Statement-1 : The fundamental frequency of an organ pipe increases as the temperature increases
Statement-2 : As the temperature increases, the velocity of sound increases more rapidly than length of the pipe.

Options

A. Statement-1 is true, Statement-2 is true , Statement-2 is correct explanation for Statement-20
B. Statement-1 is true,Statement-2 is true , Statement-2 is NOT a correct explanation for Statement-20
C. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true

Answer

To analyze the statements given in the question, we can break down the problem step by step.

### Step 1: Understanding the Fundamental Frequency of an Organ Pipe
The fundamental frequency (f) of an organ pipe is determined by the speed of sound (V) in the medium and the length (L) of the pipe. The formulas for the fundamental frequency are:
- For a closed organ pipe:
\[ f = \frac{V}{4L} \]
- For an open organ pipe:
\[ f = \frac{V}{2L} \]

### Step 2: Effect of Temperature on Speed of Sound
The speed of sound in air is affected by temperature. The relationship can be expressed as:
\[ V = \sqrt{\frac{\gamma RT}{M}} \]
where:
- \( \gamma \) is the adiabatic index (ratio of specific heats),
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature,
- \( M \) is the molecular mass of the gas.

As the temperature (T) increases, the speed of sound (V) also increases.

### Step 3: Effect of Temperature on Length of the Pipe
When the temperature increases, the length of the organ pipe (L) may also change due to thermal expansion. The change in length can be expressed as:
\[ \Delta L = \alpha L \Delta T \]
where:
- \( \alpha \) is the coefficient of linear expansion of the material,
- \( \Delta T \) is the change in temperature.

However, for most materials, this change in length is relatively small compared to the change in speed of sound.

### Step 4: Analyzing Statement 1
Statement 1 claims that the fundamental frequency of an organ pipe increases as the temperature increases. Since the speed of sound increases significantly with temperature while the change in length of the pipe is negligible, we can conclude that:
- The increase in speed of sound (V) leads to an increase in frequency (f), thus making Statement 1 true.

### Step 5: Analyzing Statement 2
Statement 2 states that as the temperature increases, the velocity of sound increases more rapidly than the length of the pipe. Given that the speed of sound is highly sensitive to temperature changes, while the thermal expansion of the pipe is minimal, we can conclude that:
- This statement is also true.

### Conclusion
Both statements are true, and Statement 2 provides a valid explanation for Statement 1. Therefore, the answer is that both statements are correct.