A closed organ pipe has a fundamental frequency of 1.5 kHz. The… | JEE Main 2019 (10 Jan, Shift 2)

Q99JEE Main 2019 · 10 JAN · SHIFT 2Easy

Organ Pipes & Resonance Tube

A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be (Assume that the highest frequency a person can hear is 20,000 Hz)

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Answer: (b)

Closed pipe frequencies: $(2n+1)\times1.5\text{ kHz}$ .
$(2n+1)\times1.5 \le 20 \Rightarrow 2n+1 \le 13.3$ , so the highest audible is the 13th harmonic ( $19.5\text{ kHz}$ ).
Audible tones: harmonics 1, 3, 5, 7, 9, 11, 13, i.e. 7 tones, of which 6 are overtones.
The key counts all 7 audible frequencies: answer (b) 7.

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