The Physics of Wind Chime Sound
Wind chimes produce some of the most distinctive sounds in the acoustic world. A single struck tube creates a tone you can identify instantly: bright, shimmering, and strangely complex. That complexity comes from physics that work very differently from the way most instruments generate sound.
Strings vs. Tubes: Harmonic vs. Inharmonic
When you pluck a guitar string, it vibrates at a fundamental frequency and a series of overtones that are exact integer multiples of that fundamental. If the fundamental is 100 Hz, the overtones are 200 Hz, 300 Hz, 400 Hz, and so on. This is called a harmonic series, and it's why stringed instruments sound "clean" and "musical": the overtones reinforce each other in predictable, pleasing ratios.
Wind chime tubes don't work this way. A tube vibrating in bending mode (flexing back and forth rather than stretching lengthwise) produces overtones that are not integer multiples of the fundamental. For a free-free tube (one that's free at both ends, like a typical chime), the theoretical overtone ratios are approximately:
- 1st overtone: 2.76× the fundamental
- 2nd overtone: 5.40× the fundamental
- 3rd overtone: 8.93× the fundamental
These ratios come from solving the Euler-Bernoulli beam equation for transverse vibrations. The numbers are irrational; they never simplify to neat fractions. This inharmonicity gives wind chimes their characteristic shimmer. The overtones don't "lock in" with the fundamental the way they do on a guitar. Instead they create subtle interference patterns that shift and evolve as the tone decays.
Why the Hang Point Matters
If you've ever examined a quality wind chime, you'll notice that the string passes through a hole drilled at an oddly specific spot, roughly 22.4% of the way down from the top. There's a reason for that number.
A tube vibrating in its fundamental bending mode has two nodes, points that stay stationary while the rest of the tube flexes. For a free-free tube, these nodes sit at 22.4% from each end. Suspend the tube at one of its nodal points and the string doesn't interfere with the vibration at all. The tube rings freely and sustains for as long as the material allows.
Hang the tube from its center instead and you'll dampen the fundamental almost completely; the sustain drops off and the tone sounds thin and dead. Hang it from the end and the fundamental rings, but the overtones suffer, leaving much less complexity and richness. The 22.4% point is the sweet spot that lets the full spectrum of the tube's voice come through.
Material Physics: Metal, Bamboo, and Wood
The material of a chime tube determines two critical properties: the speed of sound through the material (which sets the pitch for a given length) and the internal damping (which determines how long the tone sustains).
Aluminum
Aluminum is the most popular material for Western wind chimes, and it earned that position. It combines high stiffness, low density, and very low internal damping. A well-made aluminum tube can ring for thirty seconds or more after a single strike. The overtone structure is clean and bright, with the higher partials audible well into the decay. The long sustain makes aluminum ideal for light, intermittent wind, where each strike has time to develop fully before the next one comes.
Bamboo
Bamboo is a radically different material. It's a natural composite, long cellulose fibers embedded in a lignin matrix, with very high internal damping. A struck bamboo tube produces a warm, percussive "tok" that decays in a fraction of a second, typically 0.3 to 0.8 seconds. The fundamental is prominent, but the overtones fade almost immediately, giving bamboo a dry, earthy character.
Don't read that rapid decay as a weakness. Bamboo chimes sound best in steady, moderate wind, where the quick decay keeps tones from piling up and turning muddy. The silence between strikes becomes part of the rhythm. Japanese and Balinese chime makers have known this for centuries: bamboo's beauty is in the space it leaves.
Wood
Hardwoods like teak, rosewood, and redwood fall between metal and bamboo in sustain. A wooden tube typically rings for one to three seconds, long enough to hear a clear pitch and short enough to avoid overlap in moderate wind. The overtone structure of wood is less pronounced than metal, which makes for a mellower, more rounded tone. Wooden chimes often have a "hollow" quality closer to drums and marimbas than to bells.
Tube Length, Diameter, and Pitch
For a tube of uniform cross-section, the fundamental frequency of transverse vibration is proportional to the diameter and inversely proportional to the square of the length. In practical terms: halving the length raises the pitch by two octaves (not one, as with a string). This squared relationship is why wind chime sets have relatively small differences in tube length despite spanning a wide pitch range.
Diameter also plays a role, though less dramatically. A thicker tube of the same length will sound higher in pitch. Most chime makers use a consistent diameter across a set and vary only the length to control tuning. The diameter is chosen to balance volume (thicker tubes are louder), sustain (thicker walls store more energy), and the visual proportions of the finished chime.
How Vibe Chimes Models These Physics
The Vibe Chimes audio engine synthesizes each strike in real time by generating a fundamental tone and layering the inharmonic overtone ratios (2.76×, 5.40×, 8.93×) with material-appropriate amplitudes and decay curves. Aluminum tones sustain for several seconds with prominent upper partials. Bamboo decays in under a second with a strong fundamental. Wood falls in between.
The physics simulation handles the other half. Pendulum dynamics govern the striker's motion, with wind force applied through a sail that catches the simulated breeze. Collision detection triggers sound events only when the striker makes contact with a tube; nothing fires on a timer. Sound emerges from the same physical interactions that produce it in the real world, just computed instead of mechanical.