the fundamental frequency of a closed organ pipe is `50 Hz`. The frequency of the second overtone is

Options

A. `100 Hz`
B. `150 Hz`
C. `200 Hz`
D. `250 Hz`

Explanation

To find the frequency of the second overtone of a closed organ pipe given that the fundamental frequency is 50 Hz, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Frequencies in a Closed Organ Pipe**:
- For a closed organ pipe, the harmonics are given by the formula:
- Fundamental frequency (1st harmonic) = \( f_0 \)
- First overtone (2nd harmonic) = \( 3f_0 \)
- Second overtone (3rd harmonic) = \( 5f_0 \)

2. **Identify the Given Information**:
- The fundamental frequency \( f_0 \) is given as 50 Hz.

3. **Calculate the Second Overtone**:
- The second overtone corresponds to the 5th harmonic.
- Therefore, we can calculate it as:
\[ f_{\text{second overtone}} = 5f_0 \]
- Substitute the value of \( f_0 \):
\[ f_{\text{second overtone}} = 5 \times 50 \, \text{Hz} = 250 \, \text{Hz} \]

4. **Conclusion**:
- The frequency of the second overtone is 250 Hz.

### Final Answer:
The frequency of the second overtone is **250 Hz**.

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