Acoustics

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Lindsay's Wheel of Acoustics, which shows fields within acoustics Lindsay's Wheel of Acoustics.svg
Lindsay's Wheel of Acoustics, which shows fields within acoustics

Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries.

Contents

Hearing is one of the most crucial means of survival in the animal world and speech is one of the most distinctive characteristics of human development and culture. Accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound and hearing as a key element of mating rituals or for marking territories. Art, craft, science and technology have provoked one another to advance the whole, as in many other fields of knowledge. Robert Bruce Lindsay's "Wheel of Acoustics" is a well accepted overview of the various fields in acoustics. [1]

History

Etymology

The word "acoustic" is derived from the Greek word ἀκουστικός (akoustikos), meaning "of or for hearing, ready to hear" [2] and that from ἀκουστός (akoustos), "heard, audible", [3] which in turn derives from the verb ἀκούω(akouo), "I hear". [4]

The Latin synonym is "sonic", after which the term sonics used to be a synonym for acoustics [5] and later a branch of acoustics. [5] Frequencies above and below the audible range are called "ultrasonic" and "infrasonic", respectively.

Early research in acoustics

The fundamental and the first 6 overtones of a vibrating string. The earliest records of the study of this phenomenon are attributed to the philosopher Pythagoras in the 6th century BC. Harmonic partials on strings.svg
The fundamental and the first 6 overtones of a vibrating string. The earliest records of the study of this phenomenon are attributed to the philosopher Pythagoras in the 6th century BC.

In the 6th century BC, the ancient Greek philosopher Pythagoras wanted to know why some combinations of musical sounds seemed more beautiful than others, and he found answers in terms of numerical ratios representing the harmonic overtone series on a string. He is reputed to have observed that when the lengths of vibrating strings are expressible as ratios of integers (e.g. 2 to 3, 3 to 4), the tones produced will be harmonious, and the smaller the integers the more harmonious the sounds. For example, a string of a certain length would sound particularly harmonious with a string of twice the length (other factors being equal). In modern parlance, if a string sounds the note C when plucked, a string twice as long will sound a C an octave lower. In one system of musical tuning, the tones in between are then given by 16:9 for D, 8:5 for E, 3:2 for F, 4:3 for G, 6:5 for A, and 16:15 for B, in ascending order. [6]

Aristotle (384–322 BC) understood that sound consisted of compressions and rarefactions of air which "falls upon and strikes the air which is next to it...", [7] [8] a very good expression of the nature of wave motion. On Things Heard , generally ascribed to Strato of Lampsacus, states that the pitch is related to the frequency of vibrations of the air and to the speed of sound. [9]

In about 20 BC, the Roman architect and engineer Vitruvius wrote a treatise on the acoustic properties of theaters including discussion of interference, echoes, and reverberation—the beginnings of architectural acoustics. [10] In Book V of his De architectura (The Ten Books of Architecture) Vitruvius describes sound as a wave comparable to a water wave extended to three dimensions, which, when interrupted by obstructions, would flow back and break up following waves. He described the ascending seats in ancient theaters as designed to prevent this deterioration of sound and also recommended bronze vessels (echea) of appropriate sizes be placed in theaters to resonate with the fourth, fifth and so on, up to the double octave, in order to resonate with the more desirable, harmonious notes. [11] [12] [13]

During the Islamic golden age, Abū Rayhān al-Bīrūnī (973–1048) is believed to have postulated that the speed of sound was much slower than the speed of light. [14] [15]

Principles of acoustics have been applied since ancient times: a Roman theatre in the city of Amman Amman Roman theatre.jpg
Principles of acoustics have been applied since ancient times: a Roman theatre in the city of Amman

The physical understanding of acoustical processes advanced rapidly during and after the Scientific Revolution. Mainly Galileo Galilei (1564–1642) but also Marin Mersenne (1588–1648), independently, discovered the complete laws of vibrating strings (completing what Pythagoras and Pythagoreans had started 2000 years earlier). Galileo wrote "Waves are produced by the vibrations of a sonorous body, which spread through the air, bringing to the tympanum of the ear a stimulus which the mind interprets as sound", a remarkable statement that points to the beginnings of physiological and psychological acoustics. Experimental measurements of the speed of sound in air were carried out successfully between 1630 and 1680 by a number of investigators, prominently Mersenne. Meanwhile, Newton (1642–1727) derived the relationship for wave velocity in solids, a cornerstone of physical acoustics (Principia, 1687).

