Sound

Sound is defined as a phenomenon involving the propagation of pressure disturbances through an elastic material medium. From a physics perspective, it is characterized as a mechanical wave of pressure or associated quantities, such as displacement. Conversely, in physiological and psychological contexts, sound denotes the reception of these waves and their subsequent perception by the brain. While sensitivity to sound varies across organisms, the human auditory system typically detects frequencies between 20 Hz and 20 kHz. Significant applications of sound encompass music, medical imaging, spoken language, and various scientific disciplines.

Sound is a phenomenon in which pressure disturbances propagate through an elastic material medium. In the context of physics, it is characterised as a mechanical wave of pressure or related quantities (e.g. displacement), whereas in physiological-psychological contexts it refers to the reception of such waves and their perception by the brain. Though sensitivity to sound varies among all organisms, the human ear is sensitive to frequencies ranging from 20 Hz to 20 kHz. Examples of the significance and application of sound include music, medical imaging techniques, oral language and parts of science.

Definition

The American National Standard for Acoustical Terminology, ANSI/ASA S1.1-2013, provides the following technical definition of sound:

(a) Oscillations in pressure, stress, particle displacement, particle velocity, or similar quantities, propagated within a medium possessing internal forces (e.g., elastic or viscous), or the superposition of such propagated oscillations.

(b) The auditory sensation elicited by the oscillations detailed in (a).

This bipartite definition establishes sound as either a wave motion within an elastic medium, thereby functioning as a physical stimulus, or as an excitation of the auditory mechanism leading to the perception of sound, thus constituting a sensation.

Acoustics

Acoustics represents the interdisciplinary scientific investigation of mechanical waves, encompassing vibrations, sound, ultrasound, and infrasound, as they manifest in gaseous, liquid, or solid media. A scholar engaged in the field of acoustics is termed an acoustician, whereas a professional specializing in acoustical engineering is designated an acoustical engineer. In contrast, an audio engineer focuses on the processes of recording, manipulating, mixing, and reproducing sound.

Acoustics finds extensive application across numerous sectors of contemporary society. Its diverse subdisciplines comprise aeroacoustics, audio signal processing, architectural acoustics, bioacoustics, electroacoustics, environmental noise, musical acoustics, noise control, psychoacoustics, speech, ultrasound, underwater acoustics, and vibration studies.

Physics

Sound propagates as a mechanical wave through various media, including water, crystalline structures, and air. Sound waves originate from a source, such as the vibrating diaphragm of a loudspeaker. When the sound source vibrates, it generates mechanical disturbances that propagate outwards from the source at the local speed of sound, thereby forming a sound wave. At a constant distance from the source, the pressure, velocity, and displacement of the medium's constituent particles exhibit temporal variation. Concurrently, at any given instant, these properties—pressure, velocity, and displacement—demonstrate spatial variation. Crucially, the medium's particles do not traverse with the sound wave; rather, the disturbance and its associated mechanical energy are transmitted through the medium. While this principle is self-evident for solids, it equally applies to liquids and gases. During propagation, sound waves may undergo reflection, refraction, or attenuation by the medium.

The material facilitating sound transmission is termed the transmission medium. Media can encompass any state of matter, including solids, liquids, gases, and plasmas. Nevertheless, sound is unable to propagate through a vacuum due to the absence of a medium capable of supporting mechanical disturbances.

The propagation of sound in a medium is influenced primarily by:

• The intricate relationship between the medium's density and pressure. This correlation, which is also temperature-dependent, dictates the speed of sound within that medium.
• The intrinsic motion of the medium. Should the medium be in motion, this movement can either augment or diminish the absolute speed of the sound wave, contingent upon the direction of motion. For instance, sound propagating with the wind will experience an increase in its propagation speed equivalent to the wind's velocity, whereas propagation against the wind will result in a corresponding decrease.
• The viscosity of the medium. Medium viscosity governs the rate at which sound undergoes attenuation. In numerous media, such as air and water, viscous attenuation is considered negligible.

When sound traverses a medium characterized by non-uniform physical properties, it may undergo refraction, leading to either dispersion or focusing.

Theoretical investigations propose that sound waves could possess an exceedingly minute negative net mass, which would correlate with a weak repulsive gravitational field. This phenomenon arises because sound waves transiently decrease the local density of their propagation medium. The magnitude of this effect is negligible, as it relies on nonlinear adjustments to the wave motion equations.

Waves

In fluid media, such as gases, plasmas, and liquids, sound propagates as longitudinal waves, also known as compression waves. Conversely, within solid materials, sound can manifest as both longitudinal and transverse waves. Longitudinal sound waves are characterized by alternating pressure deviations from the equilibrium state, resulting in localized zones of compression and rarefaction. In contrast, transverse waves in solids involve alternating shear stress perpendicular to the propagation direction. A distinguishing feature of transverse sound waves, unlike their longitudinal counterparts, is their capacity for polarisation.

