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Designing A Chime, resonance of a metal tube?
3

Designing A Chime, resonance of a metal tube?

Designing A Chime, resonance of a metal tube?

(OP)
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

RE: Designing A Chime, resonance of a metal tube?

I answered this question once before, and for some reason the thread disappeared. Its a genuine design question, and presumably not a student post, so I can't imagine why it happened. In the previous post there was something about an air resonator, which didn't make a lot of sense, (at least to me). This was my reply as far as I can remember it :

The lowest natural frequency in Hz of a free-free single span beam is given approximately by :

fn = 4.73^2/(2*pi*L^2)*(E*I*gc/m)^0.5  .. (eg : Blevins)

where L = length                 : in
      E = Youngs modulus         : lbf/in^2
      I = Second moment of area  : in^4
      m = mass per unit length   : lbm/in
      gc = 386.4
      pi = 3.14159

The ideal suspension point would be at a node, of which there are two, situated approximately 0.22*L from each end.

You will find that tubular wind chimes are often suspended at such a location.


RE: Designing A Chime, resonance of a metal tube?

   As I found out from a very recent web search of the subject "musical chimes frequencies", the design of chimes is a rather complicated engineering problem. The #1 hit on the list is the following
  http://home.fuse.net/engineering/Chimes....;

This discusses, at considerable length, the best range of musical tones, the overtone frequency ratios and provides length formulas. It also cites a more recent review by a kindred spirit that can be called up. This later treatise complements the first one and includes a discussion of best material for chimes (steel and aluminum much better than copper) and talks about the design of "strikers" and the locations of tube bending mode nodal points for best response. Your hoped for "pipe whacked with a wooden mallet" looks like a forlorn hope after reading the above stuff. Good luck and hope you make it in time for Christmas services!

RE: Designing A Chime, resonance of a metal tube?

(OP)
Yes, I suspect it was my post in another area of this forum that was deleted.  I was disappointed because this is a real design question.  I thought this would be a great place to try my luck, and so far it has generated the only quality response.  Also, as you recall, I asked about seeking a length that would correspond to both the fundamental frequency of vibration of the tube and the resonant frequency of an air column.  To explain further what I mean there I will describe a simple physics experiment we did in high school (about twenty years ago).  We had a beaker of water, a glass tube and a tuning fork.  We held the glass tube in the beaker so one end was immersed in the water and the other end at the top was open to the air.  Next we struck the tuning fork and held it over the "air" end of the glass tube.  Then by moving the glass tube up and down we were able to change the length of the resonating chamber.  When we had the length matched to the frequency of the tuning fork, it became quite loud because the air in the tube resonated at the same note.

Getting back to my problem, it seems to me the best effect will be acheived when the note of the tube matches the resonant length of a column of air in the tube.  That is why I am trying to work the problem from two variables.  Essentially, the length of the chime is known because that is a direct correllation between the desired frequency and the resonant length.  I don't remember what the number was excatly, but it was about sixty inches.  So now I have to find a material, a wall thickness and a diameter that resonates at about the right frequency.

Since I first posted, my dad purchased a stock piece of steel tube.  I may just solve the problem the brute force way.  I will strike the tube and measure the frequency using a program I downloaded this past weekend.  Then I will plot the frequency against the length.  Then I will cut an inch off and do the same thing.  I should be able to develop a curve that will give me a reasonable chance of solving the problem.

If you have any more theoretical help, I will keep checking back here.  Thanks for those who have answered.  My appologies for rambling and/or any severe spelling errors.  In this you will know I am a stereotypical engineer.  -  Ed

RE: Designing A Chime, resonance of a metal tube?

vanstoja : very interesting - at least your reference seems to confirm the 0.22L node support point - so, Dinosaur, I would use that as a hanging location. I think your column of air idea is somewhat questionable, since even if the longitudinal air column resonant frequency can be arranged to match the bending natural frequency of the tube, its not certain that the one resonance will sympathetically excite the other very much, at least to an audible level. But maybe it will. Good luck.

RE: Designing A Chime, resonance of a metal tube?

