Assertion : Two successive frequency of an organ pipe are `450 H_(Z)` and `750 H_(Z)` . Then, this pipe is a closed pipe.
Reason : Fundamental frequency of this pipe is `150 h_(Z)`.

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-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that two successive frequencies of an organ pipe are 450 Hz and 750 Hz, and concludes that this pipe is a closed pipe.
- To determine if the organ pipe is closed, we need to check the relationship between these frequencies.

2. **Calculating the Ratio of Frequencies**:
- Let \( f_1 = 450 \, \text{Hz} \) and \( f_2 = 750 \, \text{Hz} \).
- We can find the ratio of these frequencies:
\[ \frac{f_1}{f_2} = \frac{450}{750} = \frac{3}{5} \]
- The ratio \( \frac{3}{5} \) indicates that these frequencies are in the ratio of odd harmonics.

3. **Identifying the Type of Pipe**:
- For a closed organ pipe, the frequencies are given by odd harmonics: \( f_n = n \frac{v}{4L} \) where \( n \) is an odd integer (1, 3, 5,...).
- Since the ratio \( \frac{3}{5} \) corresponds to odd harmonics, we can conclude that the assertion is true: the pipe is indeed a closed pipe.

4. **Understanding the Reason**:
- The reason states that the fundamental frequency of this pipe is 150 Hz.
- To verify this, we can use the relationship for the fundamental frequency of a closed pipe:
\[ f_1 = \frac{v}{4L} \]
- The next harmonic (3rd harmonic) would be:
\[ f_3 = 3 \cdot f_1 = 3 \cdot 150 \, \text{Hz} = 450 \, \text{Hz} \]
- The next odd harmonic (5th harmonic) would be:
\[ f_5 = 5 \cdot f_1 = 5 \cdot 150 \, \text{Hz} = 750 \, \text{Hz} \]
- Therefore, the fundamental frequency is indeed 150 Hz.

5. **Conclusion**:
- Both the assertion and the reason are true.
- However, the reason does not correctly explain the assertion, as it simply states the fundamental frequency without linking it to the conclusion about the type of pipe.

### Final Answer:
- The assertion is true, and the reason is true, but the reason is not the correct explanation of the assertion.