What modes of vibration contribute to the sound of wind chimes?

[Dr.D]

TL;DR Summary

Are tubular wind chimes (open at both ends) coupling to the air primarily the result of bending vibration, vibratory distortion of the circular section, or something else?

I recently read a site dealing with tubular wind chimes. The author give some references that seemed to indicate that the sound we hear is the result of beam bending vibrations after the tube is struck. I'm not so sure about that. It is certainly true that striking the side of an open cylinder will induce many modes of vibration. Does anyone have any experimental evidence as to what modes of vibration we hear?

 

[Baluncore]

Wind chimes with rectangular bars, or with hollow tubes, work just as well.
The only common factor is the beam bending and the suspension string.

 

[Dr.D]

I'm certainly aware that rectangular bars (or round rods) can be used as well as tubes. My question is specific to tubes.

When the tube is struck, what evidence is there that it is the beam bending vibration is the mode that we hear? There are other modes possible such as those that involve deforming the cross section into elliptical or star shaped patterns. Why is it thought that it is the beam bending mode that we hear since all modes will radiate to some degree?

 

[anorlunda]

When the tube is struck, what evidence is there that it is the beam bending vibration is the mode that we hear?

Search YouTube. You may find high speed camera videos of the vibrations. People like The Slow Motion Guys film lots of things like that.

To measure the tone that you hear, many smart phone apps will do that for you.

 

[Baluncore]

When the tube is struck, what evidence is there that it is the beam bending vibration is the mode that we hear?

The fundamental frequency is determined by the length of the resonator.
Some wind chimes are made from tube of only one section, cut to different lengths. All tubes would have the same sectional spectrum.

If you put a light-weight plug in both ends of a tube, the added mass will lower the frequency slightly, but it will totally eliminate any internal air-column, or sectional resonance.
Can you hear a difference?

 

[FEAnalyst]

There are even simulations for that:

And those simulations could be extended to include not only the fluid flow but also solid mechanics and acoustics.

 

[Dr.D]

Thanks for the comments guys. I'll have to wait until tomorrow to look at all of this as today is very full.

 

[Vanadium 50]

When the tube is struck, what evidence is there that it is the beam bending vibration is the mode that we hear?

You are almost certainly not hearing that. You're probably hearing the vibration of the air column inside. It's the sum of several normal modes. Which ones are excited is a function of the initial tube being struck and subsequent it's vibrations.

In short - strike the bell and the energy gets transformed into multiple vibrational modes, and those modes couple to the inner air column, and then the inner air column couples to the outer air, and makes sound.

 

[Dr.D]

You are almost certainly not hearing that. You're probably hearing the vibration of the air column inside. It's the sum of several normal modes. Which ones are excited is a function of the initial tube being struck and subsequent it's vibrations.

In short - strike the bell and the energy gets transformed into multiple vibrational modes, and those modes couple to the inner air column, and then the inner air column couples to the outer air, and makes sound.

I am well acquainted with the vibration response of a solid struck a blow. The questions comes down to simply "what motions couple to the air?" Do bending motions of the tube couple to the air so that we hear them, or is it one of the other mode shapes that couples to the air?

 

[Vanadium 50]

All of them do. The impedance matching depends on shape - "liberty bell" shaped bells have a wider range of frequencies that are well coupled than tubular bells, which is why they sound different.

 

[Dr.D]

@Vanadium 50, as I've stated above, my interest is specifically in tubular chimes, not the traditional "bell shaped" bells. Do you have either theory or data to support what you said? If so, I'd like to see it.

 

[Vanadium 50]

That's how all bells work. It's all in Rossing, I believe. But it's clear that trying to help is only insulting you. Be well.

 

[hutchphd]

You got me interested: Please see two wikipedia articles

https://en.wikipedia.org/wiki/Wind_chime
and
https://en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory#Example:_unsupported_(free-free)_beam

These support my initial supposition that these are bending modes of the pipes. I got roughly 300 hz for a one meter piece of hanging steel 1" thin wall conduit using WIKI formulae. I think any "fussier" radial mode would be very much higher frequency.

Tubular bells.

The Ace Hardware had a set of 6 foot - 3 foot x 2inch diameter chimes a few years back that were quite wonderful and deep. I should've sprung for them.

 

[Baluncore]

Re: Neville H. Fletcher, Thomas D. Rossing (auth.) - The Physics of Musical Instruments-Springer-Verlag New York (1998)
Here are a couple of extracts that show it is not as simple as might be expected;

From page 95;
“An orchestral chime or tubular bell, on the other hand, is essentially a long narrow pipe, as also is the common wind-chime. The dimensions are such that this cylindrical shell can best be considered as a form of bar, with a radius of gyration as defined in Fig. 2.18. The mode frequencies for simple transverse vibrations are then given by Eq. (2.63) and vary with the longitudinal mode number n approximately as ( n + ½ )² . There are, of course, higher modes to be considered, particularly those with m > 0 associated with distortions of the tube cross section. There are also corrections to the simple formula (2.63) for the transverse mode frequencies to allow for coupling to distortions of the cross-section, rotary inertia, and other minor effects (Flugge, 1962). The effect of these corrections, broadly, is to slightly lower the frequencies of the higher modes relative to those predicted by the thin-bar formula.”

From page 641;
“One of the interesting characteristics of chimes is that there is no mode of vibration with a frequency at, or even near, the pitch of the strike tone one hears. This is an example of a subjective tone created in the human auditory system. Modes 4, 5, and 6 appear to determine the strike tone.
This can be understood by noting that these modes for a free bar have frequencies in the ratios 9²:11²:13², or 81:121:169, which are close enough to the ratios 2:3:4 for the ear to consider them nearly harmonic and to use them as a basis for establishing a pitch. The largest near-common factor in the numbers 81,121, and 169 is 41.”