Harmonic analysis
Breaking a complicated repeating signal into a sum of simple sine waves, used to predict tides and to build sounds.
Many complicated, wavy patterns can be built by adding together simple, smooth sine waves of different sizes, speeds and starting points. Harmonic analysis, also called Fourier analysis, works the other way: it takes a messy signal and finds the set of simple waves that make it up.
Tides are the classic example. The rise and fall of the sea at a port is driven by the regular motions of the Moon and Sun, and each motion contributes its own steady wave, called a constituent, with its own period. The main lunar constituent repeats about every 12 hours 25 minutes, the main solar one every 12 hours, and dozens of smaller ones add detail. Record the tide at a port for long enough, work out the size and timing of each constituent, and you can add them back together to predict tides years ahead.
In 1873 William Thomson, later Lord Kelvin, built a tide-predicting machine that summed 10 constituents with a system of pulleys and gears. An American machine completed in 1910 handled 37. Such machines prepared tide tables for decades, until electronic computers took over.
Sound works the same way. A note from an instrument is a fundamental frequency plus a set of higher harmonics, and the mix gives it its character. Building a sound by adding sine waves is called additive synthesis, the principle behind some early electric organs and synthesisers.
Coming up in future stories
- The Tide Machine That Picked D-Day 1943-1944 · Liverpool & Normandy