Dinosaur:
Further note : I have a copy of Lord Rayleigh's classic "Theory of Sound", which you can probably still get from Dover. After wading through his somewhat circumlocuitous Victorian prose, I think I am correct in saying that, for the axial vibration of an air column inside a tube, the frequency in Hz of the first mode is given by V/(2*L) for a tube open at both ends, and V/(4*L) for a tube with one end blocked, where L is the length of the tube and V is the speed of sound in air in length units per second. The diameter does not affect the frequency. However, I'm still of the opinion that bending vibration of the tube is not likely to impart much axial momentum into the air column, and hence you would not notice much sound amplification if the mechanical bending and air column frequencies were arranged to coincide. But I've been wrong before! There are of course going to be many complex harmonics above the fundamental, which will give the chime a distinct character. As with many musical instruments, the nature of the striking device will have a considerable effect on these harmonics. A soft striker will damp out the higher frequencies, and a hard one will permit them.

RE: Designing A Chime, resonance of a metal tube?

Yes those are the right relationships for wavelength to tube length. An organ pipe is a quarter wave long, and an open tube is like two quarter waves back to back, ie half a wave long. A sticky toffee to the first person with the correct explanation why they don't have to be one wavelength long.

I agree that I'd be pessimistic about the chances of getting an axial pressure wave excited by a transverse bending mode of the pipe, but it can't hurt. Oh, here's how to test it - find a pipe with the right length diameter and thickness to give matching bending mode and acosustic mode, then compare the noise made with and without one end blocked off.

Incidentally there is another effect that may be important, the coincident frequency. That's the frequency at which the wave speed of air matches wave speed of the bending mode of  the pipe - which can give radiation efficiencies >1. I suggest you look at Bernek for that, there's too much handwaving for a post.  

Cheers

Greg Locock

RE: Designing A Chime, resonance of a metal tube?

That's Beranek.

Cheers

Greg Locock

RE: Designing A Chime, resonance of a metal tube?

(OP)
Thanks everyone for your assistance.  I had already looked up the length of the open and closed tube and recognised it did not depend on the diameter.  My motivation for getting the transverse vibration length to match the resonant air column length is an effort to enhance the final sound.  First, by getting the lengths to match, a softer hammer may be used thus eliminating upper harmonics.  Also, because the fundamental will be enhanced, the upper harmonics will hopefully be even further dominated by the fundamental.

My back up plan is to build a resonating chamber at the mouth of the tube that is tuned to the proper frequency of the chime.  One benefit of this is that if made of the proper wood, it will give the chime a softer tone.

The reason I suspect to derive a noticable benefit from the resonant air column is because the air inside the tube will have much of the sound energy and it has to escape at the end of the tube.  So I suspect most of the sound radiating from the chime emanates from the end of the tube.  I do understand the transverse mode vs. the longitudinal mode decreases the effect but I am doing this as much for fun as anything else.  In the end I do hope to get a nice low ringing sound though.  Oh, and one more thing, I am trying to get this ready for Advent, not Christmas, so I have one month less to fool around.  Thanks again.  Dinosaur

RE: Designing A Chime, resonance of a metal tube?

GregLocock :  You seem to be implying that you know the correct answer to your question - you just want to see if anyone else does. I suppose I could reproduce Lord Rayleigh's extremely involved explanation, which I'm sure nobody would dare to argue with, but I'm not sure whether I want one of your sticky toffees, even if it didn't have to make the trip from Australia. Actually, I wouldn't be surprised if your toffees come from the UK, in which case it would have travelled an even greater overall distance! (Can you still get Sharps by the way ?)

RE: Designing A Chime, resonance of a metal tube?

Dunno about Sharps. OK, no bites, no toffees. The velocity wave undergoes a 180 degree phase shift at the reflection plane at the end of the tube, so the characteristic length is twice what you'd expect. The reason I asked is that I hoped someone had an intuitive explanation - it certainly surprises me that the quarter wavelength is the important property of a closed ended tube.

 

Cheers

Greg Locock

RE: Designing A Chime, resonance of a metal tube?

This looks pretty interesting:

http://home.fuse.net/engineering/Chimes....

Note especially the section on the PERCEIVED pitch of a chime in relation to its natural frequencies!

Also: When discussing acoustic modes in pipes don't forget that there is a radiation loading on the moving mass of air at the open ends of the tube. This depends on the radius of the tube. Dimensionally, this load impedance seen by the tube is a mass. If you add mass to a dynamic system you decrease its natural frequencies. It effectively makes the natural frequency of the tube lower than it would be without the radiation loading.