Age of Enlightenment and onward

Substantial progress in acoustics, resting on firmer mathematical and physical concepts, was made during the eighteenth century by Euler (1707–1783), Lagrange (1736–1813), and d'Alembert (1717–1783). During this era, continuum physics, or field theory, began to receive a definite mathematical structure. The wave equation emerged in a number of contexts, including the propagation of sound in air. [16]

In the nineteenth century the major figures of mathematical acoustics were Helmholtz in Germany, who consolidated the field of physiological acoustics, and Lord Rayleigh in England, who combined the previous knowledge with his own copious contributions to the field in his monumental work The Theory of Sound (1877). Also in the 19th century, Wheatstone, Ohm, and Henry developed the analogy between electricity and acoustics.

The twentieth century saw a burgeoning of technological applications of the large body of scientific knowledge that was by then in place. The first such application was Sabine's groundbreaking work in architectural acoustics, and many others followed. Underwater acoustics was used for detecting submarines in the first World War. Sound recording and the telephone played important roles in a global transformation of society. Sound measurement and analysis reached new levels of accuracy and sophistication through the use of electronics and computing. The ultrasonic frequency range enabled wholly new kinds of application in medicine and industry. New kinds of transducers (generators and receivers of acoustic energy) were invented and put to use.

Definition

Jay Pritzker Pavilion
20070919 Pritzker Pavilion from stage.JPG
20070919 Pritzker Pavilion speakers.JPG
At Jay Pritzker Pavilion, a LARES system is combined with a zoned sound reinforcement system, both suspended on an overhead steel trellis, to synthesize an indoor acoustic environment outdoors.

Acoustics is defined by ANSI/ASA S1.1-2013 as "(a) Science of sound, including its production, transmission, and effects, including biological and psychological effects. (b) Those qualities of a room that, together, determine its character with respect to auditory effects."

The study of acoustics revolves around the generation, propagation and reception of mechanical waves and vibrations.

Cause-effect diagram for acoustics.svg

The steps shown in the above diagram can be found in any acoustical event or process. There are many kinds of cause, both natural and volitional. There are many kinds of transduction process that convert energy from some other form into sonic energy, producing a sound wave. There is one fundamental equation that describes sound wave propagation, the acoustic wave equation, but the phenomena that emerge from it are varied and often complex. The wave carries energy throughout the propagating medium. Eventually this energy is transduced again into other forms, in ways that again may be natural and/or volitionally contrived. The final effect may be purely physical or it may reach far into the biological or volitional domains. The five basic steps are found equally well whether we are talking about an earthquake, a submarine using sonar to locate its foe, or a band playing in a rock concert.

The central stage in the acoustical process is wave propagation. This falls within the domain of physical acoustics. In fluids, sound propagates primarily as a pressure wave. In solids, mechanical waves can take many forms including longitudinal waves, transverse waves and surface waves.

Acoustics looks first at the pressure levels and frequencies in the sound wave and how the wave interacts with the environment. This interaction can be described as either a diffraction, interference or a reflection or a mix of the three. If several media are present, a refraction can also occur. Transduction processes are also of special importance to acoustics.

Fundamental concepts

Wave propagation: pressure levels

Spectrogram of a young girl saying "oh, no" Oh No Girl Spectrogram 2.jpg
Spectrogram of a young girl saying "oh, no"

In fluids such as air and water, sound waves propagate as disturbances in the ambient pressure level. While this disturbance is usually small, it is still noticeable to the human ear. The smallest sound that a person can hear, known as the threshold of hearing, is nine orders of magnitude smaller than the ambient pressure. The loudness of these disturbances is related to the sound pressure level (SPL) which is measured on a logarithmic scale in decibels.

Wave propagation: frequency

Physicists and acoustic engineers tend to discuss sound pressure levels in terms of frequencies, partly because this is how our ears interpret sound. What we experience as "higher pitched" or "lower pitched" sounds are pressure vibrations having a higher or lower number of cycles per second. In a common technique of acoustic measurement, acoustic signals are sampled in time, and then presented in more meaningful forms such as octave bands or time frequency plots. Both of these popular methods are used to analyze sound and better understand the acoustic phenomenon.

