The frequency of a tuning fork depends on its dimensions and the material from which is made:
, and, if the prongs are cylindrical,
Where:
* f is the frequency the fork vibrates at in hertz.
* A is the cross-sectional area of the prongs (tines) in square metres.
* 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.
* ρ is the density of the material the fork is made from in kilogrammes per cubic metre.
* R is the radius of the prongs in metres
The tuning fork was invented by Handel’s trumpeter, John Shore, in 1712 as
a small, portable standard of pitch to substitute for the pitch pipe. Since then
tunning forks have become familiar especially to musicians and physicists.
The frequency of vibration of a tuning fork in its fundamental mode
(principal symmetrical in-plane mode) is given by the equation:
f = (0.162t/L2) v
where f is the frequency (in Hz), t is the thickness of the tuning fork prongs in the
direction of movement, L is the length of the prongs, and v is the velocity of sound
in metal (for steel 5250 m/s, brass 3500 m/s, aluminum 5150 m/s, copper 3650
m/s, tin 2730 m/s, tungsten 4320 m/s). Most tuning forks used in general physics
labs are made of aluminum.
When the tuning fork is fixed at its base, the second possible (symmetrical
in-plane) mode of vibration (sometimes called the “clang tone”) is a high-pitched
(6.26 f) tone which is usually decays away fairly rapidly as compared to the
normal, the fundamental f. In fact, the modes of vibration of a tuning fork can be
classified into four groups: (1) symmetrical modes in the plane of the fork (2)
antisymmetrical modes in the plane, (3) symmetrical modes out of the plane, (4)
antisymmetrical modes out of the plane. The relative amplitudes of excitation of
various modes depend upon where the tuning fork is struck. Striking near a node
provides the least excitation for a given mode, while striking near an antinode
generally excites the mode strongly.