Pendulum Waves: Why Do Pendulums Create Waves?
Slightly different lengths. Mesmerizing patterns. The physics of sync.
Slightly different lengths. Mesmerizing patterns. The physics of sync.
A pendulum is one of the simplest things in physics: a weight hanging from a string, swinging back and forth. Drag the bob below and release it to watch it swing. Then try changing the string length.
Drag the bob to pull it, then release to swing
A longer pendulum swings slower. A shorter one swings faster. The mass of the bob does not matter, and for small swings, the amplitude does not change the period either. Only the length of the string determines how fast it goes.
Here are two pendulums side by side. Each has its own length slider. Set them to different lengths and watch: the shorter one always completes a swing faster than the longer one.
Galileo noticed this around 1602: the period of a pendulum depends only on its length and the strength of gravity. Double the length and the period grows by a factor of √2 (about 1.41). This is why grandfather clocks use a pendulum exactly 1 meter long for a 2-second period.
Now watch what happens when two pendulums have almost the same length. They start in sync, slowly drift apart, and then come back together. This repeating pattern is called a "beat."
When two oscillators have slightly different frequencies, they produce a "beat" pattern. Musicians tune instruments by listening for beats: the slower the beat, the closer the two notes are to matching. The same physics applies here.
Add more pendulums, each slightly longer than the last. With three, it is just a jumble. But as you increase the count, something beautiful happens: a wave pattern appears.
Start with "Classic Wave" to see the full effect, then experiment
Each pendulum swings at its own natural frequency. Because the lengths increase linearly, the phase differences fan out evenly. Your eye connects the bobs into a smooth curve, and that curve shifts over time, creating the illusion of a traveling wave.
A full 15-pendulum wave cycles through distinct phases. Watch the pattern and the label below: they start in sync, form a wave, scatter into chaos, reform the wave, and come back to sync.
The time it takes for all pendulums to return to sync depends on how different their periods are. Real pendulum wave machines are tuned so that the longest pendulum completes exactly one fewer swing than the shortest in a set time (often 60 seconds).
Pendulum physics is everywhere. Grandfather clocks use a 1-meter pendulum for precise timekeeping. Earthquake engineers study pendulum dynamics to design buildings that absorb seismic waves. Even the Foucault pendulum at the Smithsonian demonstrates Earth's rotation using the same principle.
Now it is your turn. Adjust the number of pendulums, the spread of lengths, gravity, and simulation speed. Try the Moon or Jupiter to see how gravity changes the wave.
Try Moon gravity for slow, graceful waves, or Jupiter for rapid oscillation
Set pendulums to 30 with a low spread to see an extremely smooth wave. Switch to Moon gravity to watch the whole pattern play out in slow motion. Or crank the speed to 5x and watch cycles fly by.
You now understand how pendulums with slightly different lengths drift in and out of sync, creating mesmerizing wave patterns from simple physics.
A pendulum's period depends only on its length, not its mass or amplitude (for small swings).
Small differences in length cause pendulums to drift in and out of phase over time.
When many pendulums have incrementally different lengths, a wave pattern emerges from phase differences alone.
The wave you see is an illusion created by phase offsets. No energy travels sideways between the pendulums.
Pendulum physics appears in clocks, metronomes, earthquake engineering, and the study of coupled oscillators.
Put your new knowledge into practice!