A sufficiently long closed organ pipe has a small hole at its bottom. Initially the pipe is empty. What poured into the pipe at a constant rate. The fundamental frequency of the air column in the pite

Options

A. continously increases
B. first incrases and then becomes constant
C. continously decreases
D. first decrease and then become constant

Answer

To solve the problem of how the fundamental frequency of the air column in a closed organ pipe changes as water is poured into it, we can follow these steps:

### Step 1: Understand the Setup
We have a long closed organ pipe with a small hole at the bottom. Initially, the pipe is empty. As water is poured into the pipe at a constant rate, the air column above the water will change in height.

### Step 2: Fundamental Frequency of a Closed Organ Pipe
The fundamental frequency (first harmonic) of a closed organ pipe is given by the formula:
\[ f = \frac{v}{4L} \]
where:
- \( f \) is the fundamental frequency,
- \( v \) is the speed of sound in air,
- \( L \) is the length of the air column.

### Step 3: Effect of Water on Length of Air Column
As water is poured into the pipe, the height of the air column \( L \) decreases because the total length of the pipe remains constant, but the effective length of the air column decreases as the water level rises.

### Step 4: Analyze the Frequency Change
Since the length \( L \) of the air column is decreasing as water is added, the fundamental frequency \( f \) will increase because:
- As \( L \) decreases, \( f \) increases (since \( f \) is inversely proportional to \( L \)).

### Step 5: Determine the Behavior of Frequency
Initially, as water is poured in, the frequency will increase continuously as the air column length decreases. Eventually, if the pipe fills up completely (or if the water reaches the top), the air column will be at its minimum length (which is zero), and the frequency will stabilize or stop increasing.

### Conclusion
Thus, the correct answer is that the fundamental frequency of the air column in the pipe continuously increases as water is poured into it.

### Final Answer
The correct option is: **The fundamental frequency of the air column continuously increases.**

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