In physics, end correction is the anomal difference between the frequency of a tuning fork

Tuning fork

A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs formed from a U-shaped bar of elastic metal . 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...

 and the corresponding sound waves inside of a tube. It is caused because generally there is space between the fork and the pipe end, causing the air column to vibrate a short distance beyond the edge of the tube.

A theoretical basis for computation of the end correction is the radiation acoustic impedance

Acoustic impedance

The acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given air vibration at that frequency. The acoustic impedance Z is frequency dependent and is very useful, for example, for describing the behaviour of musical wind instruments...

 of a circular piston

Piston

A piston is a component of reciprocating engines, reciprocating pumps, gas compressors and pneumatic cylinders, among other similar mechanisms. It is the moving component that is contained by a cylinder and is made gas-tight by piston rings. In an engine, its purpose is to transfer force from...

. This impedance represents the ratio of acoustic pressure

Sound pressure

Sound pressure or acoustic pressure is the local pressure deviation from the ambient atmospheric pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water...

 at the piston, divided by the flow rate

Volumetric flow rate

The volumetric flow rate in fluid dynamics and hydrometry, is the volume of fluid which passes through a given surface per unit time...

 induced by it. The air speed

Airspeed

Airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are: indicated airspeed , calibrated airspeed , true airspeed , equivalent airspeed and density airspeed....

 is typically assumed to be uniform across the tube end. This is a good approximation, but not exactly true in reality, since air viscosity

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 reduces the flow rate in the boundary layer

Boundary layer

In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface where effects of viscosity of the fluid are considered in detail. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by diurnal...

 very close to the tube surface. Thus, air column inside the tube is loaded by the external fluid due to sound energy radiation

Acoustic radiation pressure

Acoustic radiation pressure is the apparent pressure difference between the average pressure at a surface moving with the sound displacements and the pressure that would have existed in the fluid of same mean density at rest...

. This requires an additional length to be added to the regular length for calculating the natural frequency of the pipe system.