This question assesses the understanding of the resonance air-column experiment used to determine the speed of sound. Let's analyze each option step-by-step.

Step 1: Analyze Option A

Statement: The intensity of the sound heard at the first resonance was more than that at the second resonance.

• Concept: In a resonance air-column, a standing wave is formed. The sound source (tuning fork) continuously supplies energy to the air column. This energy travels down the tube, reflects off the water surface, and travels back up.
• Damping: As the sound wave travels through the air column, some of its energy is dissipated due to factors like air viscosity and interactions with the tube walls. This phenomenon is known as damping.
• Path Length: The first resonance occurs at a shorter air-column length ($L_1$), while the second resonance occurs at a longer length ($L_2$). Consequently, the sound wave travels a longer distance for the second resonance ($L_2 > L_1$).
• Intensity: Due to the longer path, the energy loss due to damping is greater for the second resonance. This results in a smaller amplitude for the standing wave compared to the first resonance. Since the intensity of sound is proportional to the square of the amplitude of vibration, the sound heard at the first resonance is louder (more intense) than at the second resonance.
• Conclusion: Option A is correct.

Step 2: Analyze Option B

Statement: The prongs of the tuning fork were kept in a horizontal plane above the resonance tube.

• Concept: This relates to the experimental technique for efficiently transferring energy from the tuning fork to the air column.
• Vibration Direction: The prongs of a tuning fork vibrate in a direction perpendicular to their length. The air column is vertical, so to excite the longitudinal wave most effectively, the air at the mouth of the tube should be driven vertically.
• Orientation: If the prongs are held in a horizontal plane, they vibrate up and down (vertically). This vertical vibration efficiently transfers energy to the vertical air column. This is the optimal orientation.
• Alternative Orientation: However, the experiment also works if the tuning fork is held with its prongs vertical. In this case, the prongs vibrate horizontally. While less efficient, enough sound energy enters the tube to produce resonance.
• Deduction: The question asks for conclusions that can be drawn from the fact that resonance was observed. Since resonance can be achieved with either orientation, we cannot definitively conclude that the prongs were kept in a horizontal plane. It is a statement about the procedure, not a necessary physical consequence of the result.
• Conclusion: Option B is not a necessary conclusion, so it is considered incorrect.

Step 3: Analyze Option C

Statement: The amplitude of vibration of the ends of the prongs is typically around 1 cm.

• Concept: This statement is about the typical physical characteristics of a laboratory tuning fork.
• Amplitude: A tuning fork is a rigid instrument designed to produce a nearly pure tone with minimal damping. To achieve this, the amplitude of vibration is generally very small. A typical amplitude is on the order of a fraction of a millimeter to at most a few millimeters.
• Scale: An amplitude of 1 cm (10 mm) is extremely large for a standard tuning fork. Such a large vibration would require striking the fork very hard, which would introduce significant overtones (making the sound impure), cause the vibration to dampen very quickly, and could potentially damage the fork.
• Conclusion: Option C is incorrect.

Step 4: Analyze Option D

Statement: The length of the air-column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air.

• Concept: This statement relates to the phenomenon of end correction in open-ended pipes.
• Ideal vs. Real Case: For an ideal closed pipe (closed at one end, open at the other), the displacement antinode is located exactly at the open end. In this ideal case, the first resonance length would be exactly $L_1 = \lambda/4$.
• End Correction: In reality, the air particles just outside the open end are also part of the vibration. The reflection of the wave effectively occurs at a point slightly above the open end. This means the antinode is formed at a small distance 'e' (the end correction) outside the tube.
• Resonance Condition: The condition for the first resonance is that the effective length of the air column is equal to $\lambda/4$. The effective length is the physical length $L_1$ plus the end correction 'e'. $L_1 + e = \frac{\lambda}{4}$
• Result: Since the end correction 'e' is a positive value (typically $e \approx 0.6r$, where $r$ is the radius of the tube), the physical length of the air column must be less than $\lambda/4$. Rearranging the equation gives: $L_1 = \frac{\lambda}{4} - e$
• Conclusion: Option D is correct.

Final Summary

Based on the analysis:

• Option A is correct.
• Option B is not a necessary conclusion.
• Option C is factually incorrect.
• Option D is correct.

Therefore, the correct options are A and D.