Explanation:
Because the tuning fork is in resonance with air column in the pipe closed at one end, the frequency is \(f=\dfrac{(2 n-1) v}{4 l}\) where \(n=1,2,3 \ldots\) corresponds to different mode of vibration putting \(f = 340\;Hz,v = 340\;m/s\), the length of air column in the pipe can be
\(l = \frac{{(2n - 1)340}}{{4 \times 340}} = \frac{{(2n - 1)}}{4}m = \frac{{(2n - 1) \times 100}}{4}\;cm\)
For \(n=1,2,3, .\). we get \(l = 25\;cm,75\;cm,125\;cm \ldots \)
As the tube is only \(120\;cm\) long, length of air column after water is poured in it may be \(25\;cm,{\text{ }}75\;cm\), only The corresponding length of water column in the tube will be \((120 - 25)cm = 95\;cm\,\,{\text{or}}\,\,(120 - 75)cm = 45\;cm\).
Thus minimum length of water column is \(45\;cm\).