Question

Formation of standing waves in closed organ pipe

Answer 1

The pipe is open to the air (at fixed background/equilibrium pressure) so that there must be a pressure node at the open end. Pressure and displacement are  out of phase, so that the open end is also a displacement antinode.

Actually, the air pressure in the standing wave doesn't instantly equalize with the background pressure at an open end - it sort of ``bulges'' out of the pipe a bit. The displacement antinode is therefore just outsidethe pipe end, not at the pipe end. You may still draw a displacement antinode (or pressure node) as if they occur at the open pipe end; just remember that the distance from the open end to the first displacement node is not a very accurate measure of a quarter wavelength and that open organ pipes are a bit ``longer'' than they appear from the point of view of computing their resonant harmonics.

Answer 2

Answer:

The pipe is open to the air (at fixed background/equilibrium pressure) so that there must be a pressure node at the open end. Pressure and displacement are  out of phase, so that the open end is also a displacement antinode.

Actually, the air pressure in the standing wave doesn't instantly equalize with the background pressure at an open end - it sort of ``bulges'' out of the pipe a bit. The displacement antinode is therefore just outsidethe pipe end, not at the pipe end. You may still draw a displacement antinode (or pressure node) as if they occur at the open pipe end; just remember that the distance from the open end to the first displacement node is not a very accurate measure of a quarter wavelength and that open organ pipes are a bit ``longer'' than they appear from the point of view of computing their resonant harmonics.

Explanation: