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A pipe of length 20 cm is closed at one end. What harmonic mode will be resonantly excited by a sound source of frequency 1237.5 Hz? (Speed of sound in air = 330 m/s)

1. 1st harmonic
2. 2nd harmonic
3. 3rd harmonic
4. 4th harmonic

Correct answer: 3rd harmonic

Solution

Fundamental frequency: f1 = v/(4L) = 330/(4*0.20) = 330/0.80 = 412.5 Hz. For closed-end pipe, allowed frequencies are f1, 3f1, 5f1,... (odd harmonics only). 3 * 412.5 = 1237.5 Hz. This is the 3rd harmonic. Note: In the counting convention for closed pipes, some textbooks call this the 2nd overtone or the 3rd harmonic. Among the given options {1st, 2nd, 3rd, 4th harmonic}, the 3rd harmonic matches.

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