Noise - Wikiparency

# Noise > *For the effect of unwanted sound on people and the environment, see [[Noise_pollution]]. For noise as an electronic-circuit phenomenon, see [[Noise_(electronics)|Noise (electronics)]].* **Noise** is a random signal — one whose value at a future instant cannot be predicted exactly from its past, only described statistically. In acoustics it usually means an unwanted or featureless [[Sound|sound]] made of many frequencies at once rather than a single tone, but the mathematics of noise is the same whether the signal is air pressure, a voltage, a pixel value or a stock price. What distinguishes one noise from another is not its average level but the shape of its power spectral density (PSD): how the signal's power is distributed across frequency. The [[Noise|Noise]] microsim draws five named noises side by side — white, pink, brown, blue and violet — as scrolling waveforms and as a measured spectrum on log-log axes, and lets the reader pick a colour, change the sound level, and reseed the random generator to see a fresh realization of the same statistics. Colour names for noise are borrowed from light by analogy: a signal with equal power at every frequency is called white noise, just as white light mixes all visible frequencies equally; a signal whose power falls with frequency is called pink or red (brown), leaning toward the bass, the way pink or red light leans toward the low-frequency end of the visible spectrum.[^thinkdsp-ch4] The colours are not exact — human colour vision and human hearing are shaped very differently — but the label has stuck because it is a fast way to say where a noise's energy sits. Outside the laboratory, noise more often means the everyday din of traffic, machinery, aircraft and neighbors, and the second half of this article follows that meaning: how it is recorded, how it is regulated, what it does to health, and how writers have complained about it. ## Measurement All the standard noise colours can be written as a single family, a power law in frequency: `S(f) ~ 1/f^β` where S(f) is the power spectral density and β is the spectral exponent. β = 0 gives a flat spectrum — equal power at every frequency — which is white noise. As β increases toward 2, the spectrum tilts more steeply toward the bass, and β = 2 is called red noise or, more commonly in acoustics, brown or Brownian noise, because it can be generated as a random walk: each sample is the previous sample plus an independent random step, the same construction that describes Brownian motion.[^thinkdsp-ch4] Negative β tilts the other way, toward the treble: β = −1 is called blue noise and β = −2 violet noise, each obtained from white noise the way brown noise is obtained from it, but by differencing successive samples instead of summing them. Because power is proportional to the square of amplitude, dividing the power spectrum by f^β corresponds to dividing the amplitude spectrum by f^(β/2); one standard synthesis method starts from white noise, takes its Fourier transform, divides each frequency component's amplitude by f^(β/2), and inverse-transforms back to a waveform — the low-pass or high-pass filter that gives the coloured noise its character.[^thinkdsp-ch4] Fitting a straight line to a measured spectrum on log-log axes (linear regression of log power against log frequency) recovers an estimate of β directly from its slope; that regression, run on 66.5 seconds of the sound made by a pink-noise generator's software model, returned a slope of about −1, consistent with the design target β = 1.[^thinkdsp-ch4] The name **pink noise** is reserved for the case where 0 < β < 2, most often β = 1 exactly. A power law with β = 1 has a special property for how humans and most animals perceive frequency: because an octave is a doubling of frequency regardless of where it sits, and the power in the band from f to 2f is proportional to ∫ f^−1 df = ln 2, a constant independent of f, pink noise carries the same total energy in every octave. On a linear power-vs-frequency plot it slopes down about 3 dB for every doubling of frequency; on a plot of power per octave band it is flat. Wide-band white noise, by contrast, has that same 3 dB-per-octave rise built into its per-octave energy simply because each higher octave is twice as wide as the one below, which is one reason white noise sounds thin and hissy to an ear that groups frequency by octave rather than by hertz. This octave-band way of measuring a spectrum — summing energy into fixed fractional-octave bins rather than reading raw hertz — is also how sound level meters and environmental-noise instruments report a spectrum in practice, since it matches how the ear and most regulations divide up frequency. *Try: in the [[Noise|Noise]] microsim, switch the colour control between white, pink, brown, blue and violet and watch both curves — the raw log-log spectrum (a straight line whose slope is β) and the ten-band bar chart, which goes flat only for pink. Reseed to see a different random draw of the same statistics, and raise the level to hear how the 1 kHz octave is calibrated.* ### White, pink and brown noise White noise has, on average, equal power at every frequency: β = 0. It is the noise obtained most simply from a sequence of independent, identically distributed random samples, and its spectrum on a log-log plot is a horizontal line — no consistent slope at all.[^thinkdsp-ch4] Because higher octaves are wider, white noise's per-octave energy still climbs about 3 dB per octave, which is audible as a hiss weighted toward high frequency. Pink noise (β = 1, discussed above) is the noise most often described as sounding "balanced" or natural, and is used as a calibration and masking signal in audio testing for that reason — every octave band, from the lowest to the highest a system reproduces, is expected to carry the same amount of energy. Brown, or red, noise (β = 2) is built as a random walk: each new sample equals the previous sample plus an independent Gaussian step, exactly the model of Brownian motion in one dimension.