When the open organ pipe resonates in its fundamental mode then at the centre of the pipe

Options

A. The gas molecules undergo vibrations of maximum amplitude
B. The gas molecules are at rest
C. The pressure of the gas is constant
D. The pressure of the gas undergoes maximum variation

Answer

To solve the question regarding the behavior of an open organ pipe resonating in its fundamental mode, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Structure of an Open Organ Pipe**:
- An open organ pipe has two open ends, which means that both ends can vibrate freely. In the fundamental mode, the pipe will resonate with a specific pattern of pressure variations.

2. **Identifying Nodes and Antinodes**:
- In the fundamental mode of an open pipe, there is one antinode at each open end and one node at the center of the pipe. This means that at the center of the pipe, the pressure variation is at its minimum, while at the ends, the pressure variation is at its maximum.

3. **Pressure Variation in the Pipe**:
- As the pipe resonates, the pressure at the center (node) remains constant (neither maximum nor minimum), while the pressure at the ends (antinodes) fluctuates between maximum and minimum values. This indicates that there is a pressure variation along the length of the pipe.

4. **Conclusion**:
- Therefore, when the open organ pipe resonates in its fundamental mode, at the center of the pipe, the pressure is constant (neither maximum nor minimum), and the gas molecules are not at rest; they are oscillating due to the pressure variations.

5. **Final Answer**:
- The correct option is that at the center of the pipe, the pressure is constant.