Changing the tone of a wind chime using slits or cuts

[twincam]

TL;DR Summary

may have the wrong thread but question is:
Is there a formula for changing the tone on a chime by making cuts along the length of the chime running towards the other end of the chime........usually what appears to be approximately 1/4 to 1/2 the length? This cut/cuts lowers the tone of the chime.

I am trying to fabricate a chime or pipe gong and I want it to have a very low, sustaining tone. In viewing retail products (specifically, Hamacher Schelemmer online catalog item # 90774) I have noticed some products have a slit cut along the partial length of the chime to lower the tone. Is there a formula to calculate the effect different lengths of cuts would have on the chime tone given a certain length and diameter? Does the location of the cuts make a difference? Width of the cuts? The pipe I am thinking about using is a 7' long x 4.5"diameter steel support pipe for a deck.

thank you

https://www.hammacher.com/product/deep-resonance-serenity-bell

 

[Nugatory]

Is there a formula to calculate the effect different lengths of cuts would have on the chime tone given a certain length and diameter?

The qualitative explanation for why the slits lower the tone is fairly straightforward: the mass of the air being vibrated is determined by the volume inside the cylinder while the force doing the vibration is determined by the tangential stiffness of the cylinder. The slits have the effect of reducing the stiffness while leaving the volume unchanged, reducing the frequency of the oscillation.

Mathematically this can be modeled as a simple harmonic oscillator, and the solution will show all the right qualitative dependencies. However, to get an exact quantitative solution you will also need a bunch of unknown parameters such as the exact numerical values of the stiffness and density of the cylinder material and how the stiffness varies with the lengths and widths of the slits. Thus I expect you won't be able to hit a precisely desired target frequency without a fair bit of trial and error.

 

[Nugatory]

The qualitative explanation for why the slits lower the tone is fairly straightforward: the mass of the air being vibrated is determined by the volume inside the cylinder while the force doing the vibration is determined by the tangential stiffness of the cylinder.

Although it occurs to me that that may not be the correct qualitative explanation... The oscillation may be driven by the mass of the metal components instead of the air in the cylinder, rather like a tuning fork. That doesn't change the basic harmonic oscillator behavior or the key property that larger slits reduce the stiffness, nor that it will take some experimentation to tune for an exact desired frequency.

 

[twincam]

Thank you. Think I will start with a .25% cut then go 1/2 that distance as a check. I assume the general result will be that longer cuts make for a deeper tone. Will be incremental as there may be a point of diminishing returns.

 

[berkeman]

Think I will start with a .25% cut then go 1/2 that distance as a check.

0.25% or 25%?

 

[Baluncore]

The cuts convert the tube into a tuning fork. The length of the cut sets the length and so the resonant frequency.
The cuts in the tube attenuate higher frequency modes of oscillation in the tube.

 

[sophiecentaur]

The cuts convert the tube into a tuning fork. The length of the cut sets the length and so the resonant frequency.
The cuts in the tube attenuate higher frequency modes of oscillation in the tube.

Very much so. What's needed is a high Q factor with long reverb time. An air column would not vibrate for long at all. Also, the tubes are pretty short - which would correspond to a high frequency range (as with a piccolo and kids penny whistle). Energy in the vibrating tube would be a lot higher than the energy in the air column, although the air column would act as a parasitic matching component. I'm thinking of a marimba in which the vibrating bar is matched to the surrounding air with an air column which would not define the note of the bar.
To get the best Q factor would be quite hard from theory but a hacksaw would let you get a fair result quite easily. Though think the width of the slot could count (damping), so a hacksaw blade may be thinner than optimum. Best to look at images to get the best idea.

PS Having said all that, not all wind chimes actually have a slot so where does that take us? Some strange vibrational mode of the metal wall?

 

[twincam]

Very helpful observations.
I think almost all chime like products I have seen have an assortment of mid to upper/tinkly tones and I am looking for a lone, single, low tone with a lot of duration.

Thanks to all.

 

[Baluncore]

I think almost all chime like products I have seen have an assortment of mid to upper/tinkly tones and I am looking for a lone, single, low tone with a lot of duration.

Then you must change the clapper position, and lengthen the tubes.
The clapper usually hangs part way down a string to the sail that is blown by, and swings in the wind. The clapper is usually deliberately arranged to hit the tubes a distance 22.4% from the top suspension point so as to excite higher frequency non-harmonic sounding chimes.
https://en.wikipedia.org/wiki/Wind_chime#Sounds_and_music

For low frequency notes you need long tubes without slots. To excite only the lowest note you should arrange a soft felt or rubber clapper to hit the tubes only at the 50% point, the tube mid-point. If you have tubes of different lengths for different low notes you must adjust the individual tube heights to be symmetrical about the one clapper.
This reference from the wiki article discusses low note fundamentals.
https://milwaukeemakerspace.org/2011/09/giant-ominous-wind-chimes/

For longer lasting notes you need longer suspension strings to reduce the damping of the fundamental.
You might also consider suspending the tubes from an internal point slightly above the midpoint, on one internal string. Maybe drill a small through hole in the tube about 10% above the central clapper contact point, then insert a bent 'W' shaped wire through a loop in the internal string.

You can generate lower notes from shorter tubes by loading the tube with equal solid masses at both ends, and a bigger mass at the exact midpoint.