[^thinkdsp-ch4] Summing white noise this way multiplies its spectrum by an extra factor of 1/f² (each integration in time adds 2 to the exponent β), so an ideal random walk shows a slope of −2 on the same log-log plot; a leaky version of the integrator, needed to keep the walk from wandering off to infinity over a long recording, flattens the spectrum below some low corner frequency instead of letting it keep climbing without bound. ### Blue and violet noise Blue noise (β = −1) and violet noise (β = −2) tilt toward the treble instead of the bass, and are generated from pink and white noise respectively by taking the first difference of the sequence (subtracting each sample from the one after it) rather than the running sum used for brown noise; differencing subtracts, rather than adds, 2 from the exponent.[^thinkdsp-ch4] Both sound thin and fizzy, with blue noise commonly used in image dithering because the eye is less sensitive to error patterns concentrated at high spatial frequency. Not every colour name attached to noise has the same precise footing as white, pink or brown: **grey noise** is white noise reshaped by an equal-loudness curve so that it sounds subjectively flat to a human ear rather than being flat in raw power, and **black noise** describes near-silence with occasional random bursts, used loosely for background dominated by rare events rather than a continuous spectrum. These usages are looser than the power-law family above and are not standardized the way β is. ## Recording and reproduction Identifying which colour a recorded noise belongs to is a curve-fitting problem: compute a spectral estimate (in the microsim, a Welch average of eight Hann-windowed 4096-point Fourier transforms, which trades frequency resolution for a smoother, less noisy estimate), take its logarithm in both frequency and power, and fit a straight line by least squares. The fitted slope estimates −β directly, and the y-intercept sets the noise's overall level.[^thinkdsp-ch4] The same regression, applied to a real recording rather than a synthetic sequence, is how an engineer checks whether a measured hiss, rumble or interference is closer to white, pink or brown before deciding how to filter or reproduce it faithfully. In practice a computer or a piece of studio hardware generates coloured noise either by filtering — starting from white noise (independent samples) and passing it through a filter whose gain rolls off or rises as a power of frequency — or by a direct recursive rule, such as the running sum for brown noise or Paul Kellet's widely used three-pole approximation for pink noise, which needs no Fourier transform at all and can run sample by sample in real time.[^thinkdsp-ch4] The microsim's white sequence is drawn from independent Gaussian samples (via the Box–Muller transform); its pink sequence uses Kellet's filter; its brown sequence uses a leaky running sum; and its blue and violet sequences are first differences of the pink and white sequences respectively. Pink and white noise generated this way are routine test signals in audio recording and reproduction: pink noise is played through loudspeakers to set up room equalization and to measure a room's [[Reverberation|reverberation]] time, because a signal with equal energy per octave excites every band a listener will actually hear, while white noise is used to characterize a microphone or converter's flat-frequency response directly in hertz rather than in octaves. *Try: read the β and dB/octave readouts under any of the five colours; a well-formed pink signal reports a slope close to −1 on the raw spectrum and close to 0 dB/octave on the band chart, while white reports β near 0 and roughly +3 dB/octave on the band chart, because each band is twice the width of the one below it.* ## Environmental noise Environmental noise is unwanted sound from transportation, industry and recreation that reaches people outdoors or in their homes — road and rail traffic, aircraft, construction and neighborhood activity are its largest sources in most countries. Unlike the synthetic colours above, environmental noise is rarely a clean power law: it is measured instead with time-averaged descriptors such as the equivalent continuous sound level (L_Aeq) over an hour, day or year, or day–evening–night indices that add a penalty to noise heard at night, when the same sound level is judged more disturbing. These descriptors, not a spectral slope, are what environmental-noise regulation and health guidance are built around. ## Regulation ### United States In the United States, workplace noise exposure is regulated by the Occupational Safety and Health Administration under 29 CFR 1910.95, the Occupational Noise Exposure standard, which sets a permissible exposure limit of 90 dBA averaged over an 8-hour time-weighted average, with a 5 dB exchange rate (each 5 dB increase in level halves the allowed exposure time) and a hearing-conservation program — audiometric testing and hearing protection — required once an employee's time-weighted average reaches 85 dBA.[^osha-1910-95] The rule targets occupational rather than general environmental noise; separate federal and state programs address community exposure. ### Europe Environmental noise across the European Union is governed by Directive 2002/49/EC, the Environmental Noise Directive, which requires member states to produce strategic noise maps for major roads, railways, airports and agglomerations above set traffic and population thresholds, to report exposure using the harmonized day–evening–night level (L_den) and night-level (L_night) indicators, and to adopt action plans to manage and reduce noise and preserve quiet areas, with the mapping and planning cycle repeated on a five-year schedule.