# Sound > On the **[[PORTAL_Acoustics|Acoustics]]** vibration spine · article face [[Acoustics]]. Microsim first, then the physics. ## Microsims — p5.js <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/CN9h2kEA0" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Sound — p5.js microsim"></iframe> </div> <div class="microsim-fallback"><em>Live p5.js microsim (desktop) · <a href="https://editor.p5js.org/sciencenibber/sketches/CN9h2kEA0">open / fork the sketch in the p5.js editor</a></em></div> **Sound (p5.js).** A horizontal column of 220 "air particles" oscillates longitudinally under s(x, t) = A sin(kx − ωt), making the sweeping bands of compression (red) and rarefaction (blue) that define a sound wave directly visible. Below the column, a green polyline draws the analytic acoustic-pressure profile P(x, t) in quadrature with displacement. A triggered oscilloscope tracks the actual audio [[Signal|signal]] coming out of `p5.FFT.waveform()` so the reader sees what they hear. Three sliders expose frequency f (40–2000 Hz), amplitude A, and a visualization-time multiplier; the canonical relation c = f·λ updates live in the bottom-right HUD. ## Overview **Sound** is a mechanical disturbance that propagates through an elastic medium — air, water, or solids — as a longitudinal pressure [[Wave|wave]]. Each particle of the medium oscillates back and forth along the direction of travel, producing alternating regions of compression (higher [[Density|density]] and pressure) and rarefaction (lower density and pressure). The disturbance moves outward at the medium's characteristic speed of sound: about **343 m/s** in air at 20 °C, **1,480 m/s** in water, and **5,100 m/s** in [[Steel|steel]]. The defining relationship for any periodic wave is **c = f · λ**, tying speed *c*, frequency *f* (in hertz), and wavelength *λ* (in metres). Frequency, perceived by listeners as pitch, ranges across the human hearing band of roughly 20 Hz to 20 kHz; amplitude corresponds to perceived loudness and is reported in decibels of sound pressure level. The physical theory descends from **Mersenne**, **Newton**, and **Helmholtz**, with modern treatments in Kinsler *et al.*'s *Fundamentals of Acoustics* and Pierce's *Acoustics*. Sound is foundational to music, speech, sonar, ultrasound imaging, room acoustics, and noise control, and is the parent topic for every other article in the Audio room. ## On the Acoustics spine Neighbours on the vibration spine: [[Wave]] · [[Oscillation]] · [[Vibration]] · [[Acoustic_wave]] · [[Mechanical_wave]] · [[Plane_wave]]. Bridge portal [[PORTAL_Acoustics]] · index [[PORTAL_INDEX]] · systems root [[PORTAL_Systems]]. ## Definition Sound has two meanings, and acoustics keeps both. The Acoustical Society of America's standard terminology defines sound first as a physical event, an oscillation in pressure, stress, particle displacement or particle velocity propagated through a medium with internal forces, and second as the auditory sensation that such an oscillation evokes.[^asa-sound] The first meaning covers vibrations far above and below what anyone can hear; the second covers only what reaches a listener. The OpenStax physics text draws the same line in one sentence: "Hearing is the perception of sound, just as seeing is the perception of visible light."[^up17-1] Physically, sound is a [[Mechanical_wave|mechanical wave]]. It needs matter to travel through, which is why sound cannot cross a vacuum, and it moves energy from place to place while the medium itself only [[Oscillation|oscillates]] about a fixed position. On the atomic scale the disturbance is far more ordered than the random thermal motion of the molecules carrying it; for a steady tone each parcel of air undergoes simple harmonic motion.