Statement-1: The fundamental frequency of an organ pipe remains unchanged, if the ratio of speed of sound in it to its length remains constant.
Statement-2: Fundamental frequency of an organ pipe is proportional to `(V)/(l)`, v=speed of sound, l=length of pipe.

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-1
C. statement-1 is true, statement-2 is false
D. statement-1 is false, statement-2 is true

Answer

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

### Step 1: Understand the Fundamental Frequency of an Organ Pipe
The fundamental frequency (f) of an organ pipe is determined by the speed of sound (V) in the pipe and the length (L) of the pipe. The relationship can be expressed as:
\[ f = \frac{V}{\lambda} \]
where \(\lambda\) is the wavelength of the sound wave.

### Step 2: Relate Wavelength to Length of the Pipe
For an open organ pipe, the fundamental frequency corresponds to the wavelength being twice the length of the pipe:
\[ \lambda = 2L \]
Substituting this into the frequency equation gives:
\[ f = \frac{V}{2L} \]

### Step 3: Analyze Statement 1
Statement 1 claims that the fundamental frequency remains unchanged if the ratio of the speed of sound in the pipe to its length remains constant. This means:
\[ \frac{V}{L} = \text{constant} \]
If this ratio is constant, then any changes in V and L must maintain this ratio, thus keeping the frequency (f) constant as well.

### Step 4: Analyze Statement 2
Statement 2 states that the fundamental frequency of an organ pipe is proportional to \(\frac{V}{L}\). From the derived equation:
\[ f = \frac{V}{2L} \]
It is clear that frequency is indeed proportional to \(\frac{V}{L}\).

### Step 5: Conclusion
Both statements are true. Statement 2 correctly explains Statement 1, as the condition of constant ratio of speed of sound to length ensures that the fundamental frequency remains unchanged.

### Final Answer
- **Statement 1**: True
- **Statement 2**: True
- **Explanation**: Statement 2 is a correct explanation for Statement 1.