Observations in Resonance Air Column Experiment for Sound Speed

To determine the correct statements regarding the resonance air-column experiment:

1. Option (A): Intensity of Sound
   At the first resonance, the length of the air column is shorter ($l_1 \approx \frac{\lambda}{4} - e$), while at the second resonance, the length is longer ($l_2 \approx \frac{3\lambda}{4} - e$). For the longer air column, there is greater dissipation and attenuation of sound energy due to multiple reflections and visco-thermal damping along the length of the tube. Consequently, the standing wave formed in the shorter air column has higher amplitude, and the intensity of the sound heard at the first resonance is greater than that at the second resonance.
   Therefore, Option (A) is correct.

2. Option (B): Orientation of the Tuning Fork
   To produce strong longitudinal sound waves directed into the resonance tube, the prongs of the tuning fork must vibrate in a vertical plane above the open end of the tube (so that the motion of the prongs effectively compresses and rarefies the air column along its axis). Holding them in a horizontal plane is incorrect.
   Therefore, Option (B) is incorrect.

3. Option (C): Amplitude of Vibration of the Prongs
   The typical amplitude of vibration of a tuning fork prong used in acoustic experiments is very small, typically of the order of a fraction of a millimeter (less than $1\text{ mm}$). An amplitude of $1\text{ cm}$ is extraordinarily large and physically unrealistic for a standard tuning fork.
   Therefore, Option (C) is incorrect.

4. Option (D): Length of the Air-Column at First Resonance
   Taking into account the end correction $e \approx 0.6r$ (where $r$ is the radius of the tube), the antinode forms slightly outside the open end. The condition for the first resonance is:
   $l_1 + e = \frac{\lambda}{4} \implies l_1 = \frac{\lambda}{4} - e$
   Since $e > 0$, the actual length of the air column $l_1$ is somewhat shorter than $\frac{1}{4}\text{th}$ of the wavelength $\lambda$.
   Therefore, Option (D) is correct.

Correct Answer: A, D