruments.
The tuning fork was invented in 1711 by British musician John Shore, Sergeant Trumpeter and
Lutenist to the court.
Description
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, and little at the overtones. The reason for this is that the frequency of the
first overtone is about 52/22 = 25/4 = 6¼ times the fundamental. By comparison, the
first overtone of a vibrating string or metal bar 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 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, which amplifies the sound
of the fork. The fork is usually struck, and then the handle is pressed against a wooden
box resonator, or a table top. Without the resonator 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. Although commercial tuning forks are normally
tuned to the correct pitch at the factory, 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, because this is the standard concert pitch, which is used as tuning
note by some orchestras, it being the pitch of the violin's second string, the first string
of the viola, and an octave above the first string of the cello, all played open. Tuning
forks used by orchestras between 1750 and 1820 mostly had a frequency of A = 423.5 Hz,
although there were many forks and many slightly different pitches. Standard tuning forks are
available that vibrate at all the 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. The pitch of a tuning fork can vary slightly
with weathering and temperature. A change in frequency of one vibration in 21,000 for
each °F change is typical for a steel tuning fork, flattened by heat and sharpened by cold.
The standard temperature is now 68 °F but 59 °F is an older standard. The pitches
of a musical instrument such as an organ are also subject to variation with temperature
change. Calculation of frequency
The frequency of a tuning fork depends on its dimensions and the material from which
it is made:
Where: f is the frequency the fork vibrates at in
Hertz. 1.875 the smallest positive solution of cos(x)cosh(x)
= -1. 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.
I is the second moment of area of the cross-section in metres to the fourth power.
ρ is the density of the material the fork is made from in kilogrammes per cubic metre.
A is the cross-sectional area of the prongs in square metres.
The ratio in the equation above can be rewritten as if the prongs are cylindrical of radius
r, and if the prongs have rectangular cross-section of width a along the direction of motion.
Uses
Forks have traditionally been used to tune musical instruments, although electronic tuners
are replacing them in many applications. 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 and uses electric amplification
of the generated sound. The earlier, unamplified dulcitone used tuning forks directly; it suffered
from faintness of volume.
In clocks and watches The quartz crystal that serves as the timekeeping
element in modern quartz clocks and watches is in the form of a tiny tuning fork. It usually
vibrates at a frequency of 32,768 Hz in the ultrasonic range, above the range of human
hearing. It is made to vibrate by small oscillating voltages applied to metal electrodes plated
on the surface of the crystal, by an electronic oscillator circuit. Quartz is piezoelectric,
so the voltage causes the fork tines to bend rapidly back and forth.
The Accutron, an electromechanical watch developed by Max Hetzel 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 allowed it to achieve greater
accuracy than conventional balance wheel watches. The humming sound of the tuning fork could
be heard when the watch was held to the ear. Medical and scientific uses
An alternative to the usual A440 diatonic scale is that of philosophical or scientific
pitch with standard pitch of C512. According to Rayleigh, the scale was used by physicists
and acoustic instrument makers. The tuning fork that John Shore gave to Handel gives
a pitch of C512. 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 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 for which they are calibrated.
In gyroscopes Doubled and H-type of tuning forks are used
for tactical-grade Vibrating Structure Gyroscopes like QuapasonTM and different types of MEMS.
See also Electronic tuner
Pitch pipe Savart wheel
Weber test Rinne test
References
External links Onlinetuningfork.com, an online tuning fork
using Macromedia Flash Player. Usneurologicals.com, numerous examples of
medical uses of tuning forks.