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 closed pipe and an open pipe.

### Step-by-Step Solution:

1. **Identify the given information**:
- The fundamental frequency of a closed pipe (f_closed) is given as 100 Hz.

2. **Understand the formula for the fundamental frequency of a closed pipe**:
- The fundamental frequency (f) of a closed pipe is given by the formula:
\[ f = \frac{v}{4L} \]
where \( v \) is the speed of sound in air and \( L \) is the length of the pipe.

3. **Set up the equation for the closed pipe**:
- From the given information, we can write:
\[ \frac{v}{4L} = 100 \text{ Hz} \]

4. **Understand the formula for the fundamental frequency of an open pipe**:
- The fundamental frequency (f_open) of an open pipe is given by the formula:
\[ f = \frac{v}{2L} \]

5. **Relate the frequencies**:
- We can express the fundamental frequency of the open pipe in terms of the closed pipe's frequency. Notice that:
\[ f_{open} = \frac{v}{2L} = 2 \cdot \frac{v}{4L} \]

6. **Substitute the value from the closed pipe**:
- Since we know that \( \frac{v}{4L} = 100 \text{ Hz} \), we can substitute this into our equation for the open pipe:
\[ f_{open} = 2 \cdot 100 \text{ Hz} = 200 \text{ Hz} \]

7. **Conclusion**:
- Therefore, the fundamental frequency of the same pipe when the closed end is opened is **200 Hz**.

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

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