The effect of making a hole exactly at `(1//3^(rd))` of the length of the pipe from its closed end is such that :

Options

A. its fundamental frequency is an octave higher thanthe open pipe of same length
B. its fundamental frequency is thrice of that before making a hole
C. the fundamental frequency is `3//2` time of that before making a hole
D. the fundamental alone is changed while the harmonics expressed as ratio of fundamentals remain the same

Answer

To solve the problem of determining the effect of making a hole at one-third of the length of a closed pipe, we can follow these steps:

### Step 1: Understand the Closed Pipe
A closed pipe has one end closed and the other end open. In this configuration, the fundamental frequency (the lowest frequency of vibration) is determined by the length of the pipe. The closed end has a node (point of no displacement), and the open end has an antinode (point of maximum displacement).

### Step 2: Write the Formula for Fundamental Frequency
The formula for the fundamental frequency \( f \) of a closed pipe is given by:
\[ f = \frac{V}{4L} \]
where \( V \) is the speed of sound in air and \( L \) is the length of the pipe.

### Step 3: Determine the New Length After Making the Hole
When a hole is made at one-third of the length of the pipe from the closed end, the new effective length of the pipe becomes \( L' = \frac{L}{3} \).

### Step 4: Calculate the New Fundamental Frequency
The new fundamental frequency \( f' \) of the modified pipe can be calculated using the same formula:
\[ f' = \frac{V}{4L'} = \frac{V}{4 \cdot \frac{L}{3}} = \frac{3V}{4L} \]

### Step 5: Compare the New Frequency with the Original Frequency
Now, we can compare the new fundamental frequency \( f' \) with the original frequency \( f \):
\[ \frac{f'}{f} = \frac{\frac{3V}{4L}}{\frac{V}{4L}} = 3 \]
This shows that the new fundamental frequency \( f' \) is three times the original frequency \( f \).

### Conclusion
Thus, the effect of making a hole at one-third of the length of the closed pipe is that the fundamental frequency becomes three times that of the original frequency.

### Final Answer:
The correct option is: **The fundamental frequency is thrice of that before making a hole.**

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