## Summary

The vibration of a guitar string results from the sum of an infinite number of vibrations whose frequencies are all multiples of a reference frequency called the **fundamental**. These individual vibrations are the vibration **modes **or harmonics.

The frequency of these vibrations depends on the length of the string. The shorter the string, the higher the frequency, and so the higher in pitch the sound is.

The first harmonic (the fundamental) is the one that contains the most energy. It is thus the one that we hear the most of.

This simulation enables us to isolate the first few harmonics, one by one, while knowing that, in reality, such a separation is impossible.

**Click **on "capo" to shorten the string.

**Click **on "harmonics" to see the beginning of the harmonic series.

## Learning goals

- To teach that a vibration can be decomposed into a sum of individual vibrations: the modes (or harmonics)
- To present a real life application of a vibrating string.
- To introduce the notions of musical harmony, apart from the octave, the 5
^{th}, the third, the perfect chord....

*Remark*: It is not possible to isolate a single mode on a guitar string. The timbre of any single note results from the simultaneous superposition of all the modes. One should not teach that, to change a note, the guitarist selects just one harmonic to the detriment of others. It is in fact the length of the string that he must change, and this causes a whole new series of harmonics to be produced.

## Learn more

A string held fixed at both ends is a **resonance cavity** that acts as a **very selective filter**.

The tension in and the length of the string impose conditions of frequency and wavelength on…

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