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Derive an equation for the first mode of...

Derive an equation for the first mode of vibration of an air column in an open organ pipe.

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First mode of vibration of an air column for open organ pipe :
Let `lambda_(1)` be the wavelength of the standing waves set up in the air column corresponding to m = 1.
we have
`" "lambda_(1)=2l`
`" "l=lambd_(1)/2" ...(i)"`
There are anti-nodes (A) at the two ends and a node (N) in the middle of the pipe. The frequency of vibration in this mode is given by :
`" "n_(1)=v/lambda_(1)=v/(2l)`

This is the lowest frequency of vibration and is called the fundamental frequency of the air column in the open organ pipe.
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