An open organ pipe has fundamental frequency
100 Hz. What frequency will be produced if its one
end is closed ?

Options

A. 100, 200, 300….
B. 50, 150, 250….
C. 50, 100, 200, 300….
D. 50, 100, 150, 200….

Explanation

To solve the problem of determining the frequency produced by an organ pipe when one end is closed, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Fundamental Frequency of an Open Pipe**:
- The fundamental frequency (first harmonic) of an open organ pipe is given by the formula:
\[ f_1 = \frac{V}{2L} \]
- Here, \(f_1\) is the fundamental frequency, \(V\) is the speed of sound in air, and \(L\) is the length of the pipe.

2. **Given Information**:
- The fundamental frequency of the open pipe is given as \(100 \, \text{Hz}\).
- Therefore, we can write:
\[ f_1 = 100 \, \text{Hz} = \frac{V}{2L} \]

3. **Calculate the Ratio of Speed of Sound to Length**:
- Rearranging the equation gives us:
\[ \frac{V}{L} = 200 \, \text{Hz} \]

4. **Transition to a Closed Pipe**:
- When one end of the pipe is closed, the fundamental frequency is given by:
\[ f'_1 = \frac{V}{4L} \]
- This is because a closed pipe supports odd harmonics only.

5. **Calculate the New Fundamental Frequency**:
- Using the value of \(\frac{V}{L}\) we found earlier:
\[ f'_1 = \frac{V}{4L} = \frac{1}{2} \cdot \frac{V}{2L} = \frac{1}{2} \cdot 100 \, \text{Hz} = 50 \, \text{Hz} \]

6. **Determine Higher Harmonics**:
- The frequencies for a closed pipe will be:
- First harmonic: \(f'_1 = 50 \, \text{Hz}\)
- Third harmonic: \(f'_3 = 3f'_1 = 150 \, \text{Hz}\)
- Fifth harmonic: \(f'_5 = 5f'_1 = 250 \, \text{Hz}\)

### Final Answer:
The frequencies produced by the closed organ pipe will be \(50 \, \text{Hz}\), \(150 \, \text{Hz}\), and \(250 \, \text{Hz}\).