Question

An organ pipe closed at one end has fundamental frequency of (1500 Hz). The maximum number of overtones generated by this pipe which a normal person can hear is (Normal man hears up to (19.5 kHz))

• A. (6)
• B. (3)
• C. (13)
• D. [suspicious link removed]

Hint:

For closed pipes: $p^{th}$ overtone = $(2p+1)^{th}$ harmonic.

Answer 1

The Correct Option is A

Step 1: Frequency Series
A closed pipe produces only odd harmonics: $n, 3n, 5n, 7n, \dots$. Given $n = 1500 \text{ Hz}$.

Step 2: Find Maximum Harmonic
$n_{max} \le 19500 \text{ Hz}$. $(2p+1) \times 1500 \le 19500 \implies 2p+1 \le 13$. $2p \le 12 \implies p \le 6$.

Step 3: Conclusion
The $13^{th}$ harmonic is the $6^{th}$ overtone. Thus, 6 overtones are audible.
Final Answer: (A)