Often you will see this described as an "end correction" to the length of the tube (L + delta) because adding length to the tube also decreases the natural frequency.

M

PS Greg: I tend to think of it in terms of boundary conditions. The particle displacement at the closed end must be zero and the particle displacement at the open end must be maximum. So the simplest sinusoidal profile along the tube which satisfies these boundary conditions is...?

RE: Designing A Chime, resonance of a metal tube?

I have found the windchime discussion to be very interesting. I am not sure that I understand what the confusion is about the quarter wavelength tubes.  But if you go to my website, I have some theory on quarter wavelength tubes as they are applied to stereo speaker design.

Hope that helps,

Martin

Quarter Wavelength Loudspeaker Design
www.quarter-wave.com

RE: Designing A Chime, resonance of a metal tube?

Oh yes, and sorry to be picky, Greg, but most organ pipes are more like 1/2 wavelength resonators. The end nearest the wind chest (throat) has a boundary condition which approximates that of an open end. This type of pipe forms the majority of the organ (diapaisons, flutes, reed and trumpets). An 8 foot pipe sounds about middle C. The exceptions are stopped ("gedeckt") pipes which are usually square section wooden flutes which have a bung in the top. These sound 1 octave higher. Just to confuse the issue some open pipes can be "over blown" with higher pressure air. These also sound 1 octave higher than normal because the 2nd mode is excited to a greater degree. Try blowing gently into a tin whistle or recorder and then blow full pelt and you will see what I mean.

M

RE: Designing A Chime, resonance of a metal tube?

I wondered about that. It seemed to me that exciting a system at, or near, a node is a rather odd way of doing things.

Cheers

Greg Locock

RE: Designing A Chime, resonance of a metal tube?

Clarification of my last post

An 8ft organ pipe does not sound at middle C. An "8 ft" stop in organ terms means that the largest pipe in the rank is 8 ft long (approx.). On an 8 ft stop you press middle C on the keyboard and the sound you get is at middle C. On a 4 ft stop you press the middle C key and get a sound at C above middle C.

M

RE: Designing A Chime, resonance of a metal tube?

Since the generally accepted value for middle C is 256 Hz, I fail to see how you could get a fundamental resonance anywhere close to that with a 4 ft or 8 ft pipe, either closed at one end or open. See the following for a calculator.

http://hyperphysics.phy-astr.gsu.edu/hba...

RE: Designing A Chime, resonance of a metal tube?

EnglishMuffin: See my post above yours.
M

RE: Designing A Chime, resonance of a metal tube?

MickeyP : I've seen it, and I'm afraid I don't understand it. Presumably, most of us are not organists, so we don't know what an 8ft "stop" or a "rank" are supposed to be. All I know is that for an open-open pipe, you would need a 26.43 in long pipe to get middle C, assuming air at 20 deg C. For a closed-open pipe, it would be 13.21 in. (Of course, this ignores all the slight corrections etc).

RE: Designing A Chime, resonance of a metal tube?

(OP)
Thanks again.  I checked the link provided by Vanstoja and it was very helpful.

Regarding the length of an organ pipe for resonance, if it is a half wave long with open-open end conditions it will resonate at the fundamental frequency.  Except I have learned in a physics book dealing directly with sound that there is an end correction on the overall length of something near one diameter of the pipe.  The pipe acts as a pipe a little longer than it measures according to observations.  I don't recall exactly what the correction factor was reported to be in the book.

If the velocity of sound in air is 344 m/s and you wish to resonate a 256 Hz sound, the half wavelength is:
344/(2*256) = 0.672 m -or- 2.21 ft.  It appears you can get a "C" from either an 8 ft stop or a 4 ft stop.  Also remember, if you overblow the pipe you should be able to excite it to its first overtone and get a pitch twice as high.  How this effects the sound produced is something I would like to hear more about.

Looking forward to more insight.  -  Ed

RE: Designing A Chime, resonance of a metal tube?

End correction for hemholtz resonators is 0.6*diameter, offhand I can't think why it would be different for a quinkie (quarter wave) or half wave tube.

