End Correction for Pipe Open at Both Ends

The antinodes of a sound vibration in an open pipe are situated just outside the pipe. This means the wavelength of a sound wave in an open pipe is slightly longer than would be implied by considering just the length of the pipe. If the wavelength is to be calculated this factor must be taken into account. We can do this by varying the length of the pipe to find the lengthsandof the pipe for the first two maxima. The distance of the antinode outside the open end is the same for each vibration.

For the maximum in the first diagram above,and for the second vibration,

Subtracting these gives

Hence