STATEMENT-1: An open organ pipe can be used as a musical instrument but not a closed organ pipe.
STATEMENT-2: The fundamental frequency of an open orgna pipe is twice the fundamental frequency of a closed organ pipe of the same length.

Options

A. Statement -1 is True, statement -2 is True, Statement -2 is a correct explanation for Statement -1.
B. Statement -1 is True, Statement -2 is True , Statement-2 is Not a correct explanation for statement-8
C. Statement -1 is True, statement -2 is False
D. Statement -1 is False, Statement -2 is True.

Answer

To analyze the given statements and arrive at a conclusion, we can break down the problem step by step.

### Step 1: Understand the characteristics of open and closed organ pipes.
- An **open organ pipe** has both ends open, allowing air to vibrate freely at both ends.
- A **closed organ pipe** has one end closed, which restricts the air movement at that end.

### Step 2: Determine the fundamental frequency of an open organ pipe.
- For an open organ pipe, the fundamental frequency (first harmonic) can be derived from the relationship between the wavelength (λ) and the length of the pipe (L).
- The length of the pipe is equal to one full wavelength (λ):
\[ L = \lambda \]
- The fundamental frequency \( f \) is given by:
\[ f = \frac{V}{\lambda} \]
where \( V \) is the speed of sound in air.
- Substituting \( \lambda = L \):
\[ f = \frac{V}{L} \]

### Step 3: Determine the fundamental frequency of a closed organ pipe.
- For a closed organ pipe, the fundamental frequency corresponds to a quarter wavelength (λ/4) fitting into the length of the pipe:
\[ L = \frac{\lambda}{4} \]
- Therefore, the wavelength can be expressed as:
\[ \lambda = 4L \]
- The fundamental frequency \( f \) for the closed pipe is:
\[ f = \frac{V}{\lambda} = \frac{V}{4L} \]

### Step 4: Compare the fundamental frequencies of both pipes.
- The fundamental frequency of the open pipe is:
\[ f_{\text{open}} = \frac{V}{L} \]
- The fundamental frequency of the closed pipe is:
\[ f_{\text{closed}} = \frac{V}{4L} \]
- Comparing these, we find:
\[ f_{\text{open}} = 4 \times f_{\text{closed}} \]
This means the fundamental frequency of the open pipe is four times that of the closed pipe, not twice as stated in Statement 2.

### Step 5: Analyze the harmonic series of both pipes.
- The open organ pipe supports all harmonics (both even and odd), while the closed organ pipe supports only odd harmonics (1st, 3rd, 5th, etc.).
- This characteristic makes the open organ pipe more versatile as a musical instrument.

### Conclusion:
- **Statement 1** is true: An open organ pipe can be used as a musical instrument, while a closed organ pipe cannot effectively cover all harmonics.
- **Statement 2** is false: The fundamental frequency of an open organ pipe is four times that of a closed organ pipe, not twice.

### Final Answer:
- Statement 1 is true, but Statement 2 is false. Thus, the correct conclusion is that Statement 1 is true, and Statement 2 is false.