Cheers

Greg Locock

RE: Designing A Chime, resonance of a metal tube?

hello there
i am new to this forum, and hope i don't make too big a fool of myself, but this question jumped out at me.

i think the important modes of the tube, in terms of resonating with the air column, are not the lateral (beam) bending modes....they are the bell modes (or diametral modes). i have not run any numbers on this, but isn't the chime/tube more a bell than a beam?

Dave Leo

RE: Designing A Chime, resonance of a metal tube?

Well, reading the literature seems to confirm that the fundamental is primarily a free-free bending mode, but some of the the higher harmonics are probably more bell-like, depending on how and where it is struck. I agree with you that those would be the only ones that could have much effect on the air column. Personally, I don't believe the air column resonance is significant - even the added mass effect on the bending modes is almost negligable. But you never know for sure till you experiment a bit.

RE: Designing A Chime, resonance of a metal tube?

To daveleo
   I've also wondered why lobar shell response modes are not mentioned in the musical chimes discussions by Lee Hite (see vanstoja & mikeyp citations above) and Chuck (cited by Hite). Lobar responses (particularly 2,3 and 4-lobed) are definitely a factor in large diameter thin shells and bell-like structures such as high specific speed impeller front shrouds. Perhaps the critical factors causing changeover from shell lobar to beam bending modal responses is the shell L/D and t/R ratios. For Hite's brass orchestral chime the L/D and t/R ratios of 43.6 and 0.087 may be high enough to preclude lobar responses and bring up only beam bending responses when subjected to well-spaced single impacts on the outer diameter. This may be generally true of chimes geometries. Possibly, continuous excitation in the form of random vibrations (perhaps even induced by turbulent flow around a shell) might engender lobar shell responses in chime configurations. For bells, I understand that the responses are actually plate modes rather than beam or shell modes. There is an intriguing article about ancient Chinese bells (see Shen,S. "Acoustics of Ancient Chinese Bells", Scientific American, Apr.1987, pp. 104-110) that discusses plate modes in oblate bells with two different striking positions that excite two arrays of response harmonics both starting around 700-800 Hz. Cast-in nipples on the outer diameter act to suppress or moderate some of the harmonic responses presumably providing a variety of sounds. This is a 5th century BC acoustic art form that was apparently lost and and only partially recovered in the 12th century AD.
   My favorite shell frequency equation (though only approximate) gives 2,3 and 4 lobe response frequencies for Hite's brass orchestral chime of 452-689Hz, 1009-1429Hz and 1968-2647Hz, respectively for the m=1 axial halfwave mode which matches the open-open organ pipe fundamental waveform. However, Hites orchestral chime had a cap with hole on one end which may make it a quarter wave resonator which would be better excited by the m=2 shell mode which for the long L/D of 43.6 gives almost the same frequencies as the m=1 mode. The calculated shell lobar mode frequencies are apparently within the "musical" range.

RE: Designing A Chime, resonance of a metal tube?

vanstoja : So you appear to be saying that orchestral chimes are indeed designed such that the air column resonates at the same frequency as one of the shell type resonances - in which case Dinosaur is sort of on the right track. There would not seem to be much point in putting a cap on one end if the air column was not involved in some way, but what is the reason for the hole in the middle? Do I understand your post correctly ? I too recall that Scientific American article quite vividly - probably because it's one of the few that you don't have to be a theoretical physicist to understand.

RE: Designing A Chime, resonance of a metal tube?

EnglishMuffin
   Yes. It appears that some coincidence or near coincidence of beam structural bending and organ pipe aeroacoustic harmonics is involved in chime tones. Chuck, in discussing Hite's orchestral chime in
   http://www1.iwvisp.com/cllsj/windchimes/
shows a plot of the 4th beam and the 5th air harmonics intersecting at a length of about 72 inches whereas the orchestral chime length is reported by Hite to be 62.625 inches. My calculations for a 1.5 in. OD, 1.375 in. ID brass chime of that length finds the 4th free-free beam harmonic at 585 Hz and the 5th open-open pipe air harmonic at 536 Hz both of which are close to Chuck's curves at a length of 62.625 in. I presume that the failure of these two calculated frequencies to match exactly, is because the end cap with a hole screws up the end conditions of the beam and/or the organ pipe thus deviating from the ideal theoretical model. I suspect that the primary note being excited is C5 at 523 Hz on the musical scale. Apparently, the hole in the end cap is big enough to keep the organ pipe near the open-open modeshape though I don't know what it's there for.
   In my prior post, I erred in stating that a quarter-wave organ pipe would match the modeshape of an m=2 shell axial mode. Actually there are 4 quarterwaves in an m=2 shell mode (ie, a full sinewave) which clearly will not match a quarterwave in the fluid within the shell.

