Start with a fundamental tone. (a) How many harmonics are there between the firs

Question

Start with a fundamental tone.

(a) How many harmonics are there between the first and second octaves?

(b) How many harmonics are there between the second and third octaves?

Also, if you can please try to explain how to get the answer because I want to learn. Thank you

Start with a fundamental tone. (a) How many harmonics are there between the first and second octaves? (b) How many harmonics are there between the second and third octaves? Also, if you can please try to explain how to get the answer because I want to learn. Thank you

Explanation / Answer

Octaves are related by a factor of two: 1, 2, 4, 8, etc. If fundamental is 220 Hz (220 * 1), the second octave starts at 440 Hz (220 * 2), the third octave starts at 880 Hz (220 * 4), and the fourth octave starts at 1760 Hz (220 * 8).

The FIRST OCTAVE runs from 'Times 1" to "Times 2". From you diagram you can see that there is ONE harmonic in the First Octave, COUNTING the "Times 2" signal.

The SECOND OCTAVE runs from "times 2" to "Times 4". There are TWO harmonics in the SECOND octave, counting both the "Time 3" and "Time 4" harmonics.

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