Question

In a resonance column apparatus, first resonance is obtained when the water filling beaker (of cylindrical shape) is just empty as shown. The water filling beaker is lowered down and it is seen that second resonance is obtained when beaker is filled up to brim. If the tuning fork has a frequency $420\,Hz$ , what is the speed (in $ms^{- 1}$ ) of sound in air?

Answer 1

Frequency of first resonance in closed pipe is given as $f=\frac{C}{4 l_{1}}$
Frequency of second resonance in closed pipe is given as $f=\frac{3}{4 l_{2}}C$
Equating the volume of the both tubes opening, we have
$\pi \left(4\right)^{2}10=\pi \left(2\right)^{2}\Delta l_{2}$
$\Delta l_{2}=40\,cm=\frac{\lambda }{2}$
$\lambda =80\,cm$
Speed of sound in air is $C=\lambda \times \nu=0.8\times 420=336\,ms^{- 1}$