In an organ pipe of length L open at both ends, the fundamental mode has a frequency
(where v is a speed of sound in air)

Options

A. `v/(2L)` and only odd harmonies are present.
B. `v/(2L)` and only even harmonies are present.
C. `v/(2L)` and all harmonies are present.
D. `v/(4L)` and only odd harmonies are present.

Explanation

To find the fundamental frequency of an organ pipe of length \( L \) that is open at both ends, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Pipe Configuration**:
- An organ pipe that is open at both ends supports standing waves with antinodes at both ends. This means that the fundamental frequency corresponds to the simplest standing wave pattern.

2. **Determine the Wavelength**:
- For a pipe open at both ends, the fundamental mode (first harmonic) has a wavelength \( \lambda \) such that the length of the pipe \( L \) is equal to half the wavelength:
\[ L = \frac{\lambda}{2} \]
- Rearranging this gives:
\[ \lambda = 2L \]

3. **Use the Wave Speed Formula**:
- The frequency \( f \) of a wave is related to its speed \( v \) and wavelength \( \lambda \) by the formula:
\[ f = \frac{v}{\lambda} \]

4. **Substitute the Wavelength**:
- Substitute \( \lambda = 2L \) into the frequency formula:
\[ f = \frac{v}{2L} \]

5. **Conclusion**:
- Therefore, the fundamental frequency \( f \) of the organ pipe is:
\[ f = \frac{v}{2L} \]

### Final Answer:
The fundamental frequency of an organ pipe of length \( L \) open at both ends is given by:
\[ f = \frac{v}{2L} \]