Standing waves play a big role in how string instruments make sound. These waves happen when two waves move in opposite directions and interfere with each other.

Here are the main parts of standing waves:

• Nodes: These are points where the string doesn’t move at all. They sit still while the other parts of the string vibrate. If you have a string of length (L), the distance between each node is (\frac{L}{n}). Here, (n) means how many segments the string makes.

• Antinodes: These are places where the string moves the most. They create the loudest sounds. In the first harmonic, there is one antinode. In the second harmonic, there are two, and this keeps going.

The frequency of the standing wave, which helps us hear different pitches, depends on three things: the string's tension ((T)), its weight along its length ((\mu)), and its length. The basic frequency, called (f_1), can be calculated using this formula:

$$f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$$

In string instruments, different harmonics create different pitches. This variety is important for making music sound interesting and expressive.