Reverberation - Wikiparency

# Reverberation > On the **[[PORTAL_Acoustics|Acoustics]]** spine · article face [[Acoustics]]. Microsim queued; the physics is complete.  ## Microsims — p5.js ### Reverberation (p5.js) · `dense echoes` <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/MjYYSnoPW" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Reverberation — p5.js microsim"></iframe> </div> *The wash of overlapping reflections that gives a space its acoustic signature — simulated to place sound in a room.* **Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/MjYYSnoPW) · movement *VIII · Imaging, audio & sensors* · library `p5js` ### Related microsims Live sims on neighbouring articles: - [[Sonar]] - [[Ultrasound]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*  ## Microsim — queued <p class="wt-pending"><strong>Microsim in the draft queue.</strong> The interactive p5.js sim for this station is being built via the two-queue pipeline; the sourced physics below is complete and citable now.</p> ## Overview ### What it is Reverberation is the persistence of sound in an enclosed space caused by many reflections building up and then gradually decaying after the original source has stopped. ### How it works / why it matters As a sound wave strikes walls, floors, and objects, it produces a dense series of delayed and attenuated reflections that the ear perceives as a continuous decaying tail rather than distinct echoes. Reverberation time (often measured as RT60, the time for the level to drop by 60 dB) characterizes a space acoustically. In signal processing, reverberation is simulated digitally using networks of delays and feedback, or by convolving a dry signal with a measured room impulse response. **On the spine:** [[Sound]] · [[Wave]] · [[Oscillation]] · [[Vibration]] · [[Acoustic_wave]] · [[Mechanical_wave]] · [[Plane_wave]] · [[Wave_equation]] · [[Harmonic_oscillator]] · [[Ultrasound]] · [[Doppler_effect]] · [[Fourier_analysis]] · [[Digital_signal_processing]] · [[Acoustics]] · [[Sonar]] · portal [[PORTAL_Acoustics]]. ## Reverberation time **Reverberation** is the persistence of [[Sound|sound]] in an enclosed space after its source has stopped, made of reflections so many and so closely spaced that the ear hears a smooth, decaying tail rather than separate [[Echo|echoes]]. Its single most useful measure is the reverberation time, T60: the time the sound level takes to fall by 60 [[Decibel|decibels]], a factor of one million in intensity, after the source is cut off. The section's microsim, *Reverberation: how long a room rings*, lets the reader build a rectangular room, choose what its walls are made of, seat an audience, and watch a thousand sound rays lose energy at every bounce while the decay curve crosses −60 dB. Reverberation time is the central number of [[Room_acoustics|room acoustics]] because it tracks what listeners notice. Too long, and each syllable of speech is still sounding when the next arrives, blurring words; too short, and music sounds dry and thin. A lecture room is designed for roughly 0.6 s, a concert hall for about 2 s. The decay is exponential because every reflection removes the same fraction of the energy that arrives, so the level falls at a steady number of decibels per second, and a single number describes the whole tail. The time scale follows from simple geometry. Sound in air travels 343 m in a second, the [[Speed_of_sound|speed of sound]] at 20 °C; in a room 10 m × 8 m × 3 m, the mean distance between reflections is `4V/S` = 3.6 m, so the sound strikes a surface roughly 95 times a second. If each surface absorbs only 6% of what arrives, as plaster does at 500 Hz, the energy after n bounces is 0.94ⁿ, and it takes about 220 bounces, a little over two seconds, to lose 60 dB. ### Measurement T60 is measured by exciting the room and recording the decay. The classical method switches off a steady noise source and records the level falling; the impulse method fires a pistol, bursts a balloon or plays a swept sine, and records the room's [[Impulse_response|impulse response]], which contains the whole reverberant tail. In the language of signal processing, the room is a [[Linear_time-invariant_system|linear, time-invariant system]], and a gunshot "puts an impulse into the system; the sound you hear is the impulse response."[^thinkdsp10] A real decay is noisy, because the reflections arrive at random. Manfred Schroeder showed in 1965 that integrating the squared impulse response backward from its end gives a smooth curve equal to the average of infinitely many noise-burst decays, and his backward-integration method is now the standard way to read a decay.[^schroeder1965] Few rooms are quiet enough to show a full 60 dB of decay, so the international standard for performance spaces reads the slope over a smaller range and extrapolates: T20 from −5 to −25 dB and T30 from −5 to −35 dB, each scaled to 60 dB. It also defines the early decay time, from 0 to −10 dB, which correlates better with the reverberance listeners perceive while music is still playing.[^iso3382] Measurements are made with a calibrated [[Sound_level_meter|sound level meter]] or measurement microphone in octave bands, typically from 125 Hz to 4 kHz, because reverberation time varies with frequency: absorbers work differently on bass and treble, and air absorbs high frequencies in large halls. ### Sabine equation Wallace Clement Sabine, a young Harvard physicist, was asked to fix the lecture room of Harvard's Fogg Art Museum, opened in 1895, where speech could not be understood; he found a reverberation time of about 5 s.[^lindahall] Using seat cushions as a portable standard of absorption, carried in and out to change the room's total, he found that the reverberation time was proportional to the room's volume and inversely proportional to its total absorption.[^lindahall][^sabine1922] In SI units the Sabine equation is `T60 = 0.161·V/A`, with `A = Σ αi·Si`, where V is the volume in cubic meters and A is the absorption area in square meters (metric sabins): each surface's area Si weighted by its absorption coefficient αi. The constant is `24·ln 10 / c` = 0.161 s/m for c = 343 m/s. Sabine first applied his formula to design. Boston's Symphony Hall, which opened on October 15, 1900, was built to his calculation for an ideal reverberation time of 1.9–2.1 s, and it became the first auditorium designed according to scientifically derived acoustical principles.[^bso] The microsim's default is a 10 m × 8 m × 3 m classroom with plaster walls and ceiling (α = 0.06) and a wooden floor (α = 0.10). Its volume is 240 m³, its absorption area 19.3 m², and the Sabine equation gives T60 = 2.0 s: far too long for speech. Seating an audience on the floor (α = 0.85) raises A to 79 m² and cuts T60 to 0.49 s; lining walls and ceiling with acoustic panels (α = 0.80) cuts it to 0.24 s, while bare concrete (α = 0.02) stretches it to 3.3 s. In the same room the reverberant sound overtakes the direct sound only 0.62 m from the source (the critical distance, `0.057·√(V/T60)`), and below about 183 Hz (the Schroeder frequency, `2000·√(T60/V)`) separate room modes, not a smooth decay, decide what is heard; those modes are the subject of [[Acoustic_resonance|acoustic resonance]]. *Try: move length Lx, width Ly and height Lz, pick the walls + ceiling material, and tick audience on the floor — the rays in the room fade at each bounce, the orange decay curve on the chart falls toward the −60 dB line alongside the Sabine (white) and Eyring (blue) predictions, and the readout gives V, A and both values of T60; choose concrete for a stairwell and acoustic panel for a studio.* ### Eyring equation Sabine's equation assumes that absorption is spread thinly over many reflections. It fails in very absorbent rooms: with every surface a perfect absorber (α = 1), sound should die at the first bounce, yet the Sabine formula still predicts a finite decay, `0.161·V/S`. Carl Eyring corrected this in 1930 by counting reflections rather than averaging absorption. If a fraction ᾱ of the energy is absorbed at each reflection, the energy after n reflections is (1 − ᾱ)ⁿ, and the formula becomes `T60 = 0.161·V / (−S·ln(1 − ᾱ))`, where S is the total surface area and ᾱ = A/S the mean absorption coefficient.[^eyring1930] For small ᾱ, −ln(1 − ᾱ) ≈ ᾱ and Eyring's formula reduces to Sabine's; as ᾱ approaches 1 it goes to zero, as it should. In the microsim's plaster classroom (ᾱ = 0.07) the two agree within 4% (2.00 s against 1.93 s); lined with acoustic panels (ᾱ = 0.59) they differ by half (0.24 s against 0.16 s). Both formulas assume a diffuse field, in which sound arrives equally from all directions; rooms with all their absorption on one surface, or with unusual shapes, need ray tracing or measurement, the domain of [[Geometrical_acoustics|geometrical acoustics]]. ### Absorption coefficient The [[Absorption_(acoustics)|absorption]] coefficient α of a surface is the fraction of incident sound energy that it does not reflect, from 0 for a perfect reflector to 1 for an open window, which returns nothing. Sabine's original unit of absorption, the sabin, was one square foot of open window; the metric sabin is one square meter of it. The coefficients depend on frequency. Porous materials such as [[Acoustic_panel|acoustic panels]], curtains and carpet absorb well at middle and high frequencies, where the air in their pores moves fast enough for [[Viscosity|viscous]] friction to turn sound into heat; they need depth comparable to a quarter wavelength to work at low frequencies, so bass absorption calls for thick panels, air gaps behind them, or tuned resonant absorbers. | Surface (500 Hz, typical) | α | |---|---| | Concrete | 0.02 | | Brick | 0.03 | | Plaster | 0.06 | | Wood | 0.10 | | Glass | 0.18 | | Carpet | 0.30 | | Heavy curtain | 0.55 | | Acoustic panel | 0.80 | | Seated audience | 0.85 | The values are those used by the microsim, representative of published 500 Hz coefficients and ILLUSTRATIVE for any particular product.[^pack-alpha] Coefficients are measured in a reverberation chamber: the chamber's T60 is recorded with and without a sample on the floor, and the Sabine equation turns the change into the sample's absorption area.[^iso354] Single-number ratings such as the [[Noise_reduction_coefficient|noise reduction coefficient]] average the mid-band values. People are the largest absorber in most halls, which is why concert halls are tuned with the audience in place and why an empty hall sounds so much livelier than a full one. ## In music Reverberation is part of the sound of music, and musical styles grew up in the rooms they were played in. Slow music with sustained lines tolerates, and is enriched by, decays of several seconds, as in large stone churches; rapid passages and sung or spoken words need drier rooms, because each note or syllable must fade before the next arrives. Symphonic concert halls are commonly designed for about 2 s at mid frequencies with the audience present, close to the target Sabine chose for Boston.[^bso] The See-also variant for [[Architectural_acoustics|architectural acoustics]] shows the arithmetic: a 30 m × 25 m × 15 m wood-lined hall rings for 2.1 s full and 5.8 s empty. Recorded music usually adds reverberation artificially. Studios once used dedicated echo chambers, hard-walled rooms with a [[Loudspeaker|loudspeaker]] and a [[Microphone|microphone]], and later steel plates and springs. Schroeder's 1962 paper on "natural sounding artificial reverberation" introduced the electronic alternative, a network of recirculating delays and all-pass filters whose output decays like a room's; it is the ancestor of many later algorithmic reverberators.[^schroeder1962] The other modern approach is convolution: record a real hall's impulse response once, then [[Convolution|convolve]] any dry recording with it to place the performance in that hall, a standard technique of [[Digital_signal_processing|digital signal processing]].[^thinkdsp10] ## Minnesota *This section is specific to Wikitube.* Minneapolis has two concert rooms that sit at opposite ends of Sabine's equation, both central to [[Minnesota]]'s concert life. Northrop Memorial Auditorium at the University of Minnesota opened on October 22, 1929, with 4,700 seats.[^arup2014] A 2003 organ-restoration report described it as having "a very small volume-to-seat ratio (210 cubic-feet-per-seat) and a very low reverberation time of approximately .9 seconds," and noted that reflective shells and ceiling panels added from 1961 onward had "shaded the organ sound from the organist and the front section of seating."[^diapason2003] Sabine's equation explains the problem: when the audience is the main absorber, A grows with the number of seats, so T60 follows the volume per seat, and 210 ft³ (about 6 m³) per seat is small for a symphonic hall. The revitalization completed in 2014 rebuilt the interior as a 2,700-seat tiered theater; the acoustic consultant, Arup, described validating the room's shape and finishes by listening tests in its SoundLab and said in a company release that "the weak distant sound had become clear, intimate and enveloping."