One of the harmonics of a column of air open at both ends has a frequency of 448 Hz and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column?
A) 32 Hz
B) 64 Hz
C) 88 Hz
D) 128 Hz
E) 256 Hz

Question

Quizplus · Accepted Answer

The frequency of the second harmonic is two times the frequency of the first harmonic (fundamental frequency) for a column open at both ends. Therefore, 
448 Hz = 2 x frequency of the fundamental frequency 
Frequency of the fundamental frequency = 448 Hz / 2 = 224 Hz

The frequency of the third harmonic is three times the frequency of the first harmonic. Therefore, 
576 Hz = 3 x frequency of the fundamental frequency 
Frequency of the fundamental frequency = 576 Hz / 3 = 192 Hz

Therefore, the correct answer is D) 128 Hz, which is the frequency of the first harmonic (fundamental frequency).

One of the Harmonics of a Column of Air Open