The entire spectrum can be divided into three sections: audio, ultrasonic, and infrasonic. The audio range falls between 20 Hz and 20,000 Hz. This range is important because its frequencies can be detected by the human ear. This range has a number of applications, including speech communication and music. The ultrasonic range refers to the very high frequencies: 20,000 Hz and higher. This range has shorter wavelengths which allow better resolution in imaging technologies. Medical applications such as ultrasonography and elastography rely on the ultrasonic frequency range. On the other end of the spectrum, the lowest frequencies are known as the infrasonic range. These frequencies can be used to study geological phenomena such as earthquakes.

Analytic instruments such as the spectrum analyzer facilitate visualization and measurement of acoustic signals and their properties. The spectrogram produced by such an instrument is a graphical display of the time varying pressure level and frequency profiles which give a specific acoustic signal its defining character.

Transduction in acoustics

An inexpensive low fidelity 3.5 inch driver, typically found in small radios 3.5 Inch Speaker.jpg
An inexpensive low fidelity 3.5 inch driver, typically found in small radios

A transducer is a device for converting one form of energy into another. In an electroacoustic context, this means converting sound energy into electrical energy (or vice versa). Electroacoustic transducers include loudspeakers, microphones, particle velocity sensors, hydrophones and sonar projectors. These devices convert a sound wave to or from an electric signal. The most widely used transduction principles are electromagnetism, electrostatics and piezoelectricity.

The transducers in most common loudspeakers (e.g. woofers and tweeters), are electromagnetic devices that generate waves using a suspended diaphragm driven by an electromagnetic voice coil, sending off pressure waves. Electret microphones and condenser microphones employ electrostatics—as the sound wave strikes the microphone's diaphragm, it moves and induces a voltage change. The ultrasonic systems used in medical ultrasonography employ piezoelectric transducers. These are made from special ceramics in which mechanical vibrations and electrical fields are interlinked through a property of the material itself.

Acoustician

An acoustician is an expert in the science of sound. [17]

Education

There are many types of acoustician, but they usually have a Bachelor's degree or higher qualification. Some possess a degree in acoustics, while others enter the discipline via studies in fields such as physics or engineering. Much work in acoustics requires a good grounding in Mathematics and science. Many acoustic scientists work in research and development. Some conduct basic research to advance our knowledge of the perception (e.g. hearing, psychoacoustics or neurophysiology) of speech, music and noise. Other acoustic scientists advance understanding of how sound is affected as it moves through environments, e.g. underwater acoustics, architectural acoustics or structural acoustics. Other areas of work are listed under subdisciplines below. Acoustic scientists work in government, university and private industry laboratories. Many go on to work in Acoustical Engineering. Some positions, such as Faculty (academic staff) require a Doctor of Philosophy.

Subdisciplines

Archaeoacoustics

St. Michael's Cave Gibraltar 2015 10 19 1964 (24110677143).jpg
St. Michael's Cave

Archaeoacoustics, also known as the archaeology of sound, is one of the only ways to experience the past with senses other than our eyes. [18] Archaeoacoustics is studied by testing the acoustic properties of prehistoric sites, including caves. Iegor Rezkinoff, a sound archaeologist, studies the acoustic properties of caves through natural sounds like humming and whistling. [19] Archaeological theories of acoustics are focused around ritualistic purposes as well as a way of echolocation in the caves. In archaeology, acoustic sounds and rituals directly correlate as specific sounds were meant to bring ritual participants closer to a spiritual awakening. [18] Parallels can also be drawn between cave wall paintings and the acoustic properties of the cave; they are both dynamic. [19] Because archaeoacoustics is a fairly new archaeological subject, acoustic sound is still being tested in these prehistoric sites today.

