A student is performing the experiment of Resonance Column. The diameter of the column tube is $4 \ cm$. The distance frequency of the tuning for $k$ is $512 \ Hz$. The air temperature is $38^{\circ} C$ in which the speed of sound is $336 \ m / s$. The zero of the meter scale coincides with the top and of the Resonance column. When first resonance occurs, the reading of the water level in the column is
IIT 2012, Advanced
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$\frac{ V }{4(\ell+ e )}= f $
$\Rightarrow \ell+ e =\frac{ V }{4 f } $
$\Rightarrow \ell=\frac{ V }{4 f }- e $
$\text { here } \quad e =(0.6) r =(0.6)(2)=1.2 \ cm $
$\text { so } \ell=\frac{336 \times 10^2}{4 \times 512}-1.2=15.2 \ cm$
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