The visualization of sound waves can be achieved through the use of parabolic mirrors in conjunction with sound-generating objects.

The energy conveyed by a periodic sound wave oscillates between two forms: the potential energy associated with either the additional compression (for longitudinal waves) or the lateral displacement strain (for transverse waves) of the material, and the kinetic energy derived from the displacement velocity of particles within the medium.

Despite the multitude of physical processes involved in sound transmission, the signal detected at a specific point, such as a microphone or the human ear, can be comprehensively characterized as a time-varying pressure. This pressure-versus-time waveform offers a complete depiction of any acoustic or audio signal observed at that position.

For analytical purposes, sound waves are frequently idealized as sinusoidal plane waves, which are defined by the following fundamental characteristics:

• Frequency, or its reciprocal, the period.
• Wavelength, or its reciprocal, the wavenumber.
• Amplitude, encompassing sound pressure or intensity.
• Propagation speed of sound.
• Direction of propagation.

The speed and direction of sound are sometimes integrated into a single velocity vector, while the wavenumber and direction are similarly combined to form a wave vector.

For audio analysis, complex waveforms can be decomposed into a linear superposition of sinusoidal components, each possessing distinct frequencies, amplitudes, and phases.

Speed

The propagation speed of sound is contingent upon the medium through which the waves travel, constituting an intrinsic material property. Isaac Newton undertook the initial substantial endeavor to quantify the speed of sound. He posited that the speed of sound within a given substance could be calculated as the square root of the pressure exerted upon it, divided by its density:

${\displaystyle c={\sqrt {\frac {p}{\rho }}}.}$

This initial premise was subsequently disproven. The French mathematician Laplace rectified the formula by positing that sound propagation is an adiabatic, rather than an isothermal, process, contrary to Newton's earlier assumption. He incorporated an additional factor, gamma, into the equation, multiplying ${\displaystyle {\sqrt {\gamma }}}$ by ${\displaystyle {\sqrt {p/\rho }}}$. This led to the formulation of the equation ${\displaystyle c={\sqrt {\gamma \cdot p/\rho }}}$. Given that ${\displaystyle K=\gamma \cdot p}$, the ultimate expression became c = K / ρ<!-- ρ --> {\displaystyle c={\sqrt {K/\rho }}}, which is recognized as the Newton–Laplace equation. Within this equation, K represents the elastic bulk modulus, c denotes the velocity of sound, and ${\displaystyle \rho }$ signifies the density. Consequently, the speed of sound is directly proportional to the square root of the ratio between the medium's bulk modulus and its density.

The physical characteristics of a medium and the corresponding speed of sound are influenced by ambient environmental conditions. For instance, the velocity of sound in gaseous media is contingent upon temperature. At sea level in air at 20 °C (68 °F), the speed of sound is approximately 343 m/s (1,230 km/h; 767 mph), calculable using the formula v [m/s] = 331 + 0.6 T [°C]. Furthermore, the speed of sound exhibits a minor sensitivity to sound amplitude, attributable to a second-order anharmonic effect. This sensitivity implies the existence of non-linear propagation phenomena, including the generation of harmonics and mixed tones that were absent in the initial sound. When relativistic considerations become significant, the speed of sound is derived from the relativistic Euler equations.

In fresh water, the approximate speed of sound is 1,482 m/s (5,335 km/h; 3,315 mph). Within steel, sound propagates at approximately 5,960 m/s (21,460 km/h; 13,330 mph). Solid atomic hydrogen facilitates the fastest known sound propagation, reaching speeds of about 36,000 m/s (129,600 km/h; 80,530 mph).

Sound Pressure Level

Sound pressure refers to the instantaneous local deviation from the average ambient pressure within a specific medium, caused by a sound wave. The square of this pressure difference, representing the deviation from equilibrium pressure, is typically averaged across time and/or space. The square root of this average yields the root mean square (RMS) value. For instance, a 1 Pa RMS sound pressure (equivalent to 94 dBSPL) in atmospheric air indicates that the actual pressure within the sound wave fluctuates between (1 atm −<!-- − --> §1314§ {\displaystyle -{\sqrt {2}}} Pa) and (1 atm + §3536§ {\displaystyle +{\sqrt {2}}} Pa), specifically ranging from 101323.6 to 101326.4 Pa. Given the extensive range of amplitudes perceptible by the human ear, sound pressure is frequently quantified as a level on a logarithmic decibel scale. The sound pressure level (SPL), also denoted as L_p, is formally defined as

