Frequency of sound involving bamboo flutes

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Khai Xi
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Dear all,

I have been attempting to create a range of bamboo flutes with different lengths for my physics practical. I am trying to calculate the theoretical frequency that should be produced by a particular length of flute, but all my flutes have different diamaters and I am searching for an equation that takes into account the diameter of the flute as well as the length of the flute to produce a particular frequency. Can anyone help me?
 
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As this is a practical project, have you experimented with flutes of the same length and different diameters?