“How does a violin string create sound?” This simple question would give rise to the wave equation, which can describe how a string’s shape changes over time. The equation can be modified to apply to all kinds of other phenomena (like seismic waves from an earthquake). However…
…the most influential insight from the wave equation emerged from the study of Maxwell’s equations of electromagnetism. In 1820, most people lit their houses using candles and lanterns. If you wanted to send a message, you wrote a letter and put it on a horse-drawn carriage; for urgent messages, you omitted the carriage. Within 100 years, homes and streets had electric lighting, telegraphy meant messages could be transmitted across continents, and people even began to talk to each other by telephone. Radio communication had been demonstrated in laboratories, and one entrepreneur had set up a factory selling “wirelesses” to the public.
This social and technological revolution was triggered by the discoveries of two scientists. In about 1830, Michael Faraday established the basic physics of electromagnetism. Thirty years later, James Clerk Maxwell embarked on a quest to formulate a mathematical basis for Faraday’s experiments and theories.
At the time, most physicists working on electricity and magnetism were looking for analogies with gravity, which they viewed as a force acting between bodies at a distance. Faraday had a different idea: to explain the series of experiments he conducted on electricity and magnetism, he postulated that both phenomena are fields which pervade space, change over time and can be detected by the forces they produce. Faraday posed his theories in terms of geometric structures, such as lines of magnetic force.
Maxwell reformulated these ideas by analogy with the mathematics of fluid flow. He reasoned that lines of force were analogous to the paths followed by the molecules of a fluid and that the strength of the electric or magnetic field was analogous to the velocity of the fluid. By 1864 Maxwell had written down four equations for the basic interactions between the electrical and magnetic fields. Two tell us that electricity and magnetism cannot leak away. The other two tell us that when a region of electric field spins in a small circle, it creates a magnetic field, and a spinning region of magnetic field creates an electric field.
But it was what Maxwell did next that is so astonishing. By performing a few simple manipulations on his equations, he succeeded in deriving the wave equation and deduced that light must be an electromagnetic wave. This alone was stupendous news, as no one had imagined such a fundamental link between light, electricity and magnetism. And there was more. Light comes in different colours, corresponding to different wavelengths. The wavelengths we see are restricted by the chemistry of the eye’s light-detecting pigments. Maxwell’s equations led to a dramatic prediction - that electromagnetic waves of all wavelengths should exist. Some, with much longer wavelengths than we can see, would transform the world: radio waves
The somewhat accidental and independent verification/corroboration of natural phenomena is science at its best (see bold above).