The fundamental note produced by a closed organ pipe is of frequency v. The fundamental note produced by an open organ pipe of same length will be of frequency

Options

A. `upsilon/2`
B. `upsilon`
C. `2upsilon`
D. `4upsilon`

Explanation

To find the frequency of the fundamental note produced by an open organ pipe of the same length as a closed organ pipe, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Frequencies of Closed and Open Pipes**:
- The fundamental frequency \( f_c \) for a closed organ pipe is given by the formula:
\[ f_c = \frac{v}{4L} \]
- The fundamental frequency \( f_o \) for an open organ pipe is given by the formula:
\[ f_o = \frac{v}{2L} \]
where \( v \) is the speed of sound in air and \( L \) is the length of the pipe.

2. **Given Information**:
- We are told that the fundamental frequency for the closed organ pipe is \( \nu \):
\[ f_c = \nu \]

3. **Relate the Frequencies**:
- From the formula for the closed pipe, we can express the speed of sound in terms of the frequency and length:
\[ \nu = \frac{v}{4L} \]
- Rearranging this gives:
\[ v = 4L\nu \]

4. **Substituting into the Open Pipe Formula**:
- Now, we substitute \( v \) into the open pipe frequency formula:
\[ f_o = \frac{v}{2L} = \frac{4L\nu}{2L} \]
- Simplifying this gives:
\[ f_o = 2\nu \]

5. **Conclusion**:
- Therefore, the fundamental frequency produced by the open organ pipe of the same length is:
\[ f_o = 2\nu \]

### Final Answer:
The fundamental note produced by an open organ pipe of the same length will be of frequency \( 2\nu \).