Aeroacoustics

Aeroacoustics is the study of noise generated by air movement, for instance via turbulence, and the movement of sound through the fluid air. This knowledge was applied in the 1920s and '30s to detect aircraft before radar was invented and is applied in acoustical engineering to study how to quieten aircraft. Aeroacoustics is important for understanding how wind musical instruments work. [20]

Acoustic signal processing

Acoustic signal processing is the electronic manipulation of acoustic signals. Applications include: active noise control; design for hearing aids or cochlear implants; echo cancellation; music information retrieval, and perceptual coding (e.g. MP3 or Opus). [21]

Architectural acoustics

Symphony Hall, Boston, where auditorium acoustics began Symphony hall boston.jpg
Symphony Hall, Boston, where auditorium acoustics began

Architectural acoustics (also known as building acoustics) involves the scientific understanding of how to achieve good sound within a building. [22] It typically involves the study of speech intelligibility, speech privacy, music quality, and vibration reduction in the built environment. [23] Commonly studied environments are hospitals, classrooms, dwellings, performance venues, recording and broadcasting studios. Focus considerations include room acoustics, airborne and impact transmission in building structures, airborne and structure-borne noise control, noise control of building systems and electroacoustic systems. [24]

Bioacoustics

Bioacoustics is the scientific study of the hearing and calls of animal calls, as well as how animals are affected by the acoustic and sounds of their habitat. [25]

Electroacoustics

This subdiscipline is concerned with the recording, manipulation and reproduction of audio using electronics. [26] This might include products such as mobile phones, large scale public address systems or virtual reality systems in research laboratories.

Environmental noise and soundscapes

Environmental acoustics is concerned with noise and vibration caused by railways, [27] road traffic, aircraft, industrial equipment and recreational activities. [28] The main aim of these studies is to reduce levels of environmental noise and vibration. Research work now also has a focus on the positive use of sound in urban environments: soundscapes and tranquility. [29]

Musical acoustics

The primary auditory cortex, one of the main areas associated with superior pitch resolution Brodmann 41 42.png
The primary auditory cortex, one of the main areas associated with superior pitch resolution

Musical acoustics is the study of the physics of acoustic instruments; the audio signal processing used in electronic music; the computer analysis of music and composition, and the perception and cognitive neuroscience of music. [30]

Noise

The goal this acoustics sub-discipline is to reduce the impact of unwanted sound. Scope of noise studies includes the generation, propagation, and impact on structures, objects, and people.

Noise research investigates the impact of noise on humans and animals to include work in definitions, abatement, transportation noise, hearing protection, Jet and rocket noise, building system noise and vibration, atmospheric sound propagation, soundscapes, and low-frequency sound.

Psychoacoustics

Many studies have been conducted to identify the relationship between acoustics and cognition, or more commonly known as psychoacoustics, in which what one hears is a combination of perception and biological aspects. [31] The information intercepted by the passage of sound waves through the ear is understood and interpreted through the brain, emphasizing the connection between the mind and acoustics. Psychological changes have been seen as brain waves slow down or speed up as a result of varying auditory stimulus which can in turn affect the way one thinks, feels, or even behaves. [32] This correlation can be viewed in normal, everyday situations in which listening to an upbeat or uptempo song can cause one's foot to start tapping or a slower song can leave one feeling calm and serene. In a deeper biological look at the phenomenon of psychoacoustics, it was discovered that the central nervous system is activated by basic acoustical characteristics of music. [33] By observing how the central nervous system, which includes the brain and spine, is influenced by acoustics, the pathway in which acoustic affects the mind, and essentially the body, is evident. [33]

Speech

Acousticians study the production, processing and perception of speech. Speech recognition and Speech synthesis are two important areas of speech processing using computers. The subject also overlaps with the disciplines of physics, physiology, psychology, and linguistics. [34]

Structural Vibration and Dynamics

Structural acoustics is the study of motions and interactions of mechanical systems with their environments and the methods of their measurement, analysis, and control. There are several sub-disciplines found within this regime:

Applications might include: ground vibrations from railways; vibration isolation to reduce vibration in operating theatres; studying how vibration can damage health (vibration white finger); vibration control to protect a building from earthquakes, or measuring how structure-borne sound moves through buildings. [35]

Ultrasonics

Ultrasound image of a fetus in the womb, viewed at 12 weeks of pregnancy (bidimensional-scan) CRL Crown rump lengh 12 weeks ecografia Dr. Wolfgang Moroder.jpg
Ultrasound image of a fetus in the womb, viewed at 12 weeks of pregnancy (bidimensional-scan)

Ultrasonics deals with sounds at frequencies too high to be heard by humans. Specialisms include medical ultrasonics (including medical ultrasonography), sonochemistry, ultrasonic testing, material characterisation and underwater acoustics (sonar). [36]

Underwater acoustics

Underwater acoustics is the scientific study of natural and man-made sounds underwater. Applications include sonar to locate submarines, underwater communication by whales, climate change monitoring by measuring sea temperatures acoustically, sonic weapons, [37] and marine bioacoustics. [38]

Research

Professional societies

Academic journals

Conferences

See also

Related Research Articles

<span class="mw-page-title-main">Sonar</span> Acoustic sensing method

Sonar is a technique that uses sound propagation to navigate, measure distances (ranging), communicate with or detect objects on or under the surface of the water, such as other vessels.

