What is a standing wave?

A standing wave is a pattern formed when two waves of equal frequency and amplitude travel in opposite directions and superpose. The result is a stationary pattern with fixed nodes (points of zero displacement) and antinodes (points of maximum displacement). Unlike travelling waves, standing waves do not transport energy along the medium � they store it in the resonant pattern.

What are harmonics on a string?

Harmonics (also called normal modes or overtones) are the discrete resonant frequencies at which a string naturally vibrates. The fundamental frequency (1st harmonic) has one antinode and fits exactly half a wavelength along the string. The nth harmonic has n antinodes and fits n half-wavelengths along the string, giving frequency fn = n�f1. Together, harmonics determine the timbre of musical instruments.

How does tension affect wave speed on a string?

Wave speed on a stretched string is v = v(T/�), where T is tension (in Newtons) and � is linear mass density (kg/m). Increasing tension raises the wave speed, which raises all harmonic frequencies proportionally. Tuning a guitar string works by adjusting tension: tightening the string increases tension, raising pitch. Thicker strings have higher � and lower wave speed at the same tension, giving lower pitch.

What is resonance and why does it matter?

Resonance occurs when an external driving force matches the natural (resonant) frequency of a system, causing energy to build up and amplitudes to grow dramatically. For a string, resonance produces loud, sustained standing waves. Resonance is responsible for musical instrument sound production, the Tacoma Narrows Bridge collapse, MRI machines, microwave ovens, and laser cavities.

Home▸Physics & Mechanics▸Standing Waves & String Vibration

🧪 Standing Waves & String Vibration

Explore standing waves on a vibrating string: visualise harmonics, nodes, antinodes, resonance, and normal modes. Adjust tension, mass density, and frequency to satisfy boundary conditions - perfect for A-level physics.

Physics & Mechanics2DModerate60 FPS

⚙ Under the hood

This simulation explores the creation of standing waves on a string or rope. Users can manipulate parameters to observe harmonics, resonance, and normal modes of vibration, illustrating wave interference phenomena.

Standing WavesString VibrationNormal Modes

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install