Pendulum wave
A ‘Pendulum wave’ is a collective wave-like phenomenon that appears when pendulums (weights) of different lengths are arranged side by side.
Because each pendulum has a different period depending on its length, they oscillate at different speeds over time, producing beautiful wave-like patterns.
To create a pendulum wave with a 1-minute cycle, for example:
- Adjust the longest pendulum so that it completes n oscillations per minute.
- Then set the length of the next pendulum so that it makes n + 1 oscillations per minute, the next n + 2, the next n + 3, and so on.
If you have 10 or more pendulums, you can observe attractive wave patterns.
How to calculate pendulum lengths
When the amplitude isn’t too large, the period of a pendulum depends on its length as follows:\[T = 2\pi \sqrt{\frac{L}{g}}, \quad
(L: \text{pendulum length},\ g: \text{acceleration due to gravity)\]
Since frequency is the reciprocal of period:
\[f = \frac{1}{2\pi}\sqrt{\frac{g}{L}}, \quad
(L: \text{pendulum length},\ g: \text{acceleration due to gravity)\]
From these formulas, you can see that longer pendulums oscillate more slowly (lower frequency), and shorter ones oscillate faster (higher frequency).