A pipe has a fundamental frequency 100 Hz and it second ovetone is 500 Hz. The pipe is

Options

A. closed at one end
B. closed at boths ends
C. open at both ends
D. cannot be predicted.

Answer

To determine the type of pipe based on the given fundamental frequency and second overtone, we can follow these steps:

### Step 1: Understand the Frequencies of Pipes
- A pipe closed at both ends has harmonics that are integer multiples of the fundamental frequency (F):
- Fundamental frequency (1st harmonic): F
- 1st overtone (2nd harmonic): 2F
- 2nd overtone (3rd harmonic): 3F
- A pipe closed at one end has odd harmonics:
- Fundamental frequency (1st harmonic): F
- 1st overtone (2nd harmonic): 3F
- 2nd overtone (3rd harmonic): 5F

### Step 2: Identify the Given Frequencies
- Fundamental frequency (F) = 100 Hz
- Second overtone = 500 Hz

### Step 3: Calculate the Expected Frequencies
- For a pipe closed at one end:
- The second overtone (3rd harmonic) would be:
\[ \text{2nd overtone} = 5F = 5 \times 100 \text{ Hz} = 500 \text{ Hz} \]
- For a pipe closed at both ends:
- The second overtone (3rd harmonic) would be:
\[ \text{2nd overtone} = 3F = 3 \times 100 \text{ Hz} = 300 \text{ Hz} \]

### Step 4: Compare the Results
- The calculated second overtone for a pipe closed at one end is 500 Hz, which matches the given second overtone.
- The calculated second overtone for a pipe closed at both ends is 300 Hz, which does not match.

### Conclusion
Since the second overtone matches the condition of a pipe closed at one end, we conclude that the pipe is **closed at one end**.

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