Fundamental frequency of pipe is 100 Hz and other two frequencies are 300 Hz and 500 Hz then

Options

A. Pipe is open at both the ends
B. pipe is closed at both the ends
C. One end open and another end is closed
D. None of the above

Answer

To solve the problem, we need to determine the type of pipe based on the given fundamental frequency and the other two frequencies.

### Step-by-Step Solution:

1. **Identify the Frequencies**:
- Fundamental frequency (f1) = 100 Hz
- Second frequency (f2) = 300 Hz
- Third frequency (f3) = 500 Hz

2. **Understand the Types of Pipes**:
- **Open Pipe**: Frequencies are given by \( f_n = \frac{n v}{2L} \) where \( n \) is a positive integer (1, 2, 3,...).
- **Closed Pipe**: Frequencies are given by \( f_n = \frac{n v}{4L} \) where \( n \) is an odd integer (1, 3, 5,...).

3. **Check the Ratios of the Frequencies**:
- For an open pipe, the frequencies are in integer multiples of the fundamental frequency.
- For a closed pipe, the frequencies are in odd multiples of the fundamental frequency.

4. **Calculate the Ratios**:
- The second frequency (300 Hz) is \( 3 \times 100 \) Hz, which suggests it could be the third harmonic.
- The third frequency (500 Hz) is \( 5 \times 100 \) Hz, which suggests it could be the fifth harmonic.

5. **Determine the Type of Pipe**:
- Since we have both \( 3 \) and \( 5 \) as multiples of the fundamental frequency, this indicates that the pipe must be closed at one end and open at the other. This is because closed pipes only support odd harmonics.

6. **Conclusion**:
- The correct option is that the pipe is "one end open and another end closed".

### Final Answer:
The pipe is one end open and the other end closed.