[^up17-1] Everything in the portal follows from these two facts, from the [[Speed_of_sound|speed of sound]] to [[Sound_pressure|sound pressure]] and the [[Decibel|decibel]] scale. The framework microsim for this article, *Sound: a longitudinal wave in air*, shows the definition at work. A column of 2,400 air particles sways back and forth along a tube; where they crowd together the pressure is high and where they spread apart it is low, and the pressure curve drawn above the column is the same wave read as a number. White tracer particles show that no air travels down the tube: only the pattern does. ## Acoustics [[Acoustics]] is the science of sound in the broad, physical sense: the generation, propagation and reception of mechanical waves in gases, liquids and solids. Its foundations were laid in the 19th century. Hermann von Helmholtz's 1863 study of tone sensation joined the physics of vibrating bodies to the physiology of hearing,[^helmholtz1863] and Lord Rayleigh's two-volume *The Theory of Sound* (1877–1878) set out the mathematical theory of vibrating strings, bars, membranes, air columns and rooms that engineers still use.[^rayleigh1877] Modern acoustics is a family of specialties that share the [[Acoustic_wave_equation|acoustic wave equation]] and differ in their media and purposes. [[Architectural_acoustics|Architectural acoustics]] and [[Room_acoustics|room acoustics]] design halls and classrooms; [[Noise_control|noise control]] keeps unwanted sound out of homes and workplaces; [[Underwater_acoustics|underwater acoustics]] and [[Sonar|sonar]] use sound where light and radio cannot reach; [[Musical_acoustics|musical acoustics]] explains instruments and the voice; [[Psychoacoustics|psychoacoustics]] measures how listeners perceive sound; [[Bioacoustics|bioacoustics]] studies how animals make and use it; and [[Ultrasound|ultrasound]] turns frequencies too high to hear into medical images and industrial inspection. The thirty sections of the Wikitube Acoustics portal follow this map, from the [[Vibration|vibration]] of a single oscillator through waves, rooms and hearing to the trade applications. Across all of these, the working quantities are the same few: frequency, wavelength and speed; sound pressure and [[Particle_velocity|particle velocity]]; [[Sound_intensity|intensity]] and its level in decibels; and the [[Acoustic_impedance|acoustic impedance]] that decides how much sound crosses a boundary and how much is reflected. ## Physics ### Waves In air and in liquids, sound is a [[Longitudinal_wave|longitudinal wave]]: the molecules move back and forth along the direction the wave travels. Fluids resist compression but have almost no shear strength, so they cannot carry the side-to-side motion of a transverse wave. Solids can, and sound in a solid travels both as longitudinal and as transverse waves, as the [[P_wave|P waves]] and [[S_wave|S waves]] of an earthquake show.[^up17-1][^up17-2] A source such as a [[Loudspeaker|loudspeaker]] cone pushes on the air in front of it, compressing it, then pulls back, leaving a region of lower pressure. The alternating compressions and rarefactions move away at the speed of sound. The textbook models the wave two ways: as a displacement `s(x, t) = s_max cos(kx − ωt)` of the air from its rest position, and as a pressure change `ΔP(x, t) = ΔP_max sin(kx − ωt)`.[^up17-1] The two are a quarter cycle apart. Pressure is highest where the displacement passes through zero with neighboring molecules pushed toward each other, and the molecules at the center of a compression are momentarily at rest. The microsim draws both curves over the particle column. At its default of 340 Hz in air, the readout gives a speed of 343 m/s, a wavelength of 343 / 340 ≈ 1.01 m and a period of 2.94 ms. The motion is slowed hundreds of times and the displacement enormously exaggerated: at the level of ordinary conversation, a 1 kHz tone moves the air by roughly 10 nanometers. *Try: switch the medium from air to water and then to steel and watch the wavelength readout stretch from about 1 m to more than 4 m and then about 17 m at the same frequency; slide frequency from 100 Hz to 1,000 Hz and count the compressions crowding into the tube; change slow motion x to follow a single white tracer swaying about its home while the orange compressions march past it.