The fundamental frequency of a pipe closed at one end is 100Hz. If close end is open the fundamental frequency of same pipe wil be

Options

A. 100 Hz
B. 200 Hz
C. 50 Hz
D. 400 Hz

Answer

To solve the problem, we need to understand the relationship between the fundamental frequency of a pipe closed at one end and the fundamental frequency of the same pipe when the closed end is opened.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The fundamental frequency of a pipe closed at one end (closed organ pipe) is given as \( f_c = 100 \, \text{Hz} \).

2. **Understand the Frequency Formula for Closed and Open Pipes**:
- For a pipe closed at one end, the fundamental frequency is given by the formula:
\[ f_c = \frac{v}{4L} \]
where \( v \) is the speed of sound in air and \( L \) is the length of the pipe.
- For a pipe open at both ends (open organ pipe), the fundamental frequency is given by:
\[ f_o = \frac{v}{2L} \]

3. **Relate the Frequencies**:
- From the formulas, we can see that the frequency of the open pipe is double that of the closed pipe because:
\[ f_o = 2 \cdot f_c \]

4. **Calculate the Fundamental Frequency for the Open Pipe**:
- Substituting the given frequency of the closed pipe into the relationship:
\[ f_o = 2 \cdot 100 \, \text{Hz} = 200 \, \text{Hz} \]

5. **Conclusion**:
- Therefore, the fundamental frequency of the same pipe when the closed end is opened is \( f_o = 200 \, \text{Hz} \).

### Final Answer:
The fundamental frequency of the same pipe when the closed end is opened will be **200 Hz**.

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