How does the size of tube effect the pitch in wind chimes?

i know that you can change how long the tube is and that will change the pitch but i want to know how that will help the pitch.....like how does the change in size of the tube help to change the pitch???How does the size of tube effect the pitch in wind chimes?
The fundamental pitch is based on two basic factors. The mass that is swinging back and forth and the spring stiffness that turns the motion around and sends it the other way. Longer tubes are less stiff and have more mass, so have lower pitches. Shorter tubes have less mass and are stiffer, so produce higher pitches. The mass is proportional to the length, but the stiffness changes as the third power of length. I think the frequency is roughly proportional to the square root of (stiffness divided by mass)



That means that a tube that is half as long as an otherwise similar tube has half the mass, and 8 times the stiffness, for times the resonant frequency of the short tube is about 4 times higher than the one twice as long. Remember that this only works for tubes of the same material, diameter and wall thickness. And only applies to the lowest resonance, not the higher order vibrating modes.



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Regards,



John PopelishHow does the size of tube effect the pitch in wind chimes?
If you shorten the tube it will have a higher pitch. The vibrating tube will emit a shorter wavelength from a shorter tube.





Also if you are starting with untried tubes the diameter and the thickness of the tube will make a difference.