RE: Designing A Chime, resonance of a metal tube?

vanstoja :
Well, I've read Chuck's link, but I'm still skeptical. He says "Others have written that you can't predict the frequency of a tube and that the column of air is unimportant. They are wrong." This suggests that I am not the only skeptic, and that the issue is somewhat controversial, as with a lot of things having to do with musical instruments, Hi-Fi etc. What does he mean by "cut much shorter than the ideal length" ? He does not say precisely. If there was anything to this, I would have thought that you should see the effect without cutting the tube "much shorter". What happens if the tubes are, say, 5% shorter for instance? Very short tubes will not ring as long in any case - and if the frequency of those has been matched by increasing the mass, other effects might be responsible. And how was the striking force controlled ? I see there is a patent involved, but people have patented perpetual motion machines in the past, so that may not necessarily mean anything. However, I'm still ready to be convinced!

RE: Designing A Chime, resonance of a metal tube?

(OP)
In my reading, I have also run across the end cap mentioned in professionally manufactured chimes.  It would seem to have two effects on the performance of the tube.  First, by dramatically changing the mass, the frequency related to the sqrt (K/m) would be effected.  Second, with a significant mass at one end, the mode shape would be effected so the relation of mass distribution is being put to use.  Also, I wouldn't be surprised if the hole at one end is made useful as a tuning device for the final step.  If the tube is a little out of tune, maybe the hole can be increased in diameter to get it just right.  At any rate, the professional chime makers use a fair size metal plug at the top and this is where they are struck to make them sound correctly.  I thought this was going to be a fairly simple study with three variables, but it is quite a bit more involved than that.  Dinosaur

RE: Designing A Chime, resonance of a metal tube?

If you strike the tube at a point coincident with the plug, that would also perhaps have the effect of not exciting the shell modes that were being discussed. My guess would be that the plug would be there partially for that reason - ie to achieve a purer tone. Using FEA you should be able to study the resonance of all these more complex cases quite easily, if you have access to a program.

RE: Designing A Chime, resonance of a metal tube?

(OP)
EnglishMuffin,

Well I don't have access to a FE program with the power to handle that one.  I also don't know how to get the boundary conditions set up for a problem like that.  A chime tube hanging from a cable is not strictly a stable structure and would return an error message saying the matrix is singular.  That is what I would expect.  So I don't know how to set that one up.  My PDEs are not very good but given enough time I could probably get a few modes doing it that way.  Let's face it . . . I can get a tube and do some trial and error in less time.  I do think it is an interesting problem and I hope to get a handle on the mathmatics of it someday.  -  Dinosaur

RE: Designing A Chime, resonance of a metal tube?

Dinosaur:
I don't know why you would say that a chime hanging from a cable is not stable - it is stable both dynamically and statically - (assuming of course, in the latter case, that it is suspended from a point above its center of gravity). Like you, I do not at present have access to an FEA program, but I don't know which matrix you are referring to that would be singular. If, for example, you write the matrix equation for two point masses suspended in space, totally unsupported and connected only by a spring, with a sinusoidal force applied to one of them, you don't get any singular matrices, so why would you (in general) for a beam suspended in space with a sinusoidal force applied at the proposed striking point ? FEA programs should give you free body modes without any problem, unless they are based on some aspect of Newtonian mechanics of which I am not aware. As a matter of fact, the very last problem in the current edition of "Vibration Problems in Engineering - Timoshenko, Young & Weaver" is to set up the FE matrix equations for a two element prismatic beam with no restraints and calculate the frequencies and mode shapes!

RE: Designing A Chime, resonance of a metal tube?

By the way - I've just realized what the hole in the end cap is probably for - IT'S FOR THE SUSPENSION CABLE TO PASS THROUGH  (dummy!) Everyone seems to support at the node which is .224 from the end.

RE: Designing A Chime, resonance of a metal tube?

