Question

An organ pipe closed at one end has fundamental frequency of \(1500\) Hz. The maximum number of overtones generated by this pipe a normal person can hear is (neglect end connection)

• A. \(4\)
• B. \(13\)
• C. \(6\)
• D. \(9\)

Hint:

A closed pipe gives only odd harmonics. Count the odd multiples of 1500 Hz that are at most 20000 Hz.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
A pipe closed at one end produces only odd harmonics: \(f,\,3f,\,5f,\dots\). The human audible limit is \(20000\) Hz.

Step 2: Frequency Condition
The overtone frequencies are \((2n+1)f_0\) with \(f_0=1500\) Hz. We need \((2n+1)\times1500\le20000\).

Step 3: Solve
\(2n+1\le13.3\), so the largest odd value is \(13\) (the 13th harmonic).

Step 4: Count Overtones
The overtones are the harmonics 3, 5, 7, 9, 11, 13, which gives 6 overtones.

Final Answer:
A normal person can hear at most 6 overtones. \[ \boxed{\text{(C) }6} \]