* ### Speed The speed of sound depends on how stiff the medium is and how much inertia it has. In a fluid `c = √(K/ρ)`, the square root of the bulk modulus over the density; in a thin solid rod `c = √(Y/ρ)` with Young's modulus; in an ideal gas `c = √(γRT/M)`, with γ the adiabatic index, R the gas constant, T the absolute temperature and M the molar mass.[^up17-2] Measured values in the OpenStax table range from 331 m/s in air at 0 °C to 965 m/s in [[Helium|helium]], 1,480 m/s in fresh [[Water|water]] and 5,960 m/s in bulk [[Steel|steel]].[^up17-2] A thin steel rod, where only Young's modulus acts, carries sound at √(Y/ρ) ≈ 5,000–5,100 m/s, the figure quoted in the overview above. In air the speed rises with temperature, from 331 m/s at 0 °C to 343 m/s at 20 °C. The factor γ has a history. [[Isaac_Newton|Isaac Newton]] computed the speed of sound in the *Principia* of 1687 by assuming that air is compressed at constant temperature,[^newton1687] which amounts to setting γ = 1; the result, about 290 m/s at 20 °C, is some 15 percent below the measured value. Pierre-Simon Laplace resolved the gap in 1816 by pointing out that the compressions of a sound wave are too fast for heat to flow in or out, so they are adiabatic, and for air γ ≈ 1.4 raises the prediction to the observed 343 m/s.[^laplace1816] The [[Kinetic_theory_of_gases|kinetic theory of gases]] explains the same trend from the molecular side: sound in a gas is carried by molecules whose random speeds scale with √T. To a very good approximation, the speed of sound in open air does not depend on frequency. The textbook's example is a marching band heard from across a stadium: if high notes outran low ones, the music would arrive out of step.[^up17-2] ### Sound pressure level The pressure changes in a sound wave are tiny compared with atmospheric pressure, and the ear responds to a range of more than a million to one in pressure, so levels are expressed on a logarithmic scale. The [[Sound_pressure|sound pressure level]] is `L_p = 20 log10(p_rms / 20 µPa)` dB.[^iso1683] Twenty micropascals, near the threshold of hearing at 1 kHz, is 0 dB; 1 Pa is about 94 dB; normal conversation is around 60 dB and the threshold of pain about 120 dB.[^up17-3] Every factor of ten in intensity adds 10 dB, and doubling the intensity adds 3 dB.[^up17-3] The details, and a microsim that walks a listener away from a source, are in the sound pressure article. ## Perception [[Hearing]] turns a pressure wave into a small number of perceived qualities. Each has a physical correlate, but none is a simple copy of it, which is the subject of [[Psychoacoustics|psychoacoustics]]. ### Pitch [[Pitch_(music)|Pitch]] is the perception of frequency: short waves sound high, long waves low.[^bmt3-1] Listeners are extremely good at comparing pitches; the textbook reports that people can typically tell apart two tones differing by 0.3 percent, so 500.0 Hz and 501.5 Hz sound noticeably different.[^up17-3] Musicians name pitches rather than frequencies, and the one frequency most of them know is the tuning A at 440 Hz.[^bmt3-1] For a complex tone, the pitch heard is usually that of the [[Fundamental_frequency|fundamental]], even when the fundamental itself is [[Missing_fundamental|missing]] from the sound. ### Duration Duration is how long a sound lasts, and in music it is the length of a note, one of the few properties musicians notate exactly. The music theory text treats length as one of the three properties of a note, with pitch and loudness, that are separate from its timbre.[^bmt2-2] Very short sounds are heard differently from long ones: a click of a few milliseconds has no clear pitch, because the ear needs several cycles of a tone to establish one. ### Loudness [[Loudness]] is the perception of intensity, but frequency matters almost as much as level. At a given frequency a listener can discern differences of about 1 dB, and a 3 dB change is easily noticed; tones near the low and high ends of the audible range sound quieter than mid-range tones at the same level, because the ear is less sensitive there.