Question:
In an organ pipe closed at one end; the sum of the frequencies of first three overtones is $3930 \text{ Hz}$. The frequency of the fundamental mode of organ pipe is
In an organ pipe closed at one end; the sum of the frequencies of first three overtones is $3930 \text{ Hz}$. The frequency of the fundamental mode of organ pipe is
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Closed pipe: $(2n+1)f$ harmonics. 1st overtone = 3rd harmonic ($n=1$).
Updated On: May 12, 2026
- 256 Hz
- 262 Hz
- 320 Hz
- 384 Hz
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The Correct Option is B
Solution and Explanation
Step 1: Concept
In a pipe closed at one end, only odd harmonics are present ($f, 3f, 5f, 7f \dots$).
Step 2: Meaning
The first three overtones correspond to the 3rd, 5th, and 7th harmonics.
Step 3: Analysis
Sum $= 3f + 5f + 7f = 15f$. Given $15f = 3930 \text{ Hz}$. $f = \frac{3930}{15}$.
Step 4: Conclusion
$f = 262 \text{ Hz}$. Final Answer: (B)
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