Which of the following statements is wrong?

Options

A. In an open pipe the fundamental frequency is `v//2l`
B. In a closed pipe the closed end is a node
C. In an open pipe only the odd harmonics of fundamental frequency are present
D. In a closed pipe the fundamental frequency is `v//4I`

Explanation

To determine which statement is wrong, let's analyze each statement one by one based on the principles of oscillations and waves, particularly focusing on the behavior of sound waves in open and closed pipes.

### Step-by-Step Solution:

1. **Understanding Closed Pipes**:
- In a closed pipe, one end is closed and the other is open. At the closed end, there is a node (point of no displacement), and at the open end, there is an antinode (point of maximum displacement).
- **Conclusion**: The statement "In a closed pipe, the closed end is a node" is correct.

2. **Analyzing Open Pipes**:
- An open pipe has both ends open, allowing for antinodes at both ends. The fundamental frequency (first harmonic) of an open pipe is given by the formula:
\[ f_1 = \frac{v}{2L} \]
where \( v \) is the speed of sound and \( L \) is the length of the pipe.
- **Conclusion**: The statement "In an open pipe, the fundamental frequency is \( \frac{v}{2L} \)" is correct.

3. **Harmonics in Open Pipes**:
- In an open pipe, both odd and even harmonics are present. The frequencies of the harmonics can be expressed as:
\[ f_n = \frac{nv}{2L} \]
where \( n \) is any positive integer (1, 2, 3, ...). This means that both odd and even harmonics can exist in an open pipe.
- **Conclusion**: The statement "In an open pipe, only odd harmonics of fundamental frequency are present" is incorrect.

4. **Understanding Closed Organ Pipes**:
- For a closed organ pipe, the fundamental frequency is given by:
\[ f_1 = \frac{v}{4L} \]
This is because the closed end has a node and the open end has an antinode, allowing only odd harmonics.
- **Conclusion**: The statement "In closed organ pipe, the fundamental frequency will be \( \frac{v}{4L} \)" is correct.

### Final Conclusion:
The wrong statement among the options is:
- "In an open pipe, only odd harmonics of fundamental frequency are present."