White, pink and brown noise: what’s the difference?
They differ in how their power is spread from low to high pitch. White noise has equal power at every frequency, so it sounds bright, like hiss. Pink noise has less power the higher you go, about 3 dB less per octave, so it sounds deeper and more even. Brown noise falls about 6 dB per octave and sounds deepest, like a low rumble.
The three at a glance
| Colour | Power per hertz | From one octave to the next | Often described as |
|---|---|---|---|
| White | The same at every frequency | Twice the power in each higher octave | Hiss, like radio static |
| Pink | Falls as 1/f, about 3 dB per octave | The same power in every octave | Deeper and even, like steady rain |
| Brown | Falls as 1/f², about 6 dB per octave | Half the power in each higher octave | A deep rumble |
The simple math
Each colour is defined by its power spectral density, S(f): how much power the sound carries per hertz at frequency f.
White: S(f) is constant
Pink: S(f) ∝ 1/f
Brown: S(f) ∝ 1/f²
An octave is a doubling of frequency, say from 1,000 Hz to 2,000 Hz. Doubling f halves pink noise’s power per hertz, a change of 10 × log₁₀(½) ≈ −3.01 dB, and quarters brown noise’s, 10 × log₁₀(¼) ≈ −6.02 dB. Each octave also spans twice as many hertz as the one below it, so pink noise ends up with the same power in every octave, white noise doubles from one octave to the next, and brown noise halves.
That is why white noise sounds hissy: in white noise that runs up to 20,000 Hz, the top octave alone, from 10,000 to 20,000 Hz, carries half of all the power. Brown noise takes its name from Brownian motion, not the colour: adding up white noise over time, the way a randomly jostled particle drifts, gives the 1/f² shape.
Which one is best for sleep?
None of the public-health sources below names one colour as best. What they do say: CDC lists keeping your bedroom quiet, relaxing and at a cool temperature among the habits that can improve sleep, and NIOSH’s training for shift workers suggests earplugs or a machine, such as a fan or a white-noise machine, to camouflage other noises. So try each one at a low volume and keep the sound you find easiest to ignore.
How loud is too loud?
A sleep sound can play for hours, so volume matters more than colour. NIDCD, part of the National Institutes of Health, says sounds at or below 70 A-weighted decibels (dBA) are unlikely to cause hearing loss even after long exposure, while long or repeated exposure to sounds at or above 85 dBA can cause hearing loss. Normal conversation is about 60 to 70 dBA. A phone’s volume slider isn’t a decibel meter, so keep a sleep sound comfortably quieter than conversation, and use a timer if you don’t need it all night.
Using sound near a baby
The American Academy of Pediatrics warns that some infant sleep machines can produce hazardous noise levels. If you use one, it advises placing it as far from the baby’s head as possible and using it for a short time only. A sound machine doesn’t replace safe-sleep practices, which AAP’s safe-sleep guide explains.
When to talk to a doctor
CDC advises talking to your healthcare provider if you regularly have problems sleeping or notice signs of a sleep disorder, such as insomnia or sleep apnea. If you notice ringing in your ears or changes in your hearing, see a doctor too.
Where Nightwick helps
Nightwick plays white, pink and brown noise, generated in the app, alongside nine recorded sounds such as rain, fan and ocean. Mix up to three at once with a volume for each, and the sleep timer fades out over its final minute instead of cutting off. Every sound plays offline, with no account.
For parents, Settings has a Quieter start option, which starts new sounds at 25% and sets the sleep timer to 60 minutes, and guidance on using sound near infants with quotations from the American Academy of Pediatrics. Nightwick is not a medical device.
Nightwick is coming soon to iPhone and Android.
Sources
- CDC: About Sleep
- CDC / NIOSH: Training for Nurses on Shift Work and Long Work Hours, Module 6: Create a Good Sleep Environment
- NIDCD, National Institutes of Health: Noise-Induced Hearing Loss
- American Academy of Pediatrics, HealthyChildren.org: How Noise Affects Children
- American Academy of Pediatrics, HealthyChildren.org: A Parent’s Guide to Safe Sleep
- Textbook definitions: White, pink (1/f) and brown (1/f²) noise are defined by their power spectral density; the decibel arithmetic is worked in this guide.
General information, not medical advice. If sleep problems continue, talk to a doctor. Nightwick is an app from intellidip; it is not a medical device and does not diagnose, treat or prevent any condition.