Fourier Transformations

So what was Fourier’s discovery, and why is it useful? Imagine playing a note on a piano. When you press the piano key, a hammer strikes a string that vibrates to and fro at a certain fixed rate (440 times a second for the A note). As the string vibrates, the air molecules around it bounce to and fro, creating a wave of jiggling air molecules that we call sound. If you could watch the air carry out this periodic dance, you’d discover a smooth, undulating, endlessly repeating curve that’...

 The Bell Jar

A famous experiment in high school physics involves putting an electric buzzer in a bell jar, a glass container from which the air can be removed by a pump. When the air is removed, the sound of the buzzer disappears. As early as the seventeenth century, it was recognized that sound needed some medium to travel in. In a vacuum, such as exists inside the bell jar, there is nothing to carry the sound waves, so you don't hear the buzzer inside. To be more specific, sound is a pressure wave, or d...