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

### Step 1: Understand the Fundamental Frequency Formula
The fundamental frequency \( f \) of an open pipe is given by the formula:
\[ f = \frac{N \cdot V}{2L} \]
where:
- \( f \) = fundamental frequency
- \( N \) = mode number (for fundamental frequency, \( N = 1 \))
- \( V \) = speed of sound in the medium
- \( L \) = length of the pipe

### Step 2: Simplify for Fundamental Frequency
For the fundamental frequency (first harmonic), we set \( N = 1 \):
\[ f = \frac{V}{2L} \]

### Step 3: Analyze the Effect of Temperature on Speed of Sound
The speed of sound \( V \) in air (or any medium) is affected by temperature. The relationship is given by:
\[ V \propto \sqrt{T} \]
This means that as the temperature \( T \) increases, the speed of sound \( V \) also increases.

### Step 4: Relate Speed of Sound to Frequency
Since the fundamental frequency \( f \) is directly proportional to the speed of sound \( V \):
\[ f \propto V \]
Thus, if \( V \) increases due to an increase in temperature, the frequency \( f \) will also increase.

### Step 5: Conclusion
Therefore, when the temperature is increased, the fundamental frequency of the open pipe also increases.

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

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