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's made from: where is the frequency the fork vibrates at, (SI units: 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 (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 of the cross-section, (m4) is the density of the fork's material (kg/m3), and is the cross-sectional area 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 instruments, though electronic tuners have largely replaced them. Forks can be driven electrically by placing electronic oscillator-driven electromagnets close to the prongs. In musical instruments 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. 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 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