A tuning fork of frequency $340\,\, Hz$ is vibrated just above a cylindrical tube of length $120 \,\,cm$. Water is slowly poured in the tube. If the speed of sound is $340\,\, ms^{-1}$ then the minimum height of water required for resonance is .... $cm$
Medium
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The wavelength of the wave is
$\lambda=\frac{v}{\nu}$
$\lambda=\frac{340}{340}=1 m$
Therefore for different resonances, the required lengths of the air column are
$\frac{\lambda}{4}, \frac{3 \lambda}{4}, \frac{5 \lambda}{4}$ i.e. $25 \mathrm{cm}, 75 \mathrm{cm}, 125 \mathrm{cm}$
As the length of pipe is120cm, the resonance corresponding to $125 \mathrm{cm}$ is not possible.
So, when the water is slowly poured, the first resonance will occur at length
$75 \mathrm{cm}$ of air column. Hence, the height of water is
$h=120-75=45 \mathrm{cm}$
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