Harmonics and Overtones

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While the fundamental frequencyThe fundamental frequency, f0, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform, producing its simplest and most basic sound. More is the lowest frequency that can be obtained from a plucked string, higher frequencies can be produced.

“Overtone” is a term generally applied to any higher-frequency standing wave, whereas the term harmonic is reserved for those cases in which the frequencies of the overtones are integral or whole number multiples of the frequency of the fundamental, f₀ , e.g. 2f₀ , 3f₀ , 4f₀ , etc; f₀ being the first harmonic. Overtones or harmonics are also called resonances.

First Overtone or Second Harmonic:

l = \( \frac{\lambda}{2} + \frac{\lambda}{2} \\ \scriptsize = \lambda\)

The note produced is the first overtone or second harmonic, f₁

f₁ = \( \frac{V}{\lambda} \)

But l = λ

f₁ = \( \frac{V}{l} \)

Remember f₀ = \( \frac{V}{2l} \)

f₁ = \(\scriptsize 2 \left(\normalsize \frac{V}{2l} \right)\)

f₁ = 2f₀

Second Overtone or Third Harmonic:

l = \( \frac{3\lambda}{2}\)

λ = \( \frac{2l}{3}\)

But