# In a resonance tube experiment when the tube is filled with water up to a height of $17.0\; cm$ from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of $24.5\; cm$. If the velocity of sound in air is $330\; m/s$, the tuning fork frequency is :  Option: 1 Option: 2 Option: 3 Option: 4

$\begin{array}{l} \mathrm{L}-\mathrm{h}_{1}=\mathrm{n} \frac{\lambda}{2}+\frac{\lambda}{4} \\ \\ \mathrm{~L}-\mathrm{h}_{2}=(\mathrm{n}-1) \frac{\lambda}{2}+\frac{\lambda}{4} \\ \\ \Rightarrow \quad \frac{\lambda}{2}=\mathrm{h}_{2}-\mathrm{h}_{1}=24.5-17.0=7.5 \mathrm{~cm} \\\\ \Rightarrow \quad \lambda=15 \mathrm{~cm} \\\\ \mathrm{u}=\mathrm{f} \lambda \\\\ \mathrm{f}=2200 \mathrm{~Hz} \end{array}$

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