if the temperature is increased then the fundamental frequency of an open pipe is [ neglect any expansion]

Options

A. increases
B. decreases
C. remain same
D. maybe increases or decreases

Answer

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

### Step-by-Step Solution:

1. **Understanding the Fundamental Frequency**:
The fundamental frequency (first harmonic) of an open pipe can be expressed using the formula:
\[ f_1 = \frac{V}{2L} \]
where:
- \( f_1 \) = fundamental frequency
- \( V \) = speed of sound in the medium
- \( L \) = length of the pipe

2. **Effect of Temperature on Speed of Sound**:
The speed of sound in air (or any medium) is affected by temperature. Specifically, the speed of sound is directly proportional to the square root of the absolute temperature (in Kelvin):
\[ V \propto \sqrt{T} \]
where \( T \) is the absolute temperature.

3. **Increasing Temperature**:
When the temperature increases, the speed of sound \( V \) also increases. This can be expressed as:
\[ V' = k \sqrt{T'} \]
where \( T' \) is the new temperature and \( k \) is a constant.

4. **Substituting Back into the Frequency Formula**:
As the speed of sound increases with temperature, we can substitute this back into the fundamental frequency formula:
\[ f_1' = \frac{V'}{2L} \]
Since \( V' > V \) (because \( T' > T \)), it follows that:
\[ f_1' > f_1 \]
This indicates that the fundamental frequency increases when the temperature increases.

5. **Conclusion**:
Therefore, if the temperature is increased, the fundamental frequency of the open pipe will **increase**.

### Final Answer:
The fundamental frequency of an open pipe increases with an increase in temperature.

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