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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 a closed organ pipe.

Text Solution

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Closed organ pipe :
Let `lambda_(1)` be the wavelength of the standing waves set up in the air column corresponding to m = 1. Then we have
`" "lambda_(1)=4l, l=(lambda_(1))/4`

There is an antinode (A) at the open end and a node (N) at the closed end. The frequency of vibration in this mode is given by :
`" "n_(1)=v/lambd_(1)=v/(4l)`
It is called the fundamental mode.
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