The history
From Pythagoras's strings to ripples in spacetime: how people learned that sound, light and even gravity travel as waves.
Musicians knew for thousands of years that string lengths make harmony, but it took until the 1600s to see pitch as frequency and to write the laws of a vibrating string. Then came the speed of sound, patterns in sand, light's interference and Maxwell's discovery that light is an electromagnetic wave. The 20th century added radio, microwave ovens, a tabla explained by an Indian physicist, a bridge that twisted itself apart, and in 2015, waves in space itself.
1636
First measured frequency of a musical note
Marin Mersenne, Paris (about 84 Hz)
1687
First calculated speed of sound
Isaac Newton, Cambridge (298 m/s, 15 % low)
1801
First interference of light explained
Thomas Young, London
1887
First radio waves made and detected
Heinrich Hertz, Karlsruhe
2015
First gravitational wave detected
LIGO, United States
530 BCE – 1638
Harmony is found to follow whole numbers, the octave is split into equal steps, and Mersenne and Galileo tie pitch to frequency.
530 BCE
c. 530 BCE (attributed)
Greek tradition credits Pythagoras with finding that a string halved in length sounds an octave higher, and that lengths in ratios 3:2 and 4:3 give the fifth and fourth. The famous story of blacksmiths' hammers is a later legend and doesn't work physically.
Why it mattered. It was the first law of nature written as numbers, and the seed of fₙ = n v ÷ 2L.
1584
The Chinese prince and scholar Zhu Zaiyu calculated how to split the octave into 12 equal steps, each the twelfth root of 2, about 1.0595 times the last, to many decimal places. Simon Stevin reached the same idea in Europe a few decades later.
Why it mattered. Every modern piano key is tuned this way: each is 1.0595 times the frequency of the one below.
1636
In Harmonie universelle, Mersenne set out how a string's pitch depends on its length (inversely), tension (as its square root) and weight per length (inversely as its square root). He also made the first absolute measurement of a note's frequency, about 84 vibrations a second.
Why it mattered. These laws are v = √(T ÷ μ) and f = v ÷ 2L, the rules behind every stringed instrument.
1638
In Two New Sciences, Galileo argued that pitch is set by how many vibrations reach the ear each second, and compared vibrating strings with swinging pendulums, whose rhythm depends only on their length.
Why it mattered. It tied musical pitch to frequency, and the pendulum's natural rhythm is exactly what a swing resonates with.
1660 – 1816
Sound needs air, pitch is counted in clicks, its speed is calculated and corrected, and sand reveals standing waves.
1660
Using an air pump built with his assistant Robert Hooke, Boyle pumped the air from a glass jar holding a ticking watch. The ticking grew fainter as the air went and returned when it was let back in.
Why it mattered. It showed that sound needs air to travel, while light passed through the empty jar untouched.
1681
Hooke held a card against a spinning toothed brass wheel. The faster it spun, the more clicks each second and the higher the note, so he could make a sound of known frequency on demand.
Why it mattered. It showed directly that pitch is frequency, the idea behind every sound chapter since.
1687
In the Principia, Newton worked out the speed of sound from the springiness and density of air. He got about 298 m/s, some 15 % too low, and could not explain the gap.
Why it mattered. It was the first attempt to predict a wave's speed from the medium it travels through, the idea that v is set by the medium, not the source.
1787
Chladni scattered sand on metal plates and bowed their edges. The sand danced off the vibrating parts and gathered on the still lines, the nodes, making beautiful patterns that change with each note.
Why it mattered. They made standing waves visible for the first time, and gave acoustics its founder.
1816
Napoleon's Academy offered a prize for the mathematics of Chladni's patterns. Sophie Germain, a self-taught mathematician barred from universities as a woman, entered three times and won in 1816, the first woman to win a prize from the Paris Academy of Sciences.
Why it mattered. Her work began the theory of elastic plates, still used to design everything from loudspeakers to bridges.
1816
Laplace realised that squeezed air in a sound wave warms up and stretched air cools, too fast for the heat to escape. Adding that effect raised Newton's speed of sound to match the measured value, about 340 m/s.
Why it mattered. It closed a 130-year puzzle and is why the box uses v = 331 √(1 + T/273) m/s.
By the numbers
Seventeenth-century measurements and Newton's calculation scattered widely around today's 343 m/s at 20 °C.
1801 – 1887
Young's fringes, Doppler's shifting pitch, Maxwell's equations and Hertz's radio waves show that light is an electromagnetic wave.
