tuning fork

The frequency of a tuning fork depends on its dimensions and what it is made from. Using the Euler-Bernoulli beam model, the fundamental frequency of the tuning fork is: • f = \frac{\alpha^2}{2\pi L^2} \sqrt\frac{EI}{\rho A}, where • is the frequency the fork vibrates at, (SI units: Hz or 1/s) • α ≈ is the smallest positive real solution to cos(&alpha)cosh(&alpha) −1, which arises from the boundary conditions of the prong's cantilevered structure. • is the length of the prongs, (m) • is the Young's modulus (elastic modulus or stiffness) of the material the fork is made from, (Pa or N/m 2 or kg/(ms 2)) • is the second moment of area of the cross-section, (m 4) • is the density of the fork's material (kg/m 3), and • is the cross-sectional area of the prongs (tines), (m 2). The ratio in the equation above, where is the radius of gyration for the prongs, 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.

Tuning forks have traditionally been used to tune musical instruments, though electronic tuners have largely replaced them. Forks can be driven electrically by placing electronic oscillator-driven electromagnets close to the prongs.

A number of keyboard musical instruments use principles similar to tuning forks. The most popular of these is the Rhodes piano, 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, which used tuning forks directly, suffered from low volume.

• Illustration — Quartz crystal resonator from a modern quartz watch, formed in the shape of a tuning fork. It vibrates at 32,768 Hz, in the ultrasonic range. • Illustration — A Bulova Accutron watch from the 1960s, which uses a steel tuning fork (visible in center) vibrating at 360 Hz. 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 by an electronic oscillator circuit to metal electrodes plated on the surface of the crystal. Quartz is piezoelectric, 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 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 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.

• Illustration — 1 kHz tuning fork vacuum tube oscillator used by the U.S. National Bureau of Standards (now NIST) in 1927 as a frequency standard. Alternatives to the common A=440 standard include philosophical or scientific pitch with standard pitch of C=512. According to Rayleigh, physicists and acoustic instrument makers used this pitch. The tuning fork John Shore gave to George Frideric Handel 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 and Rinne test, 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 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 of the bone vibrates and fires nociceptors (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 suggests that this technique is not reliable or accurate enough for clinical use.

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

A radar gun 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.

Doubled and H-type tuning forks are used for tactical-grade Vibrating Structure Gyroscopes and various types of microelectromechanical systems.

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.