One of the harmonics of a column of air open at one end and closed at the other 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 fundamental frequency can be found by calculating the difference between the given harmonics, which is $576 Hz - 448 Hz = 128 Hz$. Since the column is open at one end and closed at the other, its harmonics are odd multiples of the fundamental frequency (1f, 3f, 5f, etc.). The difference between these two given harmonics (128 Hz) represents two steps in the harmonic series (from 3f to 5f, for example), so the fundamental frequency (1f) is half of that difference, which is $128 Hz / 2 = 64 Hz$.

One of the Harmonics of a Column of Air Open