[^eu-2002-49-ec] The directive does not itself set binding limit values; it standardizes how exposure is measured and mapped so that member states' own limits and action plans can be compared and followed up. ## Health effects The World Health Organization's *Environmental Noise Guidelines for the European Region* (2018) reviewed the evidence linking environmental noise exposure to health outcomes and issued exposure-level recommendations for road traffic, railway and aircraft noise, and for noise from wind turbines and leisure activities.[^who-2018] The guidelines report a "strong" quality-of-evidence link between environmental noise and annoyance, sleep disturbance and ischemic heart disease, recommending, for example, average road traffic noise below 53 dB L_den and below 45 dB L_night to keep adverse health effects at a low level, and treat reducing exposure from major transportation sources as a public-health priority given noise's contribution to the region's overall burden of disease. ### Hearing loss prevention Noise-induced hearing loss is preventable, and the same exposure-and-time logic behind OSHA's exchange rate underlies most hearing-conservation practice: reducing noise at its source, increasing distance or shielding along its path, limiting exposure duration, and using properly fitted hearing protection when exposure cannot otherwise be brought under the recommended limit.[^osha-1910-95] Because damage accumulates with total sound energy received over time, brief very loud exposures (impulse noise from tools or firearms) and long moderate ones (a shift near machinery) can carry comparable risk, which is why hearing-conservation programs track a time-weighted average rather than a single peak reading. ## Literary views Complaints about noise as an affliction on thought and health predate any instrument capable of measuring it. The philosopher Arthur Schopenhauer devoted a short essay, "On Noise" ("Ueber Lärm"), included in the second volume of his *Parerga und Paralipomena* (1851), to the argument that noise is an interruption disproportionately painful to a thinking person, singling out the crack of coachmen's whips in the street as a needless, remediable irritant and treating a person's sensitivity to noise as roughly proportional to their intellectual life.[^schopenhauer-1851] The essay is one of the earliest sustained arguments that unwanted sound is not merely unpleasant but a real cost — an argument later environmental-noise regulation would make in the different vocabulary of exposure limits and health guidelines. ## Minnesota *This section is specific to Wikitube.* No sourced Minnesota-specific case for this article has been verified; see the Ultrasound and Underwater acoustics articles on this spine for Minnesota-grounded sections. *Citation needed* if a Minnesota noise-measurement program or laboratory is documented for a future revision. ## See also - [[Colors_of_noise]] - [[Pink_noise]] - [[Noise_pollution]] - [[Sound]] - [[Wave]] - [[Sound_pressure]] - [[Sound_localization]] - [[Reverberation]] ## References [^thinkdsp-ch4]: Downey, Allen B. (2012). *Think DSP: Digital Signal Processing in Python*, chapter 4, "Noise" (4.1 Uncorrelated noise; 4.2 Integrated spectrum; 4.3 Brownian noise; 4.4 Pink noise; 4.5 Gaussian noise), and chapter 5, §5.3–5.4 (autocorrelation and estimated spectral slope, β ≈ 1 for a modeled pink-noise generator, slope ≈ −1.9 for a Brownian-noise example). Green Tea Press / O'Reilly. https://greenteapress.com/thinkdsp/thinkdsp.pdf [^osha-1910-95]: United States Department of Labor, Occupational Safety and Health Administration. "Occupational Noise Exposure," 29 CFR 1910.95, including Table G-16 (permissible noise exposures, 90 dBA/8 h with a 5 dB exchange rate) and the hearing conservation amendment (29 CFR 1910.95(c), action level 85 dBA as an 8-hour time-weighted average). https://www.osha.gov/laws-regs/regulations/standardnumber/1910/1910.95 [^eu-2002-49-ec]: Directive 2002/49/EC of the European Parliament and of the Council of 25 June 2002 relating to the assessment and management of environmental noise, *Official Journal of the European Communities*, L 189/12, 18 July 2002 (strategic noise mapping, L_den/L_night indicators, action plans, five-year review cycle). https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32002L0049 [^who-2018]: World Health Organization, Regional Office for Europe. *Environmental Noise Guidelines for the European Region*. Copenhagen: WHO Regional Office for Europe, 2018 (strong-evidence outcomes: annoyance, sleep disturbance, ischemic heart disease; recommended levels including road traffic noise below 53 dB L_den / 45 dB L_night). ISBN 978-92-890-5356-3. https://www.who.int/europe/publications/i/item/9789289053563 [^schopenhauer-1851]: Schopenhauer, Arthur. "Ueber Lärm und Geräusch" ("On Noise"), in *Parerga und Paralipomena*, vol. 2, ch. 30 (1851). Widely translated in English collections as "On Noise," e.g. in *Essays of Arthur Schopenhauer*, trans. T. Bailey Saunders (1891). https://www.gutenberg.org/ebooks/author/261  **Microsim — three.js (Wikitube framework):** *Noise* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/acoustics/Noise.html" data-title="Noise"></div> *Built from `MICROSIM_GUIDE/specs/acoustics/sims/Noise.json`; part of the [[PORTAL_Acoustics|Acoustics portal]] spine (section sims and See-also variants).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Noise) : [Wikitube](https://en.wikitube.io/wiki/Noise) - skeleton pinned to revision 1368229768 (2026-09-11).