Harmonics in Air Column · PhysicsBowl 2010 #17
Physics
Problem
A tube of air open at only one end is vibrating in the 5th harmonic from a tuning fork of frequency 120Hz placed at the open end. If this tube of air were to vibrate at its fundamental frequency, what frequency tuning fork would be needed at the open end? (A) 24 Hz (B) 30 Hz (C) 40 Hz (D) 125 Hz (E) 600 HzIntuitive explanation
A tube closed at one end supports only odd harmonics: the fundamental is the 1st harmonic, the 5th harmonic is five times the fundamental frequency. Since the tube is vibrating at its 5th harmonic with a 120 Hz fork, you can find the tube's fundamental frequency, then recognize that a tuning fork at that fundamental frequency will naturally excite the tube's 1st harmonic (lowest resonance).
Intuitive explanation
A tube closed at one end supports only odd harmonics: the fundamental is the 1st harmonic, the 5th harmonic is five times the fundamental frequency. Since the tube is vibrating at its 5th harmonic with a 120 Hz fork, you can find the tube's fundamental frequency, then recognize that a tuning fork at that fundamental frequency will naturally excite the tube's 1st harmonic (lowest resonance).