Harmonics and standing waves simulation

A string fixed at both ends can only vibrate at frequencies that fit a whole number of half-wavelengths between the ends. These harmonics, f₀, 2f₀, 3f₀ and so on, are the building blocks of musical sound.

Interactive, free and runs in your browser. Part of the Acoustic Physics simulations.

What you will see

Eight strings on an instrument body, each vibrating in one harmonic of the same fundamental. A faint band shows the space each string sweeps through, and bright dots mark the nodes. Click a string to pluck it and hear its note.

Try this

  1. Count the nodes on each string: the nth harmonic has n − 1 between the ends.
  2. Pluck the 1st and 2nd harmonics: they are an octave apart.
  3. Strum all eight and hear the chord.

Common misconception

A plucked string does not vibrate in just one harmonic. It vibrates in many at once, and the mix of their strengths is what makes a guitar and a piano sound different on the same note.

Exam-style question

A string 0.65 m long has a fundamental of 196 Hz. What is the wave speed on the string, and what is the frequency of the third harmonic?

The fundamental has λ = 2L = 1.30 m, so v = fλ = 196 × 1.30 ≈ 255 m/s. The third harmonic is 3 × 196 = 588 Hz.

Key equations

  • fₙ = n f₀
  • λₙ = 2L / n
  • v = fλ

Curriculum

AQA A-level physics 3.3.1, IB Physics C.4.

More acoustic physics simulations

Other topics