Strings & Music

Standing waves and harmonics

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A string fixed at both ends supports standing waves with $\lambda_n = 2L/n$.
• Harmonics: $f_n = n f_1$, where $f_1 = v/(2L)$.
• Half the length or double the frequency makes an octave. Tighter strings sound higher.

Steps

1. A vibrating string
2. Count the nodes
3. Harmonics
4. Guitar string
5. The 12th fret
6. Tighten up