The fundamental frequency of a vibrating organ pipe is `200Hz`

Options

A. The first overtone may be `400Hz`
B. The first overtone is `400Hz`
C. The first overtone may be `600Hz`
D. The second overtone may be `600Hz`

Explanation

To solve the problem regarding the fundamental frequency of a vibrating organ pipe, we need to analyze the situation for both open and closed pipes.

### Step-by-Step Solution:

1. **Identify the Fundamental Frequency**:
The fundamental frequency (first harmonic) of the vibrating organ pipe is given as \( f_0 = 200 \, \text{Hz} \).

2. **Determine the Type of Pipe**:
We need to consider two scenarios:
- An open organ pipe (open at both ends)
- A closed organ pipe (closed at one end)

3. **Calculate the Frequencies for the Open Pipe**:
For an open pipe, the harmonics are given by:
- Fundamental frequency: \( f_0 = 200 \, \text{Hz} \)
- First overtone (second harmonic): \( f_1 = 2f_0 = 2 \times 200 \, \text{Hz} = 400 \, \text{Hz} \)
- Second overtone (third harmonic): \( f_2 = 3f_0 = 3 \times 200 \, \text{Hz} = 600 \, \text{Hz} \)

4. **Calculate the Frequencies for the Closed Pipe**:
For a closed pipe, the harmonics are given by:
- Fundamental frequency: \( f_0 = 200 \, \text{Hz} \)
- First overtone (third harmonic): \( f_1 = 3f_0 = 3 \times 200 \, \text{Hz} = 600 \, \text{Hz} \)
- Second overtone (fifth harmonic): \( f_2 = 5f_0 = 5 \times 200 \, \text{Hz} = 1000 \, \text{Hz} \)

5. **Summarize the Results**:
- For the open pipe:
- Fundamental frequency: \( 200 \, \text{Hz} \)
- First overtone: \( 400 \, \text{Hz} \)
- Second overtone: \( 600 \, \text{Hz} \)
- For the closed pipe:
- Fundamental frequency: \( 200 \, \text{Hz} \)
- First overtone: \( 600 \, \text{Hz} \)
- Second overtone: \( 1000 \, \text{Hz} \)

6. **Conclusion**:
Based on the calculations:
- The first overtone for an open pipe is \( 400 \, \text{Hz} \).
- The first overtone for a closed pipe is \( 600 \, \text{Hz} \).
- The second overtone for an open pipe is \( 600 \, \text{Hz} \).
- The second overtone for a closed pipe is \( 1000 \, \text{Hz} \).