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. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Frequencies
We are given:
- Fundamental frequency (f1) = 100 Hz
- Other frequencies = 300 Hz and 500 Hz

### Step 2: Identify the Type of Pipe
There are three types of pipes:
1. Open at both ends
2. Closed at one end and open at the other
3. Closed at both ends

### Step 3: Analyze the Frequencies for Each Type of Pipe

#### Case 1: Open at Both Ends
- The fundamental frequency (first harmonic) is given by:
\[ f_1 = \frac{V}{2L} \]
- The second harmonic (first overtone) is:
\[ f_2 = \frac{V}{L} \]
- The third harmonic (second overtone) is:
\[ f_3 = \frac{3V}{2L} \]
- The frequencies would be in the ratio 1:2:3, which does not match our frequencies (100 Hz, 300 Hz, 500 Hz).

#### Case 2: Closed at One End and Open at the Other
- The fundamental frequency is:
\[ f_1 = \frac{V}{4L} \]
- The first overtone (third harmonic) is:
\[ f_2 = \frac{3V}{4L} \]
- The second overtone (fifth harmonic) is:
\[ f_3 = \frac{5V}{4L} \]
- The frequencies would be in the ratio 1:3:5. If we set \(f_1 = 100\) Hz, we can find:
- \(f_2 = 3 \times 100 = 300\) Hz
- \(f_3 = 5 \times 100 = 500\) Hz
- This matches our given frequencies.

#### Case 3: Closed at Both Ends
- The fundamental frequency is:
\[ f_1 = \frac{V}{2L} \]
- The second harmonic (first overtone) is:
\[ f_2 = \frac{2V}{L} \]
- The third harmonic (second overtone) is:
\[ f_3 = \frac{3V}{2L} \]
- The frequencies would be in the ratio 1:2:3, which again does not match our frequencies.

### Conclusion
Based on the analysis, the only configuration that matches the fundamental frequency of 100 Hz and the other two frequencies of 300 Hz and 500 Hz is a pipe that is closed at one end and open at the other.

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

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