Ultrasound is sound with frequencies greater than 20 kilohertz. This frequency is the approximate upper audible limit of human hearing in healthy young adults. The physical principles of acoustic waves apply to any frequency range, including ultrasound. Ultrasonic devices operate with frequencies from 20 kHz up to several gigahertz.

<span class="mw-page-title-main">Acoustical engineering</span> Branch of engineering dealing with sound and vibration

Acoustical engineering is the branch of engineering dealing with sound and vibration. It includes the application of acoustics, the science of sound and vibration, in technology. Acoustical engineers are typically concerned with the design, analysis and control of sound.

Computational aeroacoustics is a branch of aeroacoustics that aims to analyze the generation of noise by turbulent flows through numerical methods.

Acoustic waves are a type of energy propagation that travels through a medium, such as air, water, or solid objects, by means of adiabatic compression and expansion. Key quantities describing these waves include acoustic pressure, particle velocity, particle displacement, and acoustic intensity. The speed of acoustic waves depends on the medium's properties, such as density and elasticity, with sound traveling at approximately 343 meters per second in air, 1480 meters per second in water, and varying speeds in solids. Examples of acoustic waves include audible sound from speakers, seismic waves causing ground vibrations, and ultrasound used for medical imaging. Understanding acoustic waves is crucial in fields like acoustics, physics, engineering, and medicine, with applications in sound design, noise reduction, and diagnostic imaging.

Sound from ultrasound is the name given here to the generation of audible sound from modulated ultrasound without using an active receiver. This happens when the modulated ultrasound passes through a nonlinear medium which acts, intentionally or unintentionally, as a demodulator.

A parametric array, in the field of acoustics, is a nonlinear transduction mechanism that generates narrow, nearly side lobe-free beams of low frequency sound, through the mixing and interaction of high frequency sound waves, effectively overcoming the diffraction limit associated with linear acoustics. The main side lobe-free beam of low frequency sound is created as a result of nonlinear mixing of two high frequency sound beams at their difference frequency. Parametric arrays can be formed in water, air, and earth materials/rock.

<span class="mw-page-title-main">Underwater acoustics</span> Study of the propagation of sound in water

Underwater acoustics is the study of the propagation of sound in water and the interaction of the mechanical waves that constitute sound with the water, its contents and its boundaries. The water may be in the ocean, a lake, a river or a tank. Typical frequencies associated with underwater acoustics are between 10 Hz and 1 MHz. The propagation of sound in the ocean at frequencies lower than 10 Hz is usually not possible without penetrating deep into the seabed, whereas frequencies above 1 MHz are rarely used because they are absorbed very quickly.

<span class="mw-page-title-main">Ultrasonic transducer</span> Acoustic sensor

Ultrasonic transducers and ultrasonic sensors are devices that generate or sense ultrasound energy. They can be divided into three broad categories: transmitters, receivers and transceivers. Transmitters convert electrical signals into ultrasound, receivers convert ultrasound into electrical signals, and transceivers can both transmit and receive ultrasound.

The ASA Silver Medal is an award presented by the Acoustical Society of America to individuals, without age limitation, for contributions to the advancement of science, engineering, or human welfare through the application of acoustic principles or through research accomplishments in acoustics. The medal is awarded in a number of categories depending on the technical committee responsible for making the nomination.

The following outline is provided as an overview of and topical guide to acoustics:

<span class="mw-page-title-main">Sound</span> Vibration that travels via pressure waves in matter

In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the reception of such waves and their perception by the brain. Only acoustic waves that have frequencies lying between about 20 Hz and 20 kHz, the audio frequency range, elicit an auditory percept in humans. In air at atmospheric pressure, these represent sound waves with wavelengths of 17 meters (56 ft) to 1.7 centimeters (0.67 in). Sound waves above 20 kHz are known as ultrasound and are not audible to humans. Sound waves below 20 Hz are known as infrasound. Different animal species have varying hearing ranges.