${\displaystyle L_{\mathrm {p} }=10\,\log _{10}\left({\frac {{p}^{2}}{{p_{\mathrm {ref} }}^{2}}}\right)=20\,\log _{10}\left({\frac {p}{p_{\mathrm {ref} }}}\right){\mbox{ dB}}\,}$

Here, p denotes the root-mean-square sound pressure, while ${\displaystyle p_{\mathrm {ref} }}$ signifies a reference sound pressure. Standard reference sound pressures, as defined by ANSI S1.1-1994, are typically 20 μPa for measurements in air and 1 μPa for those in water. It is crucial to note that a decibel value cannot accurately represent a sound pressure level without a clearly specified reference sound pressure.

Given the non-uniform spectral response of the human ear, sound pressures are frequently subjected to frequency weighting to ensure that measured levels more accurately correspond to perceived sound levels. The International Electrotechnical Commission (IEC) has established various weighting methodologies for this purpose. A-weighting, for instance, is designed to approximate the human ear's response to noise, with A-weighted sound pressure levels designated as dBA. Conversely, C-weighting is employed for the assessment of peak sound levels.

Perception

Beyond its physical definition, the term sound is also employed in physiology and psychology to denote the phenomenon of perception by the brain. The discipline of psychoacoustics specifically investigates these perceptual aspects. Webster's dictionary provides a dual definition: "1. The sensation of hearing, that which is heard; specif.: a. Psychophysics. Sensation due to stimulation of the auditory nerves and auditory centers of the brain, usually by vibrations transmitted in a material medium, commonly air, affecting the organ of hearing. b. Physics. Vibrational energy which occasions such a sensation. Sound is propagated by progressive longitudinal vibratory disturbances (sound waves)." Consequently, the answer to the classic philosophical question, "If a tree falls in a forest and no one is around to hear it, does it make a sound?" varies depending on whether one applies the physical or the psychophysical definition, yielding "yes" and "no" responses, respectively.

The auditory perception of sound in any hearing organism is constrained by a specific frequency range. Humans typically perceive sound as pitch within a frequency range of approximately 20 Hz to 20,000 Hz (20 kHz); this upper threshold diminishes with advancing age. Frequencies below 20 Hz are perceived either as discrete, stuttering auditory events (in the case of individual pulses) or as rapid, continuous 'wow-wow-wow' sensations (for sustained waveforms such as sine waves). The term sound occasionally denotes only those vibrations whose frequencies fall within the human auditory spectrum, or it may refer to the specific hearing capabilities of a particular animal species. Distinct auditory ranges characterize various other species; for instance, canines are capable of perceiving vibrations exceeding 20 kHz.

Serving as a crucial sensory input, sound is employed by numerous species for purposes such as hazard detection, spatial navigation, predatory activities, and interspecies communication. The Earth's atmosphere, its aquatic environments, and nearly all physical phenomena—including fire, precipitation, wind, ocean surf, and seismic events—each generate and are defined by distinctive acoustic signatures. Furthermore, numerous species, including amphibians (e.g., frogs), avian species, and both marine and terrestrial mammals, have evolved specialized anatomical structures for sound production. Within certain species, these organs facilitate the creation of complex vocalizations, such as song and speech. Moreover, human societies have cultivated cultural practices and technological advancements (e.g., music, telephony, radio) that enable the generation, recording, transmission, and dissemination of sound.

The term 'noise' frequently denotes an undesirable auditory stimulus. Within scientific and engineering disciplines, noise is defined as an extraneous element that interferes with or masks a desired signal. Nevertheless, in the context of auditory perception, noise can often serve as a cue for identifying the origin of a sound and constitutes a significant factor in the perception of timbre.

A soundscape refers to the segment of the acoustic environment that is discernible to human perception. Conversely, the acoustic environment encompasses the totality of all sounds, irrespective of human audibility, present within a specific locale, as influenced by its surroundings and interpreted by individuals within that broader environmental context.

Historically, the analysis of sound waves has been approached through six experimentally distinct perceptual dimensions. These dimensions include pitch, duration, loudness, timbre, sonic texture, and spatial location. Certain terms among these possess standardized definitions, as exemplified by the ANSI Acoustical Terminology ANSI/ASA S1.1-2013. Contemporary methodologies have additionally incorporated temporal envelope and temporal fine structure as significant parameters for perceptual analysis.

