What are the equations for whistling in a convoluted tube?

[manjagu]

Does anyone know what the equations governing the effects of whistling in a convoluted tube as air passes trough it are? I didn't know it was called this until today, but a convoluted tube is the real name for what many cable management tubes are. These tubes are also used in medicine for things like ventilators. You used to be able purchase large ones as a toys, which you could twirl around above your head. The faster you twirl them, the higher pitch whistle you could get out of it.

Thanks!

 

[Bobbywhy]

manjagu, Welcome to Physics Forums!

The toy you mention can be purchased here:
Whirlies
An introduction to whirled music
http://www.exo.net/~pauld/summer_institute/summer_day13music/Whirly.html

The convoluted tube that produces sound is also used as a golf swing practice device described in this patent:
Golf swing practice system with convoluted tube
http://www.patentgenius.com/patent/6503149.html

For an excellent description of how it works see this from the Exploratoruim:
Aerodynamics researchers in Japan put a whirly in a wind tunnel and used very tiny hot wire anemometers to measure the airflow near the corrugations.
They discovered that air flowing over two successive corrugations in the wall of the whirly experienced "impinging shear flow instability."
This is the same effect that makes a tea kettle sing. If you look at the spout of a teakettle you will see that it has two disks separated by a short gap, each with a hole in its center. When the air, or steam, flows through the first hole and then flows through the second hole it exits in vortices which cause oscillating pressure in the air, heard by the human ear as a whistle. The ridges in the whirly tube play the same role. As the air flows first over one ridge then over a second it tumbles into a vortex. The faster the air flows through the tube the higher the frequency of the sound produced by the vortex. When the frequency of the vortex matches one of the natural resonant frequencies of the tube it is amplified.
http://isaac.exploratorium.edu/~pauld/activities/AAAS/aaas2001.html

If you still need the exact numerical methods to describe this you may search for
“Impinging shear flow instability”.

Cheers,
Bobbywhy

 

[manjagu]

Thanks for the thorough response! Very helpful.