Orientation of Tuning Fork and Resonating Air Column in Sound Speed Experiment

To determine the correct statement, let us analyze the principles and experimental setup of the resonance column experiment:

1. Orientation of the Tuning Fork:
   In the resonance column apparatus, the resonating air column is inside a vertical tube that is closed at the bottom by the water surface and open at the top. To set up longitudinal sound waves traveling down the tube, the air column must be subjected to longitudinal compressions and rarefactions along its vertical axis.

   • When the prongs of the vibrating tuning fork are kept in a vertical plane directly above the open end of the tube, the prong vibrates up and down. This motion effectively produces longitudinal compressions and rarefactions directly along the axis of the vertical air column.
   • Therefore, the prongs of the tuning fork must vibrate in a vertical plane.

2. Lengths of the Resonating Air Column:
   A resonance column acts as a pipe closed at one end and open at the other. For a sound wave of wavelength $\lambda$, the positions of resonance (taking end correction $e$ into account) occur at:
   $l_1 + e = \frac{\lambda}{4} \implies l_1 \approx \frac{\lambda}{4}$
   $l_2 + e = \frac{3\lambda}{4} \implies l_2 \approx \frac{3\lambda}{4}$

   • The first resonating length is approximately $\frac{\lambda}{4}$ (one-quarter of the wavelength).
   • The second resonating length is approximately $\frac{3\lambda}{4}$ (three-quarters of the wavelength).
   • Neither of these lengths is close to $\lambda$ or $\frac{\lambda}{2}$. Thus, options (C) and (D) are incorrect.

Hence, the correct statement is that the prongs of the tuning fork are kept in a vertical plane.

Therefore, the correct option is A.