Another purpose of the cap is there for a striking surface. The directions are adamant about only striking the cap; the body of the tube will dent. I guess they really whack them in an orchestra setting.

They are also adamant about striking the cap at a ninety degree angle, or the chime will sound "out of tune". I don't know what sort of resonances this would induce.

I got fascinated by the subject of wind chimes a while back, and in doing research came across Chuck's page. He was kind enough to share his spreadsheet model for the resonant frequencies of pipes of various sizes and materials.

I share the skepticism about the importance of the acoustic resonances. Not only are the waves inside the tube orthogonal to the tube's vibration, they are open ended tube resonances, which are weaker than closed tube resonances. How much weaker? I couldn't find a formula for this; if anyone can help me, I'd greatly appreciate it.

However, just to be safe, I modified Chuck's model to find the closest overall fit between a set of chime resonances and their acoustic resonances. If you are interested, I would be happy to email you this model.

Designing chimes for their primary resonance mode is interesting, but designing them for their 4th, 5th, and 6th modes is more rewarding: These modes resonate at close to a 2:3:4 ratio, meaning they are much more musical than the other modes.

In part because these frequencies are harmonically related, they also encourage the ear to hear additional lower frequencies -- the "missing fundamental" Lee Hite talks about.

Not only does the chime not natively produce these frequencies, it would be less able to produce them as the output rolls off at 6dB per octave. This rolloff also helps hide the inharmonic lower order resonances.

Ed, if your church is not very big, or if you've got amplification available, you can probably make a pretty good set of chimes by tuning for F4, F5, F6 and hanging the chimes by a point near these modes' nodes: They're at 0.051, 0.06, and 0.073. Then strike the chimes either gently at the end or more vigorously at a point about 15% of the way down -- this is the antinode for F5.

I built my large chimes from 1-1/2" type L copper pipe, available at Home Depot. These pipes are quite similar to the brass pipes used in orchestra chimes, though the brass may have some characteristics (such as less damping?) that I don't know about.

- Eric

RE: Designing A Chime, resonance of a metal tube?

I see my website has been discussed here and felt I should join the discussion.  First of all because a patent has been applied for doesn't make this a perpetual motion machine.  If you can find where I violate any law of physics please tell me.  I firmly believe that I can only try to work within those laws or I'm wasting my time.

How short, or for that matter how long, is too short.  This is really a gray area.  Sort of like how old is old.  I refer to the length where the acoustic and transverse frequencies meet as the "ideal" length.  As one moves away from the ideal length the next lower or higher mode of the acoustic length starts to affect the tube.  At shorter lengths it appears to stop the vibration of the tube.  At longer lengths it tends to  support the second mode of the tube which is not an even harmonic of the first mode and therefore they don't sound good.  In my length calculator I set some limits but the limits are just my best guess.

Does the acoustic mode even couple with the tube?  I wondered my self about that.  I purchased a book on acoustic and when I couldn't find the answer I wrote the author.  He suggest another book and told me what I had on my webpage was "good enough" for what I was doing.  He also told me how to proceed but my knowledge of acoustic is rather limited and I'm have a difficult time.  If anyone would like to see his respond I will post it.

I also attend a two day class on FEA of cavity acoustic related to aircraft.  I asked the instructor about this problem.  He said that at resonant I would have to use the more complex (heavy) forumula to correctly model the problem.  So I'm convince that here is coupling between tube and air column but I would have trouble proving it with an equation.

I've recently been looking at bell modes or circular modes.  I've not included this on my website yet.  I do believe these modes make the type M copper tubing used my many for chimes sound terrible.  I suspect if larger diameter (3 inch?) steel conduit was used it may also sound terrible for the same reason.  I've been looking at trying to tune the tubes such as this first circular mode is an even harmonic of the first mode.  I have used a digital filter to remove it and the tubes do sound better.

Tubular bells (chimes tuned to the four natural frequency) are capped at one end.  I made some from steel conduit and have the plans on my website.  I could not hear any difference between capping the ends and suspending them at the first node.  Then my hearing may not be as good as it should be.  I've also read that some sets of tubular chimes use different diameter at the upper and lower frequencies.  This would appear to support my "ideal" length.  Does the weight of the cap change the response of the tube?  It is going to depend on how heavy the cap is.  In my case I used a flat washer which is very small fraction of the total weight.  Since I don't have a tubular bell I just don't know.

