Which reminds me.

[tyggerjai]

There was a trigger for that rant.

Question for the physics geeks, to save me whole minutes on google.

Building wind chimes. The pitch of a tube, when struck, is a function of volume, neh? Anyone have the formula to hand?

And is it *just* volume, or does diameter specifically affect it, beyond altering the volume given a constant length? Intuitively, too narrow or too wide presumably reduces the effectiveness of the pipe, and something nags in my memory about diameter affecting frequency in some hardcore way - a teenyweeny diameter pipe will never give you a "deep" note, no matter how long it is.

Or am I smoking crack?


UPDATE: I had in mind a design with different sized (inner & outer diamter, for the smartarse punk who points out that if they're the same size, they're the same pitch...) pipes. But I could use the same pipe, at first, which makes it easy:

See also "Basic Acoustics" by Donald E. Hall, Harper & Row, NY, 1987. This book points out that for two bars being identical except in their lengths, their frequencies are related as:

f1 / f2 = (L1 / L2)^2

Which makes it trivial to plug in the frequencies I want, and calculate the lengths.

sol.
.

Comments

[lederhosen.livejournal.com]

And is it *just* volume, or does diameter specifically affect it, beyond altering the volume given a constant length? Intuitively, too narrow or too wide presumably reduces the effectiveness of the pipe, and something nags in my memory about diameter affecting frequency in some hardcore way - a teenyweeny diameter pipe will never give you a "deep" note, no matter how long it is.

...

See also "Basic Acoustics" by Donald E. Hall, Harper & Row, NY, 1987. This book points out that for two bars being identical except in their lengths, their frequencies are related as:

f1 / f2 = (L1 / L2)^2

That really doesn't look right. Let's say tube 1 is 2 meters long, tube 2 is 1 meter long... then f1/f2 = (2/1)^2 = 4, so the longer tube is two octaves *higher* in pitch, which is just wrong.

The power relationship also looks wrong. I'd expect f1/f2 = l2/l1.

[lederhosen.livejournal.com]

Sorry, meant to write more on this...

When you strike a tube, sound is created by the shockwaves that propagate through that tube. (This is a different mechanism from that in wind instruments, where the sound's created by air vibrating inside a tube.)

If the tube's diameter, thickness, and material are constant, the speed at which that shockwave propagates up and down the tube should be constant. Hence, the frequency should be directionally proportional to 1/l.

However, this is a first-order approximation based on a long skinny tube. Shockwaves don't just travel up and down the tube; they also travel around it, and the time it takes for those waves to go around the tube depends on its diameter. If you make your tube short enough and wide enough, that mode can become important, and you no longer have a simple length/frequency relationship.

See also:

http://tyala.freeyellow.com/4scales.htm

[tyggerjai.livejournal.com]

*nodnod* It intuitively made sense that at some point, too narrow or too wide interferes with the sound.

sol.
.

[tyggerjai.livejournal.com]

OMG. Google lied to me!!! Teh Intarweb was WRONG!!

Just goes to show. Windchimes are for hippies who can't count.

Hows this:

Each octave halves frequency and doubles pipe length

Which is exactly the formula you give. The original site did indeed claim that halving the length would give a two octave rise in pitch.

Cool. Your is even easier to work with :)

Windchimes in A minor, coming up.

sol.
.

[lederhosen.livejournal.com]

The original site did indeed claim that halving the length would give a two octave rise in pitch.

This one, I'm guessing?

Hmm. Now I wrangle the physics a bit more, I'm less sure of myself... the two-octave claim *might* be correct after all, if we're talking about a flexure mode, which we probably are.

Dammit, I should be able to do this; I'm rustier than I thought. Better try it out instead of relying on me :-)

At the least, though, he's got it upside-down. Longer bars should have lower frequencies.

[lederhosen.livejournal.com]

Yeah, I think the two-octave claim is correct. Dammit. That'll teach me to post when I'm tired; I was thinking of the wrong vibrational mode.

http://home.fuse.net/engineering/Chimes.htm has some good stuff, including links to calculators etc.

[thorfinn]

http://www.giftsonline.net/catalog/images/xylophone.jpg

seems to agree. One octave is not half the length. Two octaves, half length. And yes, smaller tube is higher frequency.

[tyggerjai.livejournal.com]

Eh.
I figure I can hack 24ths off a pipe until I get tones.

I think 24ths is the key, really - given that (and I should have remembered the link between doubling and octaves, which is really all I needed) I can wing it. But that site you posted really goes into details on the C2/fundamental/overtone stuff. On the one hand, this may take some work. On th othe, I doubt the el cheapo $30 windchimes from the little asian places at teh market get it right either :)

sol.
.

[ltempt.livejournal.com]

I know that I would stick a frequency generator (err, laptop) on one CRO input and a microphone on the other, and tuning would become much, much easier.

Pipe, powertools and curry? I'll bring the CRO.

[tyggerjai.livejournal.com]

I think this completely negates the point :)

But thanks for the thought. It's about doing it the hard way - craftmanship, rather than modern soulless machinery.

sol.
.