how is the frequency of a tuning fork decided
Answers
Answer:
The frequency of a tuning fork depends on its dimensions and what it's made from:[7]
{\displaystyle f={\frac {1.875^{2}}{2\pi l^{2}}}{\sqrt {\frac {EI}{\rho A}}}}{\displaystyle f={\frac {1.875^{2}}{2\pi l^{2}}}{\sqrt {\frac {EI}{\rho A}}}}
where:
f is the frequency the fork vibrates at in hertz.
1.875 is the smallest positive solution of cos(x)cosh(x) = −1.[8]
l is the length of the prongs in metres.
E is the Young's modulus (elastic modulus or stiffness) 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 kilograms per cubic metre.
A is the cross-sectional area of the prongs (tines) in square metres.
The ratio
I
/
A
in the equation above can be rewritten as
r2
/
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.