When temperature is increases, the frequency of organ pipe

Options

A. increases
B. becreases
C. remains same
D. Nothing can be said

Explanation

To solve the question regarding how the frequency of an organ pipe changes with an increase in temperature, we can follow these steps:

### Step-by-Step Solution

1. **Understand the relationship between frequency and temperature**:
The frequency of a sound wave in an organ pipe is influenced by the temperature of the gas inside it. The formula for the frequency \( f \) of an organ pipe open at both ends is given by:
\[ f = \frac{1}{2L} \sqrt{\frac{\gamma RT}{M}} \]
where:
- \( L \) is the length of the organ pipe,
- \( \gamma \) is the adiabatic index,
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature,
- \( M \) is the molecular weight of the gas.

2. **Identify the dependence on temperature**:
From the formula, we can see that the frequency \( f \) is directly proportional to the square root of the temperature \( T \):
\[ f \propto \sqrt{T} \]

3. **Analyze the effect of increasing temperature**:
If the temperature \( T \) increases, the square root of the temperature also increases. Therefore, the frequency \( f \) will increase as well.

4. **Conclusion**:
Thus, when the temperature increases, the frequency of the organ pipe also increases. This means that the correct answer is that the frequency increases.

### Final Answer:
When the temperature increases, the frequency of the organ pipe increases.

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