1801
1801–1803
In his 1801 Bakerian lecture Young explained colours by interference: waves that meet in step add, and waves out of step cancel. By 1803 he described light passing two slits and making bright and dark bands.
Why it mattered. It was strong evidence that light is a wave, against Newton's popular idea of particles.
1842
Doppler proposed that a wave's frequency depends on how its source and listener move: higher when approaching, lower when moving apart. In 1845 C. H. D. Buys Ballot tested it in the Netherlands with musicians playing a steady note on a moving train.
Why it mattered. The Doppler effect now measures blood flow, weather and the expansion of the universe.
1865
In A Dynamical Theory of the Electromagnetic Field, Maxwell showed that electric and magnetic fields can travel together as a wave. The speed his equations predicted matched the measured speed of light.
Why it mattered. It joined light, electricity and magnetism, and predicted invisible waves nobody had yet made.
1887
With a spark gap and a loop of wire, Hertz sent and detected invisible electromagnetic waves across his lab. He reflected them off a metal sheet to make standing waves a few metres long, and showed they travel at the speed of light.
Why it mattered. It proved Maxwell right and opened the way to radio, TV, Wi-Fi and microwave ovens. The unit of frequency is named after him.
1920 – 2016
Drums explained, a bridge destroyed, kitchens transformed and gravitational waves detected.
1920
Most drums make overtones that are out of tune with each other. Raman and Kumar showed in Nature that Indian drums like the tabla and mridangam give harmonic overtones, in a musical series like a string's, thanks to the loaded black patch on the drumhead.
Why it mattered. It explained, with physics, a design Indian drum makers had perfected by ear over centuries.
1940
7 November 1940
Four months after opening, the 853 m span twisted about 12 times a minute in a steady 64 km/h wind, until it tore apart and fell into Puget Sound. Film of the collapse became world famous.
Why it mattered. Often called resonance, it was really aeroelastic flutter: the twisting deck made the wind push it harder, and bridges have been wind-tested ever since.
1945
Working on radar magnetrons, Spencer noticed a chocolate bar in his pocket had melted. He tried popcorn and an egg next, and Raytheon patented microwave cooking in 1945.
Why it mattered. It led to the microwave oven, whose 12 cm standing waves this box lets you watch.
2000
10 June 2000
On opening day, thousands of walkers made London's new footbridge sway sideways by about 70 mm. People fell into step with the sway, which made it worse. It closed after two days and reopened in 2002 with 37 fluid dampers and 52 tuned mass dampers.
Why it mattered. It showed that people can drive resonance too, and changed how footbridges are designed.
2015
14 September 2015
Two detectors caught a gravitational wave from two black holes merging 1.4 billion light-years away. It stretched the 4 km arms by a thousandth of a proton's width, chirping from 35 to 250 Hz in a fifth of a second.
Why it mattered. Einstein's last untested prediction was confirmed, opening a new way to observe the universe; the leaders won the 2017 Nobel Prize.
Did you know?
The Tacoma Narrows Bridge's only death was a dog named Tubby, left in a car on the deck.
Hertz, asked what his radio waves were good for, reportedly said they were of no use whatsoever.
The LIGO signal stretched 4 km arms by about a thousandth of the width of a proton.
Every piano key is the twelfth root of 2, about 1.0595, times the frequency of the one below it.
A microwave oven's hot spots, about 6 cm apart, let you measure the speed of light with a bar of chocolate and a ruler.
The people
1588 – 1648 · Friar, mathematician and music theorist · France
Wrote the laws of vibrating strings and first measured a note's frequency.
1536 – 1611 · Prince, mathematician and music theorist · China
First to calculate twelve-tone equal temperament precisely.
1635 – 1703 · Experimenter and inventor · England
Built Boyle's air pump and made tones of known frequency with a toothed wheel.
1756 – 1827 · Physicist and musician · Germany
Made standing waves visible with sand on vibrating plates.
1776 – 1831 · Mathematician · France
Won the Paris Academy's prize for the theory of vibrating plates in 1816.
1773 – 1829 · Physician and physicist · England
Showed interference of light, evidence that light is a wave.
1831 – 1879 · Physicist · Scotland
Showed that light is an electromagnetic wave.
1857 – 1894 · Physicist · Germany
First made and detected radio waves; the unit of frequency bears his name.
1888 – 1970 · Physicist, Nobel laureate 1930 · India
Explained why the tabla and mridangam have musical overtones.
Where it happened
Sources
Dates marked “c.” are approximate, and historians sometimes disagree about who was first. If you spot a mistake, tell us.
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