[^up17-3] The [[Phon|phon]] expresses this: a sound of *n* phons is as loud as a 1 kHz tone at *n* dB. Harvey Fletcher and Wilden Munson of [[Bell_Labs|Bell Telephone Laboratories]] published the first widely used set of [[Equal-loudness_contour|equal-loudness contours]] in 1933,[^fletcher1933] and the current international set is ISO 226:2003.[^iso226] ### Timbre [[Timbre]] is everything that distinguishes two sounds of the same pitch, loudness and length, the quality that makes a flute sound unlike an oboe playing the same note. It arises because each note from an instrument contains many frequencies, for pitched instruments members of a [[Harmonic|harmonic]] series, and the ear hears the mixture not as separate tones but as the color of the sound. The attack at the start of a note carries a large share of it.[^bmt2-2] [[Fourier_analysis|Fourier analysis]] makes timbre measurable by splitting a waveform into its component frequencies and their strengths. ### Texture Texture describes how much is going on at once: whether a sound is one line or many, thick or thin, a single melody or a melody with accompaniment or several interwoven voices.[^bmt2-4] Outside music the same idea applies to sounds made of many small events, such as rain, applause or a crowded room, where the listener hears the statistics of the mixture rather than any single source. ### Spatial location Listeners locate sounds mainly by comparing the two ears. Lord Rayleigh's 1907 "duplex theory" identified the two main cues: at low frequencies, the difference in arrival time between the ears; at high frequencies, where the head casts an acoustic shadow, the difference in level.[^rayleigh1907] The time difference is small. For a sound directly to one side, the extra path around a typical adult head is on the order of 0.2 m, which at 343 m/s is roughly 0.6 ms. The outer ear's filtering, described by the [[Head-related_transfer_function|head-related transfer function]], adds the cues for elevation and front–back direction. [[Sound_localization|Sound localization]] has its own section on the portal. ## Frequency The frequency of a sound is the number of pressure cycles per second, in hertz, and it is set by the source. When sound passes from one medium into another, the frequency stays the same while the speed and the wavelength change.[^up17-2] Human hearing spans roughly 20 Hz to 20 kHz, although the upper limit falls with age.[^up17-1][^us1-6] In air at 20 °C that range covers wavelengths from about 17 m down to 17 mm, a thousandfold span that explains why a loudspeaker needs a large woofer for bass and a small tweeter for treble,[^up17-2] and why rooms, walls and barriers behave so differently at low and high pitch. ### Ultrasound Sound above about 20 kHz is [[Ultrasound|ultrasound]]. Bats emit ultrasonic clicks and locate insects by their echoes,[^up17-1] the basis of [[Animal_echolocation|animal echolocation]]. Medical imaging, or sonography, typically uses 3.5–20 MHz.[^us1-6] At 5 MHz in soft tissue, where sound travels at about 1,540 m/s,[^up17-2] the wavelength is about 0.31 mm, which sets the scale of the detail an image can resolve. Industry uses the same pulses for [[Ultrasonic_testing|ultrasonic testing]] of welds and coatings.[^up17-1] ### Infrasound Sound below about 20 Hz is [[Infrasound|infrasound]]. It is produced by earthquakes, volcanoes, thunderstorms and industrial machinery, and elephants, whales and alligators use it to communicate over long distances.