A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then,

A. the intensity of the sound heard at the first resonance was more than at the second resonance
B. the prongs of the tuning fork were kept in a horizontal plane above the resonance tube
C. the ampitude of vibration of the end of the prongs is typically around `1 cm`
D. the length of the air-column at the first resonance was somewhat than `1//4` th of the wavelength of the sound in air.

Options

A. the intensity of the sound heard at the first resonance was more than at the second resonance
B. the prongs of the tuning fork were kept in a horizontal plane above the resonance tube
C. the ampitude of vibration of the end of the prongs is typically around `1 cm`
D. the length of the air-column at the first resonance was somewhat than `1//4` th of the wavelength of the sound in air.

Explanation

To solve the question regarding the resonance air-column method for measuring the speed of sound in air, we will analyze each of the options provided.

### Step-by-Step Solution:

1. **Understanding Resonance in Air Columns**:
- In the resonance air-column method, the first resonance occurs when the length of the air column is approximately one-quarter of the wavelength of the sound wave. The second resonance occurs at a longer length, typically at three-quarters of the wavelength.

2. **Analyzing the Options**:
- **Option A**: "The intensity of the sound heard at the first resonance was more than at the second resonance."
- In resonance experiments, the first resonance (shorter air column) typically has a higher intensity than the second resonance (longer air column) because the shorter column absorbs less energy. Therefore, this statement is **correct**.

- **Option B**: "The prongs of the tuning fork were kept in a horizontal plane above the resonance tube."
- The tuning fork should be placed at the top of the resonance tube, typically in a vertical position, to ensure that the sound waves can effectively enter the tube. Hence, this statement is **incorrect**.

- **Option C**: "The amplitude of vibration of the end of the prongs is typically around 1 cm."
- The amplitude of the tuning fork's prongs can vary, but it is generally much smaller than 1 cm in practical scenarios. This statement is **not typically accurate** and is therefore **incorrect**.

- **Option D**: "The length of the air-column at the first resonance was somewhat than 1/4 of the wavelength of the sound in air."
- The first resonance indeed occurs when the length of the air column is approximately one-quarter of the wavelength. Thus, this statement is **correct**.

3. **Conclusion**:
- Based on the analysis, the correct options are **A** and **D**.

### Final Answer:
- The correct options are **A** and **D**.