End correction

In acoustics, end correction is a short distance added to the length of a resonance pipe, in order to calculate the precise resonant frequency of the pipe. Whenever a wave forms through a medium/object (such as an organ pipe) with a closed/open end, the wave may form incorrectly, i.e., it may not actually start from the opening of the object but instead before the opening, producing an error when studying it theoretically. Hence an end correction is sometimes required to appropriately study its properties. The end correction depends on the radius of the object.

An acoustic pipe, such as an organ pipe, marimba, or flute resonates at a specific pitch or frequency. Longer pipes resonate at lower frequencies, producing lower-pitched sounds. In an ideal tube, the wavelength is directly proportional to the length of the tube. A tube that is open at one end and closed at the other produces sound with a wavelength equal to four times the length of the tube. A tube that is open at both ends produces sound whose wavelength is twice the length of the tube. Thus, when a Boomwhacker with two open ends is capped at one end, the pitch goes down by one octave.

The analysis above applies only to a tube of zero diameter. When designing an organ or Boomwhacker, the diameter of the tube must be taken into account. The pitch of a real tube is lower than the pitch predicted by the theory. A finite diameter pipe acts acoustically as though it were somewhat longer than its physical length.