Pictures from the history of otorhinolaryngology, presented by instruments from the collection of the Ingolstadt German Medical History Museum". I: Invention of the tuning fork, its course in music and natural sciences. The ratio I/A in the equation above can be rewritten as r 2/4 if the prongs are cylindrical with radius r, and a2/12 if the prongs have rectangular cross-section of width a along the direction of motion. Ρ = density of the fork's material (kg/m 3), andĪ = cross-sectional area of the prongs (tines) (m 2). I = second moment of area of the cross-section, (m 4) N ≈ 3.516015 is the square of the smallest positive solution to cos(x)cosh(x) = −1, which arises from the boundary conditions of the prong’s cantilevered structure.Į = Young's modulus (elastic modulus or stiffness) of the material the fork is made from, (Pa or N/m 2 or kg/(ms 2)) Note:1.875 is the smallest positive solution ofį = frequency the fork vibrates at, (SI units: 1/s) (hertz) If the prongs are cylindrical the frequency of the tuning fork is related to the length of the radius of the cylinder section. It is frequently used as a standard of pitch to tune musical instruments.The frequency of a tuning fork depends on its dimensions and the material from which it is made. The pitch that a particular tuning fork generates depends on the length and mass of the two prongs. 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. Tuning fork (cylindrical prongs) Equation and CalculatorĪ 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). Related Resources: calculators Tuning Fork Formulae and Calculator
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