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 (tines) 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.
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