White noise is white because it’s just an amalgamation of a wide range of sound frequencies, giving one singular noise. Similar to the color white, which is the amalgamation of a wide range of light frequencies that come together and give one singular color.
So it could be said that any individual sound frequency could be a “colored sound”, but we don’t call them that. We just say what the frequency is, as it is just a long beep at a certain pitch.
There are other “colors of noise”, but they have a fairly technical definition and don’t sound meaningfully different from white noise to the untrained ear. They basically describe how power density scales with frequency. Like, white noise distributes power equally to all output frequencies, whereas brown noise distributes more power to lower frequencies and less to higher frequencies – so brown noise sounds basically like white noise with more bass.
https://en.wikipedia.org/wiki/Colors_of_noise
We generally describe noise colors in terms of light frequency and the distribution of the frequencies in the noise. So red noise has the lower frequencies at higher volume than the high frequencies, blue noise has more at the upper frequencies, and white noise is even the while way across.
Red noise sounds like the ocean, white noise sounds like static, blue noise sounds like angrier, fizzier static. Brown noise means the same thing as red noise, it’s just named after some guy called Brown for complicated science history reasons.
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