A U-tube having unequal arm-lengths contains water. A tuning fork...

The air columns in the U-tube act as closed organ pipes since they are closed by water at the bottom and open at the top.

The wavelength of the sound wave is given by:

$\lambda = \dfrac{v}{f} = \dfrac{330}{440} = 0.75 \text{ m} = 75 \text{ cm}$

For the shorter arm vibrating in its fundamental mode, the length of the air column $L_1$ is:

$L_1 = \dfrac{\lambda}{4} = \dfrac{75}{4} = 18.75 \text{ cm} \approx 18.8 \text{ cm}$

For the longer arm vibrating in its first overtone, the length of the air column $L_2$ is:

$L_2 = \dfrac{3\lambda}{4} = \dfrac{3 \times 75}{4} = 56.25 \text{ cm} \approx 56.3 \text{ cm}$

The lengths of the air columns are $18.8 \text{ cm}$ and $56.3 \text{ cm}$.