Designing A Chime, resonance of a metal tube? 3

[Dinosaur]

Hello,

I participate in other forums here and I would like some help with a problem I have accepted for my church. I am trying to make an inexpensive chime to be used during the service. I have looked in physics texts and my finite elements books but I can not figure this one out. What I want is a metal tube of a standard size pipe stock that when struck lightly with a wooden hammer will make a nice, low, pleasing tone. Can anyone help me get a formula to predict the frequency of a metal tube in free vibration supported by a string at the top? Thanks in advance for any help. - Ed

 

[cllsj]

As previously mention, tubular bells are made from brass and generally chrome plated. That being said I don't think copper produces the best sound. Both I and Lee believe aluminum produces the best sound followed by steel with copper being a distant third.

For the aluminum tube you're already drilled just add the hole at the correct location. The misdrilled hole while looking bad from a workmanship standpoint will not affect the sound produced.

I prefer to use a soft striker. I would site the dynamic amplification factor found in many text books as the reason for this. That is I'm trying to match the time constants. Tubular bells, from what I've read, use a rawhide covered mallet.

For those who don't accept that transverse vibration of the tube couples to the axial vibration of the air column, does that imply that the tube doesn't produce any axial sound waves? .... It is quite easy to show that the tube does indeed produce axial sound waves. Lee noticed this when a small thread hanging over the end of tube starting vibrating when the tube was struck. When I first started this I had the tubes suspended over my computer microphone. As the tube swung back and forth over the microphone I saw the change in intensity of the sound waves. It took away but it finally came to me to start looking at the vibration of the air column.

Jack, the gentlemen mention on my website, really pushed for the patent and did most (all) of the work. Left on my own I would never have done it. Jack has sold some chimes but I think he started just to give his children something to do. Others, who have contacted me through the Yahoo site on windchimes, are selling chimes built using my method over the internet. However, for me this is just a hobby and I have not made a single penny on this. The patent covers the matching of the primary frequency (1st mode)of the tube to the second mode of the air column. At this point I really only want the patent to say that I have it.

chuck

 

[EnglishMuffin]

It's certainly possible, indeed likely, that axial sound waves are produced, since there are going to be at least some modes present which involve a change in the volume enclosed by the tube. What is at issue is whether any such effects have any audible significance. Of course, the audio and musical world is notorious for its subjectivity, and that's OK. But from a scientific perspective, if you are really interested in what is going on, do some rigorous experiments and analyse the results. As I've said numerous times, I for one am quite ready to be convinced, but only with unambiguous data! Good luck with your patent: the examiners are only interested in determining whether an idea is novel, and has a possibility of working, so I would say that it is highly probable that they will grant it. But I don't know how you might cope with possible accidental infringement involving existing designs and how, without precise data, you can define the range of frequency ratios within which the claimed coincident frequency effect is supposed to be valid.

 

[ewesson]

The chime doesn't produce axial sound, but the transverse waves generated diffract in all directions, making it appear that waves are being generated in an axial direction. This is particularly true for the lower frequencies, which are what one would eaisly see in a string dangling in the vicinity of the end. For most frequencies, the chime acts much like a point source, radiating in all directions.

Put another way: As the end is displacing in one direction, air is rushing around the moving end to fill the other side.


One question to ponder: Tuning forks, and some wind chimes, are made of solid metal.

- Eric

 

[EnglishMuffin]

I think it might be argued that shell modes (which happen to correspond to a change in enclosed tube volume, at least locally) are somewhat more likely to lead to axially travelling waves, (by diffraction as you more correctly say), than are pure bending modes. I am really just echoing a previous thought by daveleo on Oct 13th. But to be fair to cllsj, the basic issue is whether any waves that end up travelling in an axial direction inside the tube, for whatever reason, start to resonate according to the v/(2*L) relationship, or some multiple of it. And it should be possible to settle the question experimentally fairly easily with some carefully designed experiments. And now I think it's time for me to shut up!

 

[ewesson]

Without a doubt shell modes (bell or radial modes, if I understand your term correctly) will result in axial air displacement.