To the question that started this thread I've considered this building a set of tubular bells for my church.  Based on what I know at this point I would use rigid aluminum conduit suspended at the first node point (which is not 22% of the length for the 4th mode).  I would tune them to the 4th natural frequency.  I would use the same diameter tubing for as many of the tubes as I could as there appears to be a difference in tones produced when the diameter changes.

chuck

RE: Designing A Chime, resonance of a metal tube?

Hi cllsj:
1. I didn't intend to hurt your feelings when I commented that just because something is patented does not necessarily mean that it will work - it all depends on the patent examiners involved. Some of them are better lawyers than scientists. If you happened to get Albert Einstein, for example, you'd obviously get a very rigorous analysis. At about the time that he was working as a patent examiner in Switzerland, there were people successfully patenting perpetual motion machines in the USA, something it's hard to imagine you could have got past him at the time, but on the other hand in later life he believed in stuff like pole shifts in the earths crust, which is definitely fringe science today - nobody's infallible after all, and that certainly includes me!
2. It's not clear (at least to me) what your FEA instructor meant : he may have been referring to the fact that for a really precise computation of the natural frequency, you need to consider the effect of the added mass of the air inside and outside the tube, although the effect is small, unlike the case with liquids. But this has nothing to do with axial resonance of the internal air column. However, maybe he was talking about something else which I don't understand. But in any case you shouldn't need to go to FEA to calculate simple longitudinal resonances of air columns. If your effect is real, the simple basic physics formulae discussed on this thread should suffice, with appropriate end corrections of course.
3. If your theory about the air column resonance is correct, it should be possible to prove it with experiments, such as, for example, carrying out tests at different temperatures. Since the speed of sound in air is proportional only to the square root of the absolute air temperature, then temperature should have a marked effect on the resonant frequency of the air column. A change from, say, -25deg C to 25 deg C would change the air column frequency by about 10 percent, whereas the beam resonance would hardly change at all, even counting added mass effects, so if your effect were significant you should notice something. I have no suggestions of how to achieve such a temperature change, other than using mother nature, but with the right lab facilities it would be a simple matter.
4. Are you the same person as Dinosaur, or are there two of you guys building chimes for your churches ?

RE: Designing A Chime, resonance of a metal tube?

Nope, I'm not Dinosaur.  I'm the Chuck that wrote the website Chuck's Chimes or perhaps better known as

http://www1.iwvisp.com/cllsj/windchimes/

I'd have to dig out my notes from the class but off the top of head NASTRAN (?) can use two different formulations for a fluid.  For air, other than at resonance with the structure, a light (less complex) formulation can be used.  I would assume this formulation would require less computer time to solve.

I had not thought about temperature.  If I could do this at work this would be rather easy to do; however, I don't think my employer would be willing to support my hobby.

I would point out again that author of the acoustic book I contacted didn't appear to have a problem with coupling of the axial air column and transverse vibration.  Here is what he wrote.

I'm afraid my book was the wrong place to go! It deals with the production of sound by flow, i.e. where the energy is extracted from the flow.

>From my brief look at the your website (and another linked on your site)
I gather that the excitation mechanism is a striker. In that case I
should think sound generation is certainly via the resonant excitation
of a resonant acoustic mode in the tube by a structural mode of the
tube. The resistance of the air is so small that it seems to me that the
method of calculation you appear to have been using is quite adequate to
determine the frequency.

If you want to express the acoustic amplitude in terms of the tube
motion, however, you will have to calculate the tube mode shape and use
it to determine the normal velocity distribution on the inner surface of
the tube as a function of time (the amplitude will decay, predominantly
because of structural damping). You would then have to solve the
acoustic wave equation within the tube (say with zero pressure open end
conditions, in a first approximation) for the sound generated by a point
source. Then imagine the inner surface divided into infinitesimal
surface elements, the normal velocity of each of which determines its
effective source strength, and calculate the sound produced by each of
these sources using your point source solution. Then integrate over the
inner area to get the net effect of all the sources. The result (i.e.
the solution of the wave equation due to surface forcing) will have a
large peak at the matching resonant frequency of the air in the tube,
the magnitude being dependent on the decay rate of the tube vibration.
Next use the solution to calculate the fluctuating mean axial volume
velocity of the air at the open ends, and use this as the effective
source strength of the two monopole sources (one at each end) of the
sound radiating into the ambient free pace.

chuck

RE: Designing A Chime, resonance of a metal tube?

