Assertion : The fundamental frequency of an open organ pipe increases as the temperature increases, the velocity of sound increases more rapidly than length of the pipe.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion and reason both are false.

Explanation

To solve the question, we need to analyze the assertion and the reason provided regarding the fundamental frequency of an open organ pipe and how it relates to temperature changes.

### Step-by-Step Solution:

1. **Understanding the Fundamental Frequency**:
The fundamental frequency (f) of an open organ pipe can be expressed using the formula:
\[ f = \frac{V}{2L} \]
where:
- \( f \) is the fundamental frequency,
- \( V \) is the velocity of sound in air,
- \( L \) is the length of the pipe.

2. **Effect of Temperature on Velocity of Sound**:
The velocity of sound in air is affected by temperature. It can be approximated that:
\[ V \propto \sqrt{T} \]
where \( T \) is the absolute temperature in Kelvin. As temperature increases, the velocity of sound increases.

3. **Effect of Temperature on Length of the Pipe**:
The length of the pipe may also change with temperature due to thermal expansion. However, the increase in length is generally much less significant compared to the increase in velocity.

4. **Analyzing the Assertion**:
The assertion states that the fundamental frequency increases as temperature increases. Since \( V \) increases more significantly than \( L \) due to the temperature increase, we can conclude that:
\[ \text{As } T \text{ increases, } V \text{ increases more rapidly than } L. \]
Therefore, the fundamental frequency \( f \) will indeed increase.

5. **Analyzing the Reason**:
The reason provided states that the velocity of sound increases more rapidly than the length of the pipe as temperature increases. This is correct because the increase in velocity (which is proportional to the square root of temperature) is greater than the linear increase in length due to thermal expansion.

6. **Conclusion**:
Both the assertion and the reason are correct, and the reason correctly explains the assertion. Thus, the answer to the question is that both the assertion and reason are true, and the reason is the correct explanation for the assertion.

### Final Answer:
Both the assertion and reason are correct, and the reason is the correct explanation of the assertion.