However, the air displaced by this effect is tiny, at least in comparison with the overall flexing. It's the area reduction of an ellipse versus a circle of same perimeter; much smaller than the distortion itself.

Also, for the typical chime, the radial modes are at much higher frequencies than are the transverse modes.

This doesn't prevent them from resonating with the air column, as the air column resonates at many different frequencies; it's just that this isn't the resonance we are seeking.


Ed / Dinosaur never "chimed" in with what he wanted these chimes to sound like? Does he want them to have a pure tone, like most wind chimes or a Glockenspiel? Or does he want them to sound like a bell? The aluminum design earlier was for the former.

- Eric

 

[EnglishMuffin]

Ewesson - I quite agree with all that - I am merely trying to play devil's advocate. I am highly skeptical that the coincident resonance effect exists, at least to any audible degree, which you will see if you check every post I have written. But in the face of such sparse experimental data, it is always a good idea to keep an open mind, even if it is only open a very small amount!

 

[ewesson]

Agreed -- I share your skepticism but I tuned for matching the acoustic and bar resonances anyway, as I enjoyed the exercise, figured it couldn't hurt, and didn't have the patience, inclination, and facilities to perform the experiments. So for me it remains in the realm of speculation. I appreciate your open mind and inquisitive nature. Some clever experimental methods have been suggested.

I am frustrated that there aren't more resources for this sort of question. For example, I couldn't find an equation for the amplitude of reflection off an open end.

Cheers,

- Eric

 

[cllsj]

I've decided all of you are correct to be skeptical as there is a lot of misinformation on the web. I also know that I've cut enough pipe and stared at enough fourier transforms to know that something is happening at what I refer to as the "ideal" length. This may be a coupling between the axial vibration of air column and the transverse vibration of the tube or something else entirely. I also know and the fourier transforms show as the tube get longer than "ideal" the second transverse mode of the tube becomes dominant. At short than "ideal" the fourier transforms show that the vibration of the tube or at least the sound produced drops quickly. If one graphs the modes of the tube and the air column, it is apparent that these things are happening at points where the modes of the air column and tube cross each other. I currently can't produce an equation or equations to prove this but for the pratical purpose of making wind chimes my method works. As an engineer this is good enough. As a curious individual I will keep on reading textbooks and perhaps someday I will be able to write all the necessary equations.

Dinosaur, I wish you luck in building your chimes.

chuck

 

[Dinosaur]

Chuck,

Thanks for all your help.

As you all know, I also think the longitudinal sound waves resonating in the air column play a role in the sound of the chime, but as it appears, like everyone else I am not prepared to rigorously <sp?> defend that thesis. The earlier post mentioning the fact that once created, the pressure waves radiate from their origin and as a result some travel along the length of the tube is part of the basis for my belief.

Another recent post asked me to &quot;chi..&quot; in and declare what sort of sound I am after. I would like to get a rich bell sound as you would expect to get from an orchestral <sp?> chime.

As I make progress, I have a Mathcad file where I keep my notes and equations. If I ever figure this out, I'll make it available somewhere. - Ed

 

[ewesson]

Ed,

Are you all set? Do you have all the information you need to build your chimes? If not, let me know and I'll be happy to help in any way I can.

Chuck,

Thanks again for your help.

- Eric

 

[magicme]

this has been such a fascinating discussion to read, i have promised myself to study up on chimes, and actually have started a small ANSYS model to play with the forced response of a tube (modeling the interior air will be a trick for me, as i never modeled fluid in ANSYS).
if i ever complete that study and find anything worth noting, i hope to post it here at a later date.
mostly i just wanted to compliment everyone who shared their wisdom so freely.

daveleo

 

[magicme]

due to the snow storm we have up here, i had lots of time to kill at the computer today and i did get a chance to run the mode shapes of a free-ended tube (aluminum). i posted these on this website:

http://public.wit.edu/~leod1/Chimes/FreeFreeModes.htm

the idea of doing a forced response analysis and then interpreting the &quot;quality&quot; of the tones (in terms of being music or noise) is very intimidating. i must read up on chimes first.

daveleo