I don't know anything about FEA as applied to acoustics, so its not clear to me whether he is talking about writing a program to do this from scratch, or whether you can do all this with built-in NASTRAN capability. Sounds like quite a project! And from the tone of his answer, it does not sound as though this analysis has ever been done in detail. However, the bottom line is - how big is the effect? Did he express an opinion? If so, I won't deny that it should obviously be given some weight, since he is an acoustics expert, something I certainly cannot claim to be.

RE: Designing A Chime, resonance of a metal tube?

By the way, one way you could crudely investigate the temperature effect would be to heat the air inside the tube by using a propane torch near the lower opening. If you were investigating a capped tube, the air inside would get fairly hot, since continuous convection effects inside would be minimal. I expect you could also heat the tube itself, but I'm not sure what other effects that might produce under such uncontrolled conditions.

RE: Designing A Chime, resonance of a metal tube?

(OP)
Thanks again everyone for your comments.  cllsj (chuck), I will run by the home improvement store and see if they have the copper pipe you mentioned.

Let me bring y'all up to date.  The rector wanted this in place by Advent I, today.  I ordered a 36 inch length of aluminum tube from a wind chime supplier and hung it from a chord through holes drilled eight inches from one end.  This is at the proper location of the node according to the website cited earlier.  I built a stand for it and a small wood mallet for striking.  The head was cut to an edge to provide a crisper stricking device rather than a flat round head.  When you strike it in a "sweet spot" it rings a little but if you don't it makes a sort of thud.  The inside of the nave will seat about two hundred (I'd like to see it full someday, but hasen't happened yet).  It is finished in wood and tile so a small amount of sound goes a long way.  I had hoped the tube would ring better so I am still looking for a good tube.  For the purpose of the service, we need only one note so precise tuning is not necessary, but I appreciate the additional discussion on this subject as well.

So, given where I am and where I'd like to be, I expect to do two things.  First, I am going to buy a 36 inch length of the copper tube and see how that sounds.  Second, I am going to experiment with adding an end cap to the top for striking and to see how this effects the note and the resonance.  I don't plan to give up on this before I have a nice ring in the sound.  My worry is that I will have to either purchase a tube of some variety of exotic material or that it will have to be machined to produce a satisfactory ring.  Wish me luck and thanks again.  -  Ed

RE: Designing A Chime, resonance of a metal tube?

(OP)
Whoops!  Glad I checked my facts.  I guess I won't be going to the hardware store after all.  So that leaves me with fixing my aluminum tube.

Well the bad news appears to be that I have hung the tube in the wrong spot, 8 inches from one end.  The good news is that when I ordered the tube, I asked for three sections.  Now I have two more tries to get it right, before I go back and try and change the length of the original tube.

O.K., it appears I should try again and support the tube at a node 7.35% from the top.  Do you have a recommendation where I should strike it?

I am glad to hear that my sense that the "resonant air column length" is not misplaced.  I truely believe this will play a factor in getting the tubes to sound correct.

I'll let you know how it comes out.  -  Ed

P.S.  Chuck, what will your patent cover?  Have you considered manufacturing chime tubes commercially?

RE: Designing A Chime, resonance of a metal tube?

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

RE: Designing A Chime, resonance of a metal tube?

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.

RE: Designing A Chime, resonance of a metal tube?

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

RE: Designing A Chime, resonance of a metal tube?

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!

RE: Designing A Chime, resonance of a metal tube?

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

RE: Designing A Chime, resonance of a metal tube?

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!

RE: Designing A Chime, resonance of a metal tube?

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

RE: Designing A Chime, resonance of a metal tube?

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

RE: Designing A Chime, resonance of a metal tube?

(OP)
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 "chi.." 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

RE: Designing A Chime, resonance of a metal tube?

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

RE: Designing A Chime, resonance of a metal tube?

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

RE: Designing A Chime, resonance of a metal tube?

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 "quality" of the tones (in terms of being music or noise) is very intimidating. i must read up on chimes first.

daveleo

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