Natural Frequencies and Harmonics

AI Thread Summary
Natural frequencies refer to the specific frequencies at which an object naturally vibrates, while harmonics are integer multiples of these frequencies. A taut string can vibrate at its fundamental natural frequency and also at various harmonics, each corresponding to a specific wavelength and frequency. The confusion arises because each harmonic indeed has a single frequency, but multiple harmonics can exist based on the natural frequency. Understanding this relationship clarifies how harmonics are derived from the fundamental frequency. The discussion emphasizes the distinction between a single natural frequency and the multiple harmonics that can arise from it.
ThatDude
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Homework Statement


Basically, I was reading the following passage from a textbook, and I'm confused as to why they mention natural frequencies? Doesn't each harmonic have just one frequency that it oscillates at? From what I understand, the natural frequency is just the frequency an object likes to vibrate at. Can someone please make this clear?

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A taut length of string can vibrate at a particular natural frequency, and potentially also at integer multiples of that frequency. These multiples are known as harmonics.
 
As you say, the harmonic wave has just one wavelength and one frequency.

The above given expression describes how many possible wavelenth (and therefore frequency) values a harmonics wave can have given for a complete 2 pi displacement.

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