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Designing a resonance tube with a defined ambient wind speed

by AuroraIndust
Tags: equation, resonance, speed, tube, wind
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AuroraIndust
#1
Jan25-12, 05:36 PM
P: 11
Hello,

As we know, when you blow over the neck of a bottle, it resonates at a certain frequency.

I want to build a cylinder that will resonate at a certain wind speed: 4 mph or about 1.78 m/s

I definitely know how to find the resonant frequency of a cylinder. However, I'm not sure what equation would help me solve for finding what "wind speed" over the top would cause it to resonate!

What am I missing here? Is this a more difficult problem than I anticipate?

Thanks!
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AlephZero
#2
Jan25-12, 06:37 PM
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Thanks
P: 7,112
People have been designing wind instruments empirically for thousands of years, but it seems that a theory of what works and what doesn't was first published only in 1971!

The original paper is in German and is about organ pipes, so the geometry isn't exactly the same as your situation, but here's a reference to a (very short) summary in English: http://www.mmdigest.com/Tech/isingform.html

If you investigate how well this works for bottles, you will probably be doing some genuinely original research.
AuroraIndust
#3
Feb1-12, 07:06 PM
P: 11
Do you know what Q, the "Air consumption rate" might be referring to? I don't see where any air is being "consumed".

I can find the pressure of the air at the open end of the cylinder, and I know the pressure at the bottom of the cylinder. Assuming I know those and several other things I should be able to calculate what size/volume tube will work, right?

If someone can assist me in adapting this (http://www.mmdigest.com/Tech/isingform.html) to work with my situation, that would be much appreciated. As I can not figure out a way...

Thanks for any help!

maimonides
#4
Feb2-12, 03:54 AM
P: 129
Designing a resonance tube with a defined ambient wind speed

An organ pipe (or a recorder, for that matter) needs air blown into it: Thats your air consumption rate.
Are thinking of something like a a pan flute?
You can find a lot of information and details in Fletcher/Rossing, The physics of musical instruments.
And if my experience with instruments is not totally off: I donīt think you can make a speed detector out of a flute, and 2m/sec is far too slow.
Recorders need a blowing pressure of a few cm water gauge; organs are nearer to 10cm. (Transverse) flutes are not much different.
1cm water gauge = 100Pa => ~13m/sec

In the link, Walcker is a german organ builder and Hausmitteilung is "internal communication". Iīm sure you can find the articles by Ising elswhere


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