Sound

• 1. Introduction

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  Sound cannot travel through a vacuum. In the emptiness of space, with no medium to carry a mechanical disturbance, even the loudest event would reach you in total silence. That single fact reveals something strange about what sound actually is. It is not a thing that flies through the air toward your ear. It is a pressure disturbance moving through an elastic material, leaving the matter itself behind. The human ear catches only a narrow slice of this phenomenon, from 20 Hz to 20 kHz, and even that upper limit shrinks as a person ages. So what is sound when no one is listening? Is it the wave in the air, or the sensation in the brain? Does it carry weight? How fast does it move, and why does it race faster through steel than through water? And how does a single time-varying pressure at your eardrum become a violin, a thud, or a voice you recognize in an instant?

• 2. Two Definitions, One Word

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  The American National Standard for Acoustical Terminology, ANSI/ASA S1.1-2013, splits sound into two parts. First, it is oscillation in pressure, stress, particle displacement, or particle velocity, propagated in a medium with internal forces such as elastic or viscous ones. Second, it is the auditory sensation that oscillation evokes. One half is a wave motion and a stimulus. The other half is an excitation of the hearing mechanism, a sensation. This is one of the few major standards organisations to define the concept explicitly. Physics and engineering texts often take a narrower path. They describe sound as a propagating mechanical disturbance, a wave, rather than as a vibration. In that framing it is a perturbation in pressure or particle motion that travels through a medium as compressions and rarefactions. The choice is made for conceptual clarity and scientific precision. Webster's dictionary keeps both senses alive at once, calling sound the sensation of hearing and the vibrational energy which occasions such a sensation. This double meaning is why the old puzzle about a tree falling in an empty forest yields different answers. Apply the physical definition and the answer is yes; apply the perceptual one and the answer turns on whether anyone was there to hear.

• 3. How A Disturbance Travels

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  A vibrating diaphragm of a loudspeaker pushes against the air around it, and a mechanical disturbance races away at the local speed of sound. The medium can be water, crystals, or air, any form of matter, whether solid, liquid, gas, or plasma. The particles of that medium do not travel with the wave. The disturbance and its mechanical energy move through the medium while the matter stays in place. This holds not only for solids, where it feels intuitive, but for liquids and gases too. Three factors govern how a sound propagates. The relationship between the density and pressure of the medium, itself affected by temperature, sets the speed. The motion of the medium matters as well. Sound carried by wind moving the same direction gains the wind's speed; sound and wind moving opposite each other lose it. The viscosity of the medium decides how quickly sound is attenuated, though for air and water that loss is negligible. There is a stranger result hiding in the theory. Sound waves carry an extremely small effective gravitational mass, arising from nonlinear corrections to the wave's stress-energy. They both respond to gravity and generate a very weak gravitational field of their own. For ordinary equations of state that effective mass is negative, as if the wave carried a tiny negative gravitational mass. The effect is minuscule because it appears only at nonlinear order in the governing equations.

• 4. Compression And Shear

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  Through fluids such as gases, plasmas, and liquids, sound moves only as longitudinal waves, also called compression waves. These are alternating pressure deviations from equilibrium, producing local regions of compression and rarefaction. Solids allow something more. Sound can travel through them as both longitudinal waves and transverse waves, where the transverse kind carries alternating shear stress perpendicular to the direction of travel. Unlike their longitudinal counterparts, transverse sound waves have the property of polarisation. Sound waves reflect, transmit, refract, diffract, absorb, and attenuate. Moving through a non-homogeneous medium, a wave may be refracted, either dispersed or focused. The energy in a periodic wave keeps swapping between potential energy, stored in compression for longitudinal waves or lateral displacement strain for transverse ones, and the kinetic energy of the particles' displacement velocity. Despite all this physical complexity, the signal arriving at a microphone or an ear reduces to one thing. It can be fully described as a time-varying pressure, a single waveform that completely represents any sound detected at that point. To analyse such a waveform, it can be broken into a linear combination of sinusoidal components, each with its own frequency, amplitude, and phase. The simplest model, the sinusoidal plane wave, is characterised by frequency, wavelength, amplitude, speed, and direction.