Acoustic resonance spectroscopy (ARS) is a method of spectroscopy in the acoustic region, primarily the sonic and ultrasonic regions. ARS is typically much more rapid than HPLC and NIR. It is non destructive and requires no sample preparation as the sampling waveguide can simply be pushed into a sample powder/liquid or in contact with a solid sample.

Psychoacoustics is the branch of psychophysics involving the scientific study of the perception of sound by the human auditory system. It is the branch of science studying the psychological responses associated with sound including noise, speech, and music. Psychoacoustics is an interdisciplinary field including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science.

Structural acoustics is the study of the mechanical waves in structures and how they interact with and radiate into adjacent media. The field of structural acoustics is often referred to as vibroacoustics in Europe and Asia. People that work in the field of structural acoustics are known as structural acousticians. The field of structural acoustics can be closely related to a number of other fields of acoustics including noise, transduction, underwater acoustics, and physical acoustics.

ANSI/ASA S1.1-2013, published by the American National Standards Institute (ANSI), is the current American National Standard on Acoustical Terminology. ANSI S1.1 was first published in 1960 and has its roots in a 1942 standard published by the American Standards Association, the predecessor of ANSI. It includes the following sections

  1. Scope
  2. General
  3. Levels
  4. Oscillation, vibration, and shock
  5. Transmission and propagation
  6. Transducers and linear systems
  7. Acoustical apparatus and instruments
  8. Underwater acoustics
  9. Sonics and ultrasonic testing
  10. Architectural acoustics
  11. Physiological and psychological acoustics
  12. Musical acoustics
<span class="mw-page-title-main">Gordon Eugene Martin</span> American physicist (born 1925)

Gordon Eugene Martin is an American physicist and author in the field of piezoelectric materials for underwater sound transducers. He wrote early computer software automating iterative evaluation of direct computer models through a Jacobian matrix of complex numbers. His software enabled the Navy Electronics Laboratory (NEL) to accelerate design of sonar arrays for tracking Soviet Navy submarines during the Cold War.

Ultrasonic antifouling is a technology that uses high frequency sound (ultrasound) to prevent or reduce biofouling on underwater structures, surfaces, and medium. Ultrasound is just high frequency sound. Ultrasound has the same physical properties as human-audible sound. The method has two primary forms: sub-cavitation intensity and cavitation intensity. Sub-cavitation methods create high frequency vibrations, whilst cavitation methods cause more destructive microscopic pressure changes. Both methods inhibit or prevent biofouling by algae and other single-celled organisms.

ACTRAN is a finite element-based computer aided engineering software modeling the acoustic behavior of mechanical systems and parts. Actran is being developed by Free Field Technologies, a Belgian software company founded in 1998 by Jean-Pierre Coyette and Jean-Louis Migeot. Free Field Technologies is a wholly owned subsidiary of the MSC Software Corporation since 2011. Free Field Technologies and MSC Software are part of Hexagon AB since 2017.

<span class="mw-page-title-main">Warren P. Mason</span> American electrical engineer

Warren Perry Mason was an American electrical engineer and physicist at Bell Labs. A graduate of Columbia University, he had a prolific output, publishing four books and nearly a hundred papers. He was issued over two hundred patents, more than anyone else at Bell Labs. His work included acoustics, filters, crystals and ceramics, materials science, polymer chemistry, ultrasonics, bonding to semiconductors, internal friction, and viscoelasticity.

