For a string that is **fixed at both ends**, and for which we know the **tension** and the **length**, we know how to determine the** values** of the **resonant frequencies** of waves that are able to be maintained on that string.

Each of these waves is a** mode of vibration**.

There are an infinite number of these. Here are the first four of them.

Note that the physicist, like the musician, calls these modes **harmonics**.

But when we pluck a guitar string, precisely **which** of these modes do we observe? (…)

Actually, **all of them**!

The motion of the string is in fact derived from the** superposition **of **all of the modes**.

The **first mode**, or **first harmonic**, is called the** fundamental**.

Its envelope, with a single ** antinode** at the center, is characteristic of this mode.

Its frequency, F0, is called the **fundamental frequency** and it depends, among other things, on the length L of the string.

The** shorter** the string, the **higher **the frequency, and the **higher the pitch** of the sound. (…)

The second harmonic vibrates at a frequency that is **double** that of the fundamental.

It has **two** antinodes and **three** nodes of vibration. (…)

More generally, the harmonic of rank “n” oscillates with a frequency “n” times that of the fundamental. (…)

Let’s remember that the **higher we go** in the ranks of the harmonics, the **higher** the **frequency** is, but the** lower** the **amplitude** becomes.

It is therefore the fundamental note that predominates in our auditory perception.