blowin' in the wind

[hoopy mike]

My latest project is designing a set of tubular bells. There's some really interesting physics going on with three distinct vibrational modes (stick with me, I'll get to what this has to do with whistles in a bit). Firstly, there's the bending vibration of the tube, secondly there's the vibration of the air column inside the tube and lastly, there are ovalling modes, where the tube vibrates away from a circular cross-section.

Wind chime makers (and probably tubular bell makers) tend to design chimes around an "ideal length" where the bending natural frequency of the tube matches the frequency of the vibrating air inside. Get it wrong and you end up with an unpleasant beating tone. Get it right and it's cosmic. The chimes are mounted/hung at a node point 22.4% down from the top. See the following website for more info:
http://mysite.verizon.net/cllsj/windchimes/home.htm

All of which got me wondering if whistles could be designed (or maybe are accidentally designed) around similar principles. Ok, so holding the whistle will dampen the bending modes, but maybe, just maybe a "good" whistle could be held lightly with the thumb about 22.4% of the way down where the bending node is located. I haven't checked the bending frequency of a whistle yet...

[henryz]

This could be an interesting line of whistle R&D (WRD?). You can use almost any of the mechanical FEA programs to map out the vibrational modes of a tube (or other structural shape) and simple math (or Dan B's Twcalc/spreadsheet) to get the air column resonant freq. Not too long ago, I tried taping a weight to the end of one of my more ill-behaved whistles to see that would dampen a resonant peak at the high-D note. It didn't seem to make much difference, so I didn't pursue it. I might have stopped playing (err, I mean doing acoustic science..) too soon.

Here's a link to a set of industrial-sized wind chimes (the bundle of tubes in the middle) that the company I work for did as a civic project. It was my job to "tune" the tube lengths.

http://i796.photobucket.com/albums/yy24 ... ike/wc.png

[hoopy mike]

Here's a link to a set of industrial-sized wind chimes (the bundle of tubes in the middle) that the company I work for did as a civic project. It was my job to "tune" the tube lengths.http://i796.photobucket.com/albums/yy24 ... ike/wc.png

They're great. Did you just cut to length or did you consider the frequency in the air column? There's a big difference in sound if you cut tubes to the so-called "ideal length".

[henryz]

The tube lengths were a compromise between aesthetics and sound - we wanted to the tube lengths to flow nicely from large to small. Of course that made some tubes chime quite robustly and others just sounded a bit "dead". The overall effect was reasonably pleasing, though a bit loud. It's probably a "good thing" that this sculpture sits in a public park, away from private homes (think young boys with sticks....).

If I get some free time at lunch hour, I'll see where the low-order vibrational modes fall for some typical whistle tubes, such as Gens.

[hoopy mike]

The tube lengths were a compromise between aesthetics and sound - we wanted to the tube lengths to flow nicely from large to small. Of course that made some tubes chime quite robustly and others just sounded a bit "dead".

Here's an example of some chimes I suspect to be around the ideal length:
http://www.soulvibs.com/

The overall effect was reasonably pleasing, though a bit loud. It's probably a "good thing" that this sculpture sits in a public park, away from private homes (think young boys with sticks....).

Or slightly older boys with air rifles?

If I get some free time at lunch hour, I'll see where the low-order vibrational modes fall for some typical whistle tubes, such as Gens.

Thanks - that'd be useful.

[henryz]

Ok - the first bending mode for a Gen D tube (nominally 0.500" OD/0.014" wall, brass) is approx. 843 Hz (just below first octave A). Interestingly, a 9/16" (0.562" OD)/0.040" wall aluminum D tube would have a first bending node at 1154 Hz, just shy of 2nd octave D. Maybe that's partially why some folks say aluminum sounds "brighter"

(These calcs assume that the fipple end is constrained - its makes the resonant freqs slightly different than if the tubes were totally free or held at their 22.4% length points).

PVC tubes (by virtue of the low density & elastic modulus) appear to have multiple modes that fall within the instruments' design ranges. Maybe that why they sound more complex ("woody"). Now I'll have to find some material data for typical whistle woods for additional WRD. But - have to go and do some real work, now.