This simulator models a string fixed at both ends and displays the exact standing-wave shape for whichever harmonic number you select. Because both ends must stay fixed, only certain wave patterns — the harmonics — fit the string without a mismatch at the boundaries, each with its own fixed pattern of nodes (points that never move) and antinodes (points with maximum oscillation).
• A string fixed at both ends, oscillating in the exact standing-wave shape for the selected harmonic number n (1 through 6). • A dashed envelope showing the maximum displacement bounds of the current mode. • Marked nodes (fixed points, always n+1 of them) in red and antinodes (points of maximum motion, always n of them) in yellow. • Live readouts for the number of nodes, number of antinodes, and the wavelength expressed as a fraction of the string length.
A wave reflecting back and forth between two fixed ends will mostly interfere with itself destructively and die out — unless its wavelength happens to fit the string length in a way where the reflections reinforce rather than cancel. That only happens when the string length equals a whole number of half-wavelengths: L = n·λ/2. Each integer n gives a distinct harmonic, with the fundamental (n = 1) having the longest wavelength, lowest frequency, and simplest shape — one antinode in the middle and nodes only at the two fixed ends.
Nodes are points on the string that never move — they stay at zero displacement throughout the oscillation. Antinodes are the points midway between nodes that swing through the largest displacement. A string fixed at both ends always has n+1 nodes and n antinodes for harmonic number n.
Because both ends are fixed, only wave patterns that fit an exact whole number of half-wavelengths into the string length will reinforce themselves through repeated reflection; any other wavelength interferes destructively with itself and dies out quickly, so only the discrete harmonic frequencies persist as stable standing waves.
For a string of length L fixed at both ends, the wavelength of harmonic n is λ = 2L/n. Higher harmonics have shorter wavelengths and, since v = fλ with fixed string speed, correspondingly higher frequencies.
It shows the idealized mode shape for a massless, lossless string oscillating at a chosen display rate — it does not model actual tension, mass per length, damping, or how a driving force at one end would need to match a specific frequency to excite that mode.