Sound waves are reflected at the ends of a narrow, closed, or open pipe when they are sent down the air column, with no phase reversal at the open end and phase reversal at the closed end. Under the proper circumstances, interference between the incident and reflected waves produces stationary waves in the air column. As a result, the open end of the stationary waves has an antinode.
At an open end, however, the longitudinal waves are reflected slightly outside the pipe’s rim because the air molecules in the plane of the open end are not completely free to move in all directions. End correction is the measurement of the antinode’s separation from the pipe’s open end. Reynolds calculated that the antinode’s separation from the rim was about 30% of the pipe’s inner diameter. In order to calculate the wavelength of sound accurately, this distance must be taken into consideration. The end correction is the term used to describe this distance.
Therefore, the measured length of the pipe must be increased by an end correction of e 0.3 d for each open end if d is the inner diameter of a cylindrical pipe. If l is the measured length, then the air column’s effective length is l+0.3 d for a pipe that is closed at one end and l+0.6 d for a pipe that is open at both ends.