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Suppose that I have an air column with closed-open boundary condition. The air pressure at the open end of the tube is constrained to match the atmospheric pressure of the surrounding air. Therefore, an open end of an air column is required to be a displacement antinode.

But why do we say that the antinode is actually just outside the open end (from the Textbook by Knight), not exactly at the open end?

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Actually it has been observed by experiment that the actual antinode of an air column with closed-open boundary condition is actually just outside the open end, not exactly at the open end. We do not consider the effects of viscosity of air and the radiation acoustic impedance of the open end of the pipe. Hence an end correction is applied to compensate for this error.

Quoting from wikipedia below;

A theoretical basis for computation of the end correction is the radiation acoustic impedance of a circular piston. This impedance represents the ratio of acoustic pressure at the piston, divided by the flow rate induced by it. The air speed is typically assumed to be uniform across the tube end. This is a good approximation, but not exactly true in reality, since air viscosity reduces the flow rate in the boundary layer very close to the tube surface. Thus, air column inside the tube is loaded by the external fluid due to sound energy radiation. This requires an additional length to be added to the regular length for calculating the natural frequency of the pipe system.

Hope this helps..

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