[^arup2014] Orchestra Hall, home of the Minnesota Orchestra, opened in October 1974 with acoustics by Cyril M. Harris.[^mo-building] Its shoebox auditorium, built largely of wood and plaster, is known for the white cubes that cover the ceiling and the back wall of the stage; the Orchestra's building page counts 114 of them, a 2024 Orchestra history 128.[^mo-building][^mo-at50] The cubes are diffusers rather than absorbers: they scatter each reflection in many directions, so that the reverberant field is as even and diffuse as Sabine's assumptions require; Harris described the effect as sound arriving "at your ears at all angles. That's called perfect diffusion."[^mo-at50] The hall's 2014 renovation kept the original auditorium acoustics for orchestral performance.[^mo-building] ## See also - [[Room_acoustics]] - [[Architectural_acoustics]] - [[Sound_pressure]] (section 10) - [[Acoustic_resonance]] (section 14) - [[Soundproofing]] (section 18) - [[Noise_control]] (section 19) ## References [^thinkdsp10]: Downey, Allen B. (2014). *Think DSP: Digital Signal Processing in Python*, version 1.1.4. Green Tea Press. Chapter 10, "Signals and systems," §10.1 and §10.3 "Acoustic response," p. 117. Portal Book 058. https://greenteapress.com/wp/think-dsp/ [^schroeder1965]: Schroeder, M. R. (1965). "New method of measuring reverberation time." *Journal of the Acoustical Society of America* 37 (3): 409–412. DOI not re-checked for this article. [^iso3382]: International Organization for Standardization (2009). ISO 3382-1:2009, *Acoustics — Measurement of room acoustic parameters — Part 1: Performance spaces* (definitions of T20, T30 and early decay time). [^lindahall]: Linda Hall Library. "Wallace Clement Sabine." *Scientist of the Day*. https://www.lindahall.org/about/news/scientist-of-the-day/wallace-clement-sabine/ [^sabine1922]: Sabine, Wallace Clement (1922). *Collected Papers on Acoustics*. Cambridge, Mass.: Harvard University Press. Chapter 1, "Reverberation," first published in *The American Architect and The Engineering Record* (1900). https://archive.org/details/collectedpaperso00sabiuoft [^bso]: Boston Symphony Orchestra. "The History of Symphony Hall." https://www.bso.org/symphony-hall/about/history [^eyring1930]: Eyring, Carl F. (1930). "Reverberation time in 'dead' rooms." *Journal of the Acoustical Society of America* 1 (2A): 217–241. DOI not re-checked for this article. [^pack-alpha]: Portal acoustic pack, `acoustic.room.alpha500` (MICROSIM_GUIDE `libs/wt-acoustic.js`), with the sim spec `specs/acoustics/sims/Reverberation.json`; values are typical published 500 Hz coefficients, marked ILLUSTRATIVE in the spec. [^iso354]: International Organization for Standardization (2003). ISO 354:2003, *Acoustics — Measurement of sound absorption in a reverberation room*. [^schroeder1962]: Schroeder, M. R. (1962). "Natural sounding artificial reverberation." *Journal of the Audio Engineering Society* 10 (3): 219–223. https://www.aes.org/e-lib/online/browse.cfm?elib=849 [^arup2014]: Arup (June 17, 2014). "Arup Provides Acoustics, Audiovisual, and Theater Design Services for the Revitalized Northrop Memorial Auditorium." Company release, PR Newswire. https://www.prnewswire.com/news-releases/arup-provides-acoustics-audiovisual-and-theater-design-services-for-the-revitalized-northrop-memorial-auditorium-263543911.html [^diapason2003]: Hendrickson, Charles (June 9, 2003). "Northrop Auditorium, University of Minnesota, Aeolian-Skinner Restoration." *The Diapason*. https://www.thediapason.com/content/northrop-auditorium-university-minnesota-aeolian-skinner-restoration [^mo-building]: Minnesota Orchestra. "Our Building." https://www.minnesotaorchestra.org/about/our-building [^mo-at50]: Anthony, Michael (October 3, 2024). "Orchestra Hall at 50." Minnesota Orchestra. https://www.minnesotaorchestra.org/stories/orchestra-hall-at-50  **Microsim — three.js (Wikitube framework):** *Reverberation* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/acoustics/Reverberation.html" data-title="Reverberation"></div> *Built from `MICROSIM_GUIDE/specs/acoustics/sims/Reverberation.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/Reverberation) : [Wikitube](https://en.wikitube.io/wiki/Reverberation) --- *Repopulated 2026-08-05 · text transfer from legacy Signal-Processing lane · sim queued · 0 deletions.* *Skeleton pinned to revision 1362219149 (2026-09-11) · acoustics portal section 17 · dense body appended, 0 deletions.*