In open organ pipe, first overtone produced is of such frequency that length of the pipe is equal to

Options

A. `lamda//4`
B. `lamda//3`
C. `lamda//2`
D. `lamda`

Explanation

To solve the problem regarding the length of an open organ pipe when the first overtone is produced, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Harmonics**:
- An open organ pipe supports stationary waves with both ends open. The fundamental frequency (first harmonic) has one antinode at each open end and one node in the middle. The first overtone corresponds to the second harmonic, which has two antinodes and one node in the middle.

2. **Identify the Relationship Between Length and Wavelength**:
- For an open organ pipe, the length \( L \) of the pipe is related to the wavelength \( \lambda \) of the sound wave produced. The relationship for the fundamental frequency (first harmonic) is:
\[ L = \frac{\lambda}{2} \]
- For the first overtone (second harmonic), the relationship becomes:
\[ L = \lambda \]

3. **Determine the Length of the Pipe for First Overtone**:
- Since the first overtone corresponds to the second harmonic, we can conclude that the length of the pipe \( L \) is equal to the wavelength \( \lambda \):
\[ L = \lambda \]

4. **Conclusion**:
- Therefore, the length of the open organ pipe when the first overtone is produced is equal to \( \lambda \).

### Final Answer:
The length of the pipe is equal to \( \lambda \).

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