References

  1. ↑ "What is acoustics?", Acoustical Research Group, Brigham Young University, archived from the original on 2021-04-16, retrieved 2021-04-16
  2. ↑ Akoustikos Archived 2020-01-23 at the Wayback Machine Henry George Liddell, Robert Scott, A Greek-English Lexicon, at Perseus
  3. ↑ Akoustos Archived 2020-01-23 at the Wayback Machine Henry George Liddell, Robert Scott, A Greek-English Lexicon, at Perseus
  4. ↑ Akouo Archived 2020-01-23 at the Wayback Machine Henry George Liddell, Robert Scott, A Greek-English Lexicon, at Perseus
  5. 1 2 Kenneth Neville Westerman (1947). Emergent Voice. C. F. Westerman. Archived from the original on 2023-03-01. Retrieved 2016-02-28.
  6. ↑ C. Boyer and U. Merzbach. A History of Mathematics. Wiley 1991, p. 55.
  7. ↑ "How Sound Propagates" (PDF). Princeton University Press. Archived (PDF) from the original on 2022-10-09. Retrieved 9 February 2016. (quoting from Aristotle's Treatise on Sound and Hearing)
  8. ↑ Whewell, William, 1794–1866. History of the inductive sciences : from the earliest to the present times. Volume 2. Cambridge. p. 295. ISBN   978-0-511-73434-2. OCLC   889953932.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)
  9. ↑ Greek musical writings. Barker, Andrew (1st pbk. ed.). Cambridge: Cambridge University Press. 2004. p. 98. ISBN   0-521-38911-9. OCLC   63122899.{{cite book}}: CS1 maint: others (link)
  10. ↑ ACOUSTICS, Bruce Lindsay, Dowden – Hutchingon Books Publishers, Chapter 3
  11. ↑ Vitruvius Pollio, Vitruvius, the Ten Books on Architecture (1914) Tr. Morris Hickey Morgan BookV, Sec.6–8
  12. ↑ Vitruvius article @Wikiquote
  13. ↑ Ernst Mach, Introduction to The Science of Mechanics: A Critical and Historical Account of its Development (1893, 1960) Tr. Thomas J. McCormack
  14. ↑ Sparavigna, Amelia Carolina (December 2013). "The Science of Al-Biruni" (PDF). International Journal of Sciences. 2 (12): 52–60. arXiv: 1312.7288 . Bibcode:2013arXiv1312.7288S. doi:10.18483/ijSci.364. S2CID   119230163. Archived (PDF) from the original on 2018-07-21. Retrieved 2018-11-04.
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  16. ↑ Pierce, Allan D. (1989). Acoustics : an introduction to its physical principles and applications (1989 ed.). Woodbury, N.Y.: Acoustical Society of America. ISBN   0-88318-612-8. OCLC   21197318.
  17. ↑ Schwarz, C (1991). Chambers concise dictionary.
  18. 1 2 Clemens, Martin J. (2016-01-31). "Archaeoacoustics: Listening to the Sounds of History". The Daily Grail. Archived from the original on 2019-04-13. Retrieved 2019-04-13.
  19. 1 2 Jacobs, Emma (2017-04-13). "With Archaeoacoustics, Researchers Listen for Clues to the Prehistoric Past". Atlas Obscura. Archived from the original on 2019-04-13. Retrieved 2019-04-13.
  20. ↑ da Silva, Andrey Ricardo (2009). Aeroacoustics of Wind Instruments: Investigations and Numerical Methods. VDM Verlag. ISBN   978-3639210644.
  21. ↑ Slaney, Malcolm; Patrick A. Naylor (2011). "Trends in Audio and Acoustic Signal Processing". ICASSP .
  22. ↑ Morfey, Christopher (2001). Dictionary of Acoustics. Academic Press. p. 32.
  23. ↑ Templeton, Duncan (1993). Acoustics in the Built Environment: Advice for the Design Team. Architectural Press. ISBN   978-0750605380.
  24. ↑
  25. ↑ "Bioacoustics - the International Journal of Animal Sound and its Recording". Taylor & Francis. Archived from the original on 5 September 2012. Retrieved 31 July 2012.
  26. ↑ Acoustical Society of America. "Acoustics and You (A Career in Acoustics?)". Archived from the original on 2015-09-04. Retrieved 21 May 2013.
  27. ↑ Krylov, V.V., ed. (2001). Noise and Vibration from High-speed Trains. Thomas Telford. ISBN   9780727729637.
  28. ↑ World Health Organisation (2011). Burden of disease from environmental noise (PDF). WHO. ISBN   978-92-890-0229-5. Archived (PDF) from the original on 2022-10-09.
  29. ↑ Kang, Jian (2006). Urban Sound Environment. CRC Press. ISBN   978-0415358576.
  30. ↑ Technical Committee on Musical Acoustics (TCMU) of the Acoustical Society of America (ASA). "ASA TCMU Home Page". Archived from the original on 2001-06-13. