Tuning fork (cylindrical prongs)

Description

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 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 frequency of a tuning fork depends on its dimensions and the material from which it is made. If the prongs are cylindrical the frequency of the tuning fork is related to the length of the radius of the cylinder section.
(Note:1.875 is the smallest positive solution of
cos(x)cosh(x) = -1)

Related formulas

Variables

fFrequency the fork vibrates (hertz)
πpi
lLength of the prongs (m)
rRadius circle of the cylinder's section (m)
E Young's modulus of the material the fork is made from (Pa)
ρDensity of the material the fork is made from (kg/m3)