I Sound Frequency & Pipe Wall Thickness

[Daimion]

TL;DR Summary

Why, when striking an open tube, a thicker walled tube produces a higher frequency than a thinner walled tube?

We have 2 open metal tubes, made of Stainless Steel. They both are the same length of 1 metre, and and Outer Diameter of 76mm. One pipe has a wall thickness of 1.5mm, and the other has a wall thickness of 2.0mm.

It was our reasonable guess that the tube with 2.0mm wall thickness, should producing a lower frequency. However, when we strike it, it actually produces a higher frequency than the one with 1.5mm wall thickness.

Why is that?

One consideration we had - since they both had the same Outer Diameter, the volume of air inside the tube with a thicker wall is less, and affects the frequency somehow to make it higher?

An extended question, would this "thicker wall = higher frequency" pattern have the same effect in a pipe organ? The difference that the frequency is produced by the moving air vs the vibration of the tube walls.

Thanks! Really hoping to understand wall thickness vs frequency effect better.

[Edit] I've taken a video to show clearly the sound difference between the two pipes, if that helps.

 

[Baluncore]

Welcome to PF.

There are two things happening.
Firstly; the mass of the thicker wall tube will reduce the frequency.
Secondly; the elasticity of the metal will produce a greater restoring force from the thicker wall tube, that will raise the frequency.

You must find an expression for the resonant frequency of the tube to identify which effect will be the greater.

I would want to know if the stainless steel alloy used to make the tubes was identical.
There is also a possibility that a different heat treatment, or the age of the tubes, causes a difference to the restoring force.

 

[Daimion]

Welcome to PF.

There are two things happening.
Firstly; the mass of the thicker wall tube will reduce the frequency.
Secondly; the elasticity of the metal will produce a greater restoring force from the thicker wall tube, that will raise the frequency.

You must find an expression for the resonant frequency of the tube to identify which effect will be the greater.

I would want to know if the stainless steel alloy used to make the tubes was identical.
There is also a possibility that a different heat treatment, or the age of the tubes, causes a difference to the restoring force.

Thanks for help, and yes, my understanding was that the thicker wall should reduce the frequency, yet it seems the reverse. As for materials, both pipes are made the same and from 304 stainless steel.

I've captured it on video, both with the pipes standing upright on the floor, and laid on my bed sideways (so it is open at both end).

When standing on the floor, the tube on the right is 2mm thick, and the tube on the left is 1.5mm
When laying down, the tube on the left is 2mm thick, and the tube on the right is 1.5mm

 

[Baluncore]

Video unavailable
This video is private

 

[Daimion]

Video unavailable
This video is private

My mistake, have made it viewable now

 

[Arjan82]

There was someone that posted a question about tube resonances and why the thick walled tube had a higher frequency. But it is gone?!? Anyway, I'm stubborn (and actually put some effort in the answer), so here is my answer anyway:

Question:
A tube with outer diameter of 76mm and length of 1m is hit, why does the tube with wall 2mm have a higher frequency than the one with 1.5mm diameter. How does this relate to a pipe organ.I've done a very quick FEM modal analysis. I think the deformation mode for sound is not a bending motion but rather something like below, where the wall of the pipe is deformed. In the solution below the 2mm wall has a significantly higher eigenfrequency than the 1.5mm thick wall. So stiffness wins from mass in this case.

Also, a pipe in a pipe organ is a helmholtz resonator. This is all air that is moving, not the pipes themselves. This means that thickness should not have an influence there.

1.5mm thick:

2mm thick: