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End Correction for Sound Waves in Half Open Pipe

When a standing sound waves forms in a pipe, a standing wave is formed when an antinode occurs at the open end. Actually, this is not quite true. The antinode is not AT the open end, but a short way outside it. It is important to eliminate the error caused because the antinode is not at the open end of the pipe.

We can eliminate the error correction using the fact that the antinode is the same distance beyond the open end whatever the wavelength of the standing wave in the pipe.

Take two pipes and change the lengths of the pipes so that resonance occurs for the same frequency at two different lengthandcorresponding to the fundamental and first overtone respectively.

From the first diagram above, (1)

From the second diagram above, (2)

(2)-(1) gives

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