[^us1-6] Its wavelengths are tens of meters to kilometers, so walls and air absorb it only weakly and it can travel very far. At 20 Hz a person may feel as much as hear it; well below that, strong infrasound is sensed as pressure or vibration rather than as tone. ## See also - [[Acoustic_wave]] - [[Particle_velocity]] - [[Wave]] - [[Acoustic_wave_equation]] - [[Speed_of_sound]] - [[Sound_pressure]] ## References [^asa-sound]: Acoustical Society of America (2013, reaffirmed 2020). *ANSI/ASA S1.1-2013 Acoustical Terminology*, entry "sound." ASA Standards term page: https://asastandards.org/terms/sound-2/ [^up17-1]: OpenStax (2016). *University Physics Volume 1*. Ling, S. J.; Sanny, J.; Moebs, W. Rice University. Chapter 17 "Sound," introduction and §17.1 "Sound Waves," Eq. 17.1–17.2, Fig. 17.1 and 17.3, pp. 807–810. https://openstax.org/details/books/university-physics-volume-1 (Portal Books 077). [^up17-2]: OpenStax (2016). *University Physics Volume 1*. §17.2 "Speed of Sound," Eq. 17.3–17.7, Table 17.1 "Speed of Sound in Various Media," Fig. 17.10, Example 17.1, pp. 810–818. Portal Books 077. [^up17-3]: OpenStax (2016). *University Physics Volume 1*. §17.3 "Sound Intensity," Table 17.2 and Table 17.3, subsection "Hearing and Pitch," pp. 818–826. Portal Books 077. [^helmholtz1863]: Helmholtz, Hermann von (1863). *Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik*. Braunschweig: Vieweg. English translation by A. J. Ellis, *On the Sensations of Tone* (1875). [^rayleigh1877]: Strutt, John William, Lord Rayleigh (1877–1878). *The Theory of Sound*, 2 vols. London: Macmillan. [^newton1687]: Newton, Isaac (1687). *Philosophiæ Naturalis Principia Mathematica*, Book II, Section VIII (propagation of motion through fluids; the speed of sound, Propositions 48–50). London: Royal Society. (Proposition numbers as recalled.) [^laplace1816]: Laplace, Pierre-Simon (1816). "Sur la vitesse du son dans l'air et dans l'eau." *Annales de chimie et de physique* 3: 238–241. (Volume and pages as recalled.) English translation "On the Speed of Sound in Air and Water": https://personal.lse.ac.uk/robert49/ebooks/philsciadventures/img/Laplace_VitesseEN.pdf [^iso1683]: International Organization for Standardization (2015). *ISO 1683:2015 Acoustics — Preferred reference values for acoustical and vibratory levels*. Geneva: ISO. https://www.iso.org/standard/64648.html [^bmt3-1]: Schmidt-Jones, Catherine; Jones, Russell (2013). *Understanding Basic Music Theory*. OpenStax CNX. §3.1.4 "Wavelength, Frequency, and Pitch," pp. 99–100. Portal Books 092. [^bmt2-2]: Schmidt-Jones, Catherine; Jones, Russell (2013). *Understanding Basic Music Theory*. §2.2 "Timbre," p. 72. Portal Books 092. [^bmt2-4]: Schmidt-Jones, Catherine; Jones, Russell (2013). *Understanding Basic Music Theory*. §2.4 "Texture," p. 80. Portal Books 092. [^fletcher1933]: Fletcher, Harvey; Munson, W. A. (1933). "Loudness, its definition, measurement and calculation." *Journal of the Acoustical Society of America* 5 (2): 82–108. https://pubs.aip.org/asa/jasa/article-abstract/5/2/82/651031/ [^iso226]: International Organization for Standardization (2003). *ISO 226:2003 Acoustics — Normal equal-loudness-level contours*. Geneva: ISO. (A revised edition, ISO 226:2023, has since been issued.) [^rayleigh1907]: Strutt, John William, Lord Rayleigh (1907). "On our perception of sound direction." *Philosophical Magazine* Series 6, 13 (74): 214–232. https://doi.org/10.1080/14786440709463595 [^us1-6]: *Ultrasound Physics and its Application in Medicine* (2024). Chapter 1 "Basic Principles of Ultrasound," §1.6 "Audible and Ultrasound Waves," pp. 6–7. Portal Books 091. <!-- ACOUSIM:BEGIN g22 — Acoustics portal microsim (framework build, specs/acoustics/sims/Sound.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Sound* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/acoustics/Sound.html" data-title="Sound"></div> *Built from `MICROSIM_GUIDE/specs/acoustics/sims/Sound.json`; part of the [[PORTAL_Acoustics|Acoustics portal]] spine (section sims and See-also variants).* <!-- ACOUSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Sound) : [Wikitube](https://en.wikitube.io/wiki/Sound) --- *Repopulated 2026-08-05 · microsim-first transfer from legacy GENERATIVE lane · p5 sciencenibber/CN9h2kEA0 · 0 deletions.* *Dense body appended 2026-09-11 (acoustics portal section 8, wt-article): skeleton pinned to revision [1371802017](https://en.wikipedia.org/w/index.php?oldid=1371802017) (2026-09-11).* <!-- hub tags: GENERATIVE; Centers_of_Excellence; PORTAL_Acoustics section 8 -->