Pitch

Pitch is subjectively perceived as the 'lowness' or 'highness' of an auditory stimulus, reflecting the cyclic and repetitive characteristics of the underlying vibrations that constitute the sound. In the context of simple sounds, pitch correlates directly with the frequency of the slowest vibration, known as the fundamental harmonic. For complex sounds, however, pitch perception may exhibit variability. Individuals may occasionally assign disparate pitches to an identical sound, influenced by their unique experiential history with specific acoustic patterns. The determination of a specific pitch involves a pre-conscious analysis of vibrations, encompassing their frequencies and the interrelationship among them. Particular emphasis is placed on the identification of potential harmonics. Each sound is situated along a continuous spectrum of pitch, ranging from low to high.

For instance, white noise, characterized by its even distribution of random energy across all frequencies, is perceived as having a higher pitch compared to pink noise, which distributes random energy evenly across octaves, due to white noise's greater proportion of high-frequency components.

Duration

Duration is subjectively experienced as the 'length' or 'brevity' of an auditory event, correlating with the onset and offset signals generated by neural responses to acoustic stimuli. Typically, the perceived duration of a sound extends from its initial detection until its identification as having altered or terminated. Occasionally, this perceived duration does not directly correspond to the sound's objective physical duration. For instance, within a noisy environment, intermittent sounds (characterized by pauses and resumptions) may be perceived as continuous due to the obscuring of offset cues by interfering noises within the identical general bandwidth. This phenomenon can significantly aid in the comprehension of distorted communications, such as radio signals affected by interference, as the message is consequently perceived as uninterrupted.

Loudness

Loudness is subjectively experienced as the 'intensity' or 'softness' of an auditory stimulus, and it corresponds to the aggregate pattern of auditory-nerve activity elicited by that sound. Generally, sounds of higher intensity induce a more pronounced displacement of the basilar membrane, leading to increased stimulation of auditory-nerve fibers and, consequently, a more robust neural encoding of loudness.

Perceived loudness is also contingent upon the temporal distribution of sound energy. Brief sounds are perceived as softer than longer sounds of identical physical intensity because the auditory system does not fully integrate their energy. This phenomenon, termed temporal summation, occurs within an approximate 200-millisecond window. Exceeding this duration does not further augment the perceived loudness of the sound.

The spectral intricacy of a sound similarly affects loudness perception. Complex tones, which stimulate a wider array of auditory-nerve fibers, are frequently perceived as louder than simple tones, such as sine waves, even when their physical amplitudes are equivalent.

Timbre

Timbre is the perceptual attribute distinguishing different sounds, such as the impact of a falling rock, the operational hum of a drill, the tone of a musical instrument, or vocal characteristics. It signifies the pre-conscious assignment of a unique sonic identity to a sound, for instance, recognizing an "oboe." This identity is derived from various acoustic cues, including frequency transients, inherent noisiness, temporal instability, perceived pitch, and the distribution and intensity of overtones across an extended temporal duration. The temporal evolution of a sound primarily furnishes the data necessary for timbre identification. Despite the superficial similarity of brief waveform segments from different instruments, temporal variations in loudness and harmonic content clearly differentiate instruments like the clarinet and the piano. Subtler distinctions include characteristic noises, such as the air hiss of a clarinet or the hammer strikes of a piano.

Texture

Sonic texture pertains to the quantity of sound sources and their interrelationships. Within this domain, the term texture denotes the cognitive process of segregating distinct auditory objects. In musical contexts, texture frequently distinguishes between unison, polyphony, and homophony, but it can also describe complex auditory environments, such as the ambient soundscape of a bustling cafe, which might be characterized as cacophony.

Spatial Location

Spatial location refers to the cognitive assignment of a sound within its environmental context. This encompasses the sound's positioning on horizontal and vertical planes, its distance from the source, and the specific attributes of the acoustic environment. Within a dense sonic texture, the identification of multiple sound sources can be achieved through the combined application of spatial localization and timbre recognition.

Frequency

Ultrasound

Ultrasound comprises sound waves possessing frequencies exceeding 20,000 Hz. While physically indistinguishable from audible sound, ultrasound remains imperceptible to human hearing. Ultrasound devices typically function at frequencies ranging from 20 kHz to several gigahertz.

Medical ultrasound finds widespread application in both diagnostic procedures and therapeutic interventions.

Infrasound

Infrasound consists of sound waves with frequencies below 20 Hz. Although these low-frequency sounds are below the human threshold for pitch perception, they are often perceived as distinct pulses, akin to the "popping" sound of an idling motorcycle. Various animal species, including whales and elephants, can detect and utilize infrasound for communication. Furthermore, infrasound has applications in detecting volcanic eruptions and is incorporated into certain musical genres.

References

References

Mack, Eric (20 May 2019). "Stanford scientists created a sound so loud it instantly boils water". CNET.

• Eric Mack (20 May 2019). "Stanford scientists created a sound so loud it instantly boils water". CNET.Source: TORIma Academy Archive