The simplest wave
The building block that every sound and signal is made from.
What you are looking at
Rows of dots move up and down in smooth waves. Some waves are slow and wide, and some are quick and narrow.
The idea
Imagine a point on the edge of a wheel that turns at a steady speed. Watch only how high the point is. It goes up, comes down, goes below the middle, and comes back up. If you draw that height over time, you get a smooth, wavy line. That line is a sine wave.
The sound of a tuning fork is a sine wave. Most sounds are not that simple, but here is the surprising part: any repeating sound or signal can be made by adding up sine waves of different speeds and sizes. A violin and a flute playing the same note have different mixes of sine waves, which is why they sound different.
This means you can take a sound apart into its sine waves, change some of them, and put it back together. That is what an equalizer does.
Where else you see it
- Music apps and equalizers.
- Radio and Wi-Fi signals.
- Image and sound compression like JPEG and MP3, which throw away the sine waves your senses do not notice.
Go deeper: the proper names and the math
A sine wave is A sin(2πft + φ): it is fixed by its amplitude A, frequency f, and phase φ. Fourier series: any periodic signal is a sum of sine waves at whole-number multiples of a base frequency. For example, a square wave is sin(ωt) + sin(3ωt)/3 + sin(5ωt)/5 + …
The Fourier transform extends this to signals that do not repeat, and it converts between a signal as a function of time and the same signal as a function of frequency. The fast version (the FFT) is one of the most used algorithms in engineering.