Fourier Follies

The sounds we hear – whether music, speech, or background noise – are the result of vibrations of our ear drum, stimulated by sound waves travelling through the air, created by our headphones, musical instruments, people’s voice boxes, or that annoying person behind you in the cinema opening their sweets. These vibrations can be plotted (the intensity, or pressure, of the wave plotted over time) giving us a visual representation of the sound.

The sound wave of the middle A on a tuning fork, is a perfect example of a sine wave, written mathematically as sin(x). The sound wave of speech is more complicated. But any sound wave, indeed any repeating function, can be broken up into a number of sine waves of various frequencies and amplitudes (intensities). This is the result of work that started with the French mathematician, Joseph Fourier, who lived through the French revolution in the eighteenth century. The expression of a sound wave, or any signal varying over time, as the sum of its constituent sine waves, is known as the Fourier transform of that signal. … (+Plus Magazine)