• 5. The Race Through Matter

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  Isaac Newton made the first significant effort to measure the speed of sound. He believed the speed in a substance equalled the square root of the pressure acting on it divided by its density. He was wrong on one key point. The French mathematician Laplace showed that sound travelling is not isothermal, as Newton thought, but adiabatic. Laplace added a factor, gamma, producing what became the Newton-Laplace equation, in which K is the elastic bulk modulus, c is the velocity of sound, and the speed comes out proportional to the square root of the ratio of bulk modulus to density. The numbers change with conditions. In 20 C air at sea level the speed of sound is approximately 343 m/s, following the formula v equals 331 plus 0.6 times the temperature in degrees Celsius. The speed is even slightly sensitive to amplitude through a second-order anharmonic effect, which produces harmonics and mixed tones not present in the original sound. Density rules the ranking. In fresh water sound travels at roughly 1482 m/s. In steel it reaches about 5960 m/s. The fastest known medium is solid atomic hydrogen, where sound moves at about 36000 m/s. Where relativistic effects matter, the speed is calculated from the relativistic Euler equations.

• 6. Measuring Loudness

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  At 1 Pa RMS sound pressure, equal to 94 dBSPL, the pressure in atmospheric air oscillates between 101323.6 and 101326.4 Pa. Sound pressure itself is the difference between average local pressure and the pressure in the wave, squared, averaged, and rooted to give a root mean square value. Because the human ear handles such a vast range of amplitudes, sound pressure is usually expressed on a logarithmic decibel scale as the sound pressure level. That level needs a reference. The standard ANSI S1.1-1994 sets commonly used references at 20 micropascals in air and 1 micropascal in water. Without a specified reference, a decibel value cannot represent a sound pressure level at all. The ear's response is not flat across frequencies, so measurements are often frequency weighted to match what people actually perceive. The International Electrotechnical Commission has defined several weighting schemes. A-weighting matches the ear's response to noise, and its levels are labelled dBA. C-weighting is used to measure peak levels.

• 7. From Wave To Sensation

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  In physiology and psychology, the word sound names the perceptual experience produced by acoustic stimulation, not the physics. Psychoacoustics and the broader field of psychophysics study how organisms detect and interpret these stimuli. Human sensitivity to pitch typically spans from about 20 Hz to 20 kHz, with the upper limit falling as people age. Below about 20 Hz, periodic stimuli are no longer heard as pitch but as discrete pulses or slow amplitude fluctuations. Other species draw the lines elsewhere; domestic dogs can detect frequencies above 20 kHz. Historically there are six experimentally separable ways to analyse sound waves: pitch, duration, loudness, timbre, sonic texture, and spatial location. Pitch tracks the cyclic, repetitive nature of vibration, tied for simple sounds to the fundamental harmonic. White noise, spread evenly across all frequencies, sounds higher in pitch than pink noise, spread evenly across octaves, because it holds more high-frequency content. Duration depends on onset and offset signals from nerve responses, which is why gapped sounds in a noisy environment can seem continuous when offset messages are missed. Loudness reflects the overall pattern of auditory-nerve activity, with louder sounds displacing the basilar membrane more. Brief sounds seem softer because the auditory system integrates energy only over a window of roughly 200 ms, a process called temporal summation. Timbre is the pre-conscious assignment of a sonic identity, the instant sense that it's an oboe, built from frequency transients, noisiness, and the way a sound changes over time. A clarinet hisses with air; a piano knocks with hammer strikes. Sonic texture concerns how many sound sources are present and how they interact, the cognitive separation of auditory objects. Spatial location places a sound on the horizontal and vertical plane and judges its distance, letting a listener pick out multiple sources in a thick texture.

• 8. Beyond Hearing

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  Whales, elephants, and other animals communicate using infrasound, the sound below 20 Hz that humans cannot hear as pitch and instead register as discrete pulses, like the popping of an idling motorcycle. Infrasound can detect volcanic eruptions and appears in some types of music. At the other end sits ultrasound, sound waves above 20,000 Hz, no different in physical properties from audible sound but beyond human hearing. Ultrasound devices run from 20 kHz up to several gigahertz, and medical ultrasound is commonly used for diagnostics and treatment. Across the full range, sound serves living things as a signal perceived by one of the major senses, used for detecting danger, navigation, predation, and communication. Fire, rain, wind, surf, and earthquakes each produce their own sounds, and frogs, birds, and marine and terrestrial mammals have evolved special organs to make them, some producing song and speech. Humans went further, building music, the telephone, and radio to generate, record, transmit, and broadcast sound. All of it is studied under acoustics, the interdisciplinary science of mechanical waves, vibrations, sound, ultrasound, and infrasound, whose subdisciplines reach from aeroacoustics and architectural acoustics to bioacoustics, underwater acoustics, and the study of the soundscape that humans actually perceive.