Why are the nodes of an open tubular bell located at .224*L instead of .25*L?

Say that we have a tube of length $L$. In the tube, there is a standing wave of wavelength $\lambda$. Then, $L=\lambda$.

$\hspace{2.5cm}$

In the above diagram, the wave's amplitude is highest at the ends and center of the tube. The wave has two nodes of with zero amplitude on either side of the middle of the tube.

I would expect these nodes to be at exactly 1/4 of the tube's length from each end. Beginning at the left side of the tube: If the tube contains one whole wavelength, then the first $90{}^{\circ}$ of the wave should bring the wave from the maximum down to zero. The next $90{}^{\circ}$ should take the wave to the minimum at the center of the tube, and so on. Dividing the wavelength into four equal parts should make these locations occur at even intervals, or at even quarters of the tube's length, $L$. Correct?

However, I have built tubular bells in the past. In all of the literature (and in experience), the correct locations for these node points is $0.224L$, rather than $0.25$. Would someone mind explaining this?

• Related: physics.stackexchange.com/q/214330/2451 and links therein. Apr 22, 2018 at 2:46
• Yes, the exact value of the end correction depends on the diameter.
– user137289
Apr 22, 2018 at 7:31
• You mention tubular bells (not organ pipes) Is this question about the resonant/standing wave in the gas inside the tube or the resonant wave in the tube material. The tones of wind chimes and tubular bells come primarily from the wave in the material. May 5, 2021 at 12:22