## Conceptual Physics (12th Edition)

Call the fundamental frequency $f_{o}$. If you multiply the frequency of a note by 2, you have the same note, but in the next higher octave. The note at the first octave above has frequency $2 f_{o}$. The note at the second octave above has frequency $4 f_{o}$. The note at the third octave above has frequency $8 f_{o}$. a. As seen on page 395 and in Figure 21.5, the second harmonic is at two times the fundamental frequency, or $2 f_{o}$. The third harmonic is at three times the fundamental frequency, or $3 f_{o}$. The fourth harmonic is at four times the fundamental frequency, or $4 f_{o}$, and so on. Between the first and second octaves above the fundamental, there lies the third harmonic, at three times the fundamental frequency, or $3 f_{o}$. b. Between the second and third octaves above the fundamental, at $4 f_{o}$ and $8 f_{o}$, respectively, there lie three harmonics: the fifth, sixth, and seventh harmonics, at 5, 6, and 7 times the fundamental frequency, respectively.