In a resonance tube experiment, a close organ pipe of length $120 cm$ resonates when tune with a tuning fork of frequency $340 Hz$. If water is poured in the pipe then $\left(given v_{air}=340 m/sec\right)$

As $$\begin{gathered} v=v\lambda \\ \lambda =\frac{v}{v}=\frac{340}{340}=1m \end{gathered}$$

First resonance length

$R_1=\frac{\lambda }{4}=\frac{1}{4}m=25cm.$

Therefore, $R_2=\frac{3\lambda }{4}=\frac{3}{4}m=75cm$.

Therefore, $R_3=\frac{5\lambda }{4}=\frac{5}{4}m=125cm$.

i.e., third resonance does not establish.

Now $H_{2}O$ is poured,

Therefore, Minimum length of $H_{2}O$ column to have the resonance $=45cm$.

Therefore, Distance between two successive nodes $=\frac{\lambda }{2}=\frac{1}{2}m=50cm$ and maximum length of $H_{2}O$ column to create resonance i.e., $120-25=95 cm$.