Standing Waves on a String
Pluck a string fixed at both ends into a chosen harmonic — adjust its length, tension, and mass per unit length to see how fast, and in how many nodes and antinodes, it vibrates.
Preview — sign up free to change the numbers yourself
What you can adjust
- String length
- 0.3 – 3 m
- Tension
- 0.5 – 50 N
- Linear density (mass/length)
- 0.001 – 0.05 kg/m
- Harmonic (mode number)
- 1 – 6
- Amplitude
- 0.01 – 0.3 m
Higher tension makes waves travel faster along the string, raising every mode's frequency.
A heavier string (per unit length) carries waves more slowly, lowering every mode's frequency.
n=1 is the fundamental (1 antinode, both ends fixed). Higher n packs more nodes and antinodes onto the same string and raises the frequency.
How far the string swings from its rest position at an antinode — doesn't change frequency, just how big the wave looks.
About this simulation
What it shows
A string fixed at both ends vibrates in a chosen pattern, with points that stay still (nodes) and points that swing the most (antinodes).
The key idea
Waves travel along the string at v = √(T/μ) and fit the string only in whole numbers of half-wavelengths. The frequency of harmonic n is n × v / 2L, so higher harmonics have more nodes and higher pitch.
Try this
Change Harmonic (mode number) from 1 to 3: the string shows three antinodes and vibrates at three times the frequency.