Assertion : A closed pipe and an open organ pipe are of same length. Then, neither of their frequencies can be same.
Reason : In the above case fundamental frequency of closed organ pipe will be two times the fundamental frequency of open organ pipe.

Options

A. If both Asseration and Reason are true an dthe Reason is correct explanation of the Asseration.
B. If both Asseration and Reason are true but Reason is not the correct explanation of Asseration.
C. If Asseration is true , but the Reason is false.
D. If Asseration is false but the Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that if a closed pipe and an open organ pipe are of the same length, then neither of their frequencies can be the same.

### Step 2: Understand the Frequencies of Closed and Open Pipes
The fundamental frequency (first harmonic) of a closed organ pipe (which has one closed end) is given by the formula:
\[ f_{closed} = \frac{V}{4L} \]
where \( V \) is the speed of sound in air and \( L \) is the length of the pipe.

For an open organ pipe (which has both ends open), the fundamental frequency is given by:
\[ f_{open} = \frac{V}{2L} \]

### Step 3: Compare the Frequencies
If both pipes are of the same length \( L \), we can compare their fundamental frequencies:
1. For the closed pipe:
\[ f_{closed} = \frac{V}{4L} \]
2. For the open pipe:
\[ f_{open} = \frac{V}{2L} \]

### Step 4: Analyze the Frequencies
Now, let's analyze the relationship between these two frequencies:
- The frequency of the open pipe is:
\[ f_{open} = 2 \times f_{closed} \]
This means that the frequency of the open pipe is actually twice that of the closed pipe.

### Step 5: Conclusion on the Assertion
Since the frequencies are not the same (the open pipe has a frequency that is twice that of the closed pipe), the assertion is correct.

### Step 6: Understand the Reason
The reason states that the fundamental frequency of the closed organ pipe will be two times the fundamental frequency of the open organ pipe.

### Step 7: Analyze the Reason
From our previous analysis, we found that:
\[ f_{closed} = \frac{1}{2} f_{open} \]
This means that the reason is incorrect because it incorrectly states the relationship between the frequencies.

### Final Conclusion
- The assertion is true: If a closed pipe and an open organ pipe are of the same length, their frequencies cannot be the same.
- The reason is false: The fundamental frequency of the closed organ pipe is not two times that of the open organ pipe; it is actually half.

### Final Answer
- Assertion: True
- Reason: False