Why does an antinode form at the open end of an organ pipe?

I recently learnt about reflection of waves in various media and the resultant standing waves formed. In a string which is tied at an end, the wave formed reflects with a phase difference of 180 (at the end) and therefore, the incident and reflected wave interfere destructively (at the end) and therefore, a node is formed (at the end). Now, in a string which is free at one end, the wave reflects with 0 phase difference and so the incident and reflected wave interfere constructively to form an antinode at the end.

Now, in organ pipes I have studied that the wave reflects with 180 degrees phase difference at the open end and 0 degrees phase difference at the closed end. However, an antinode forms at the open end and a node forms at the closed end Now, this is same as string but the phase differences involved in reflection are different, and it cannot be explained using the reasoning for the string.

So, how is the antinode formation in an organ pipe explained?

• This is possibly a misunderstanding: could you provide references to the sources making these claims (about the strings and about the pipes)? May 18, 2022 at 7:32
• – user329235
May 18, 2022 at 7:34
• German Wikipedia: "despite long research efforts, the formation of sounds in [wood]wind instrument is not yet fully understood" May 18, 2022 at 7:35

There are two ways of describing a sound wave.

As a (variation of displacement) wave and as a (variation of) pressure wave.

You will note that there is a $$\pi/2$$ phase difference between these two descriptions.

When considering displacement the incident and reflected waves are in phase and an antinode is formed at the open end, whereas when considering pressure the incident and reflected waves are $$\pi$$ out of phase and a node is formed.

• So does that mean that the phase difference after reflection from the open end of the organ pipe is 0 degrees?
– user329235
May 18, 2022 at 7:46
• Yes, for the displacement wave. May 18, 2022 at 7:50

I think you may be a bit confused. For both string and tube, a closed end should give a node and an open end an antinode.

You may be mixing up displacement and pressure (or force). A node for displacement means an antinode for pressure (or force) and vice versa.

Open end allows for maximum displacement and minimal force (for string) or pressure (for pipe). Closed end is the opposite.

• See the updated question please...
– user329235
May 18, 2022 at 7:41