An air column in a pipe, which is closed at one end, will be in resonance wtih a vibrating tuning fork of frequency $264\, Hz$ if the length of the column in $cm$ is (velocity of sound $= 330\, m/s$)
AIEEE 2012, Medium
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Frequency of tuning fork.
$n=264 \mathrm{Hz}$
Length of column $L=?$
For closed organ pipe
$n=\frac{v}{4l}$
$\Rightarrow l=\frac{v}{4 n}=\frac{330}{4 \times 264}=0.3125$
or, $l=0.3125 \times 100=31.25 \mathrm{cm}$
In case of closed organ pipe only odd harmonics are possible.
Therefore value of $l$ will be $(2 n-1) l$
Hence option $(b)$ i.e. $3 \times 31.25=93.75 \mathrm{cm}$ is correct
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