Editing Tuning fork (section)

==Calculation of frequency==
The frequency of a tuning fork depends on its dimensions and what it is made from: <ref>{{cite journal |doi=10.1006/jsvi.1999.2257 |title=Dynamics of Transversely Vibrating Beams Using Four Engineering Theories |year=1999 |last1=Han |first1=Seon M. |last2=Benaroya |first2=Haym |last3=Wei |first3=Timothy |journal=Journal of Sound and Vibration |volume=225 |issue=5 |pages=935–988|bibcode=1999JSV...225..935H |s2cid=121014931 }}</ref>

: <math>f = \frac{N}{2\pi L^2} \sqrt\frac{EI}{\rho A},</math>

where
: {{mvar|f}} is the [[frequency]] the fork vibrates at, ([[SI units]]: 1/s)
: {{math|{{mvar|N}}}}&nbsp;≈&nbsp;3.516015 is the square of the smallest positive solution to {{math|[[cosine|cos]](''x'')[[hyperbolic cosine|cosh]](''x'') {{=}} −1}},<ref>{{cite web | url=http://emweb.unl.edu/Mechanics-Pages/Scott-Whitney/325hweb/Beams.htm | title=Vibrations of Cantilever Beams: Deflection, Frequency, and Research Uses | last=Whitney | first=Scott | publisher=University of Nebraska–Lincoln | date=1999-04-23 | access-date=2011-11-09 }}</ref> which arises from the boundary conditions of the prong’s cantilevered structure.
: {{mvar|L}} is the length of the prongs, (m)
: {{mvar|E}} is the [[Young's modulus]] (elastic modulus or stiffness) of the material the fork is made from, (Pa or N/m<sup>2</sup> or kg/(ms<sup>2</sup>))
: {{mvar|I}} is the [[second moment of area]] of the cross-section, (m<sup>4</sup>)
: {{mvar|ρ}} is the [[density]] of the fork's material (kg/m<sup>3</sup>), and
: {{mvar|A}} is the cross-sectional [[area]] of the prongs (tines) (m<sup>2</sup>).

The ratio {{math|''I''/''A''}} in the equation above can be rewritten as {{math|''r''<sup>2</sup>/4}} if the prongs are cylindrical with radius {{mvar|r}}, and {{math|''a''<sup>2</sup>/12}} if the prongs have rectangular cross-section of width {{mvar|a}} along the direction of motion.