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Beginning of time and matter.
Scientists generally agree that the age of the universe began about 14 billion years ago. -
At about 400 million years ago, animals started developing that could communicate with one another through either sight or sound. (both of which utilize waves)
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The earliest known instruments, these flutes mark the beginning of humans manipulating sound waves using something other than their own voice.
National Geographic Article -
Pythagoras looks a little closer at how vibrating strings produce sound, and starts to try to come up with a mathematical relationship with string length.
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Robert Boyle conducted an experiment which proved that sound cannot travel in a vacuum.
Robert Boyle-Famous Scientist -
Ole Romer made observations of Jupiters moons that led him to believe that light did not travel instantaneously. It had a finite speed! Rømer's determination of the speed of light
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Isaac Newton published his "Principia", in which he calculated the velocity of sound in air.
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Jean le Rond d'Alembert develops the one-dimensional wave equation. Waves
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Swiss mathematician, Leonhard Euler, takes the wave equation into three dimensions.
Waves -
Charles Sturm and Jean-Daniel Colladon complete the first successful experiment to determine the speed of sound in water as opposed to air.
Charles Sturm Wikipedia -
James Maxwell successfully predicts oscillating waves in the electric and magnetic fields. History of electromagnetic theory
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Heinrich Hertz (does that name sound familiar? Frequency anyone?) experimentally proves Maxwell's work and they conclude that light and electromagnetic waves are one and the same. Light
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Guglielmo Marconi built the first device to communicate over distance using electromagnetic waves.
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Philo Farnsworth's camera transmitted the first electronic image leading to modern television. History of Television
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The first communications satellite, Telstar, is launched into orbit and the first television and phone calls are relayed through space. It's still in orbit today, although it's no longer functional.
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The first cellular phone system was deployed in Tokyo, Japan in 1979. America got it's first in 1983. All the mobile phones previous to that were simply radios and didn't use modern "cellular" technology.