* Fundamental Frequency: This is the lowest frequency at which a vibrating object naturally oscillates. It's the "base note" of a sound.
* Harmonics: These are multiples of the fundamental frequency. They occur naturally as a vibrating object vibrates at higher frequencies simultaneously with its fundamental frequency.
The Relationship:
* First Harmonic: This is the same as the fundamental frequency.
* Second Harmonic: This is twice the fundamental frequency.
* Third Harmonic: This is three times the fundamental frequency.
* And so on...
Example:
Let's say the fundamental frequency of a guitar string is 100 Hz. The harmonics would be:
* First Harmonic: 100 Hz (same as the fundamental)
* Second Harmonic: 200 Hz
* Third Harmonic: 300 Hz
* Fourth Harmonic: 400 Hz
* Fifth Harmonic: 500 Hz, and so on...
Importance of Harmonics:
* Timbre: Harmonics are what give musical instruments their unique sound (timbre). Different instruments have different harmonic series, contributing to their distinct qualities.
* Overtones: Harmonics are also called "overtones" because they occur "over" the fundamental frequency.
* Musical Harmony: The relationship between harmonics is a fundamental principle in music theory, influencing how chords and melodies sound together.
Key Point: Harmonics are *not* simply higher frequencies that exist independently; they are *multiples* of the fundamental frequency, and their presence is directly influenced by the fundamental frequency.
