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  4. An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is (velocity of sound = 330 m/s)

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Q. An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency $264\, Hz$ if the length of the column in cm is (velocity of sound = $330\, m/s$)

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Solution:

Given : Frequency of tuning fork, n = 264 Hz
Length of column L = ?
For closed organ pipe
$n = \frac{v}{4l}$
$\Rightarrow l = \frac{v}{4n} = \frac{330}{4\times264} = 0.3125$
or, $l= 0.3125 \times 100 = 31.25 \,cm$
In case of closed organ pipe only odd harmonics are possible.
Therefore value of $I$ will be $\left(2n - 1\right) l $ Hence option $\left(b\right) i.e. \,3 \times 31.25 = 93.75\, cm$ is correct.