If we study the vibration of a pipe open at both ends, then the following statements is not true

Options

A. open end will be antinode
B. odd harmonics of the fundamental frequency
C. All harmonics of the fundamental frequency will be generated
D. pressure change will be maxium at both ends.

Answer

To determine which statement is not true regarding the vibration of a pipe open at both ends, we can analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding the Pipe Configuration**:
- A pipe open at both ends has antinodes at both ends. This is because the open ends allow the air to vibrate freely, leading to maximum displacement (antinodes) at these points.

2. **Identifying the Harmonics**:
- For a pipe open at both ends, the harmonics that can be produced are all harmonics (both even and odd). The fundamental frequency (first harmonic) has a wavelength of \( \lambda = 2L \), where \( L \) is the length of the pipe.

3. **Analyzing Each Statement**:
- **Option A**: "Open ends will be antinodes."
- This is true. The ends of the pipe are indeed antinodes.
- **Option B**: "All harmonics of the fundamental frequency will be generated."
- This is also true. Both even and odd harmonics are present in a pipe open at both ends.
- **Option C**: "Odd harmonics of the fundamental frequency."
- This statement is misleading. While odd harmonics are present, it is not exclusive to only odd harmonics; even harmonics are also present. Thus, this statement is somewhat ambiguous but can be interpreted as true since odd harmonics do exist.
- **Option D**: "Pressure change will be maximum at both ends."
- This statement is not true. Since both ends are open, the pressure remains at atmospheric pressure, and there is no pressure change at the ends.

4. **Conclusion**:
- The statement that is not true is **Option D**: "Pressure change will be maximum at both ends." This is incorrect because there is no pressure change at the open ends of the pipe.

### Final Answer:
The statement that is not true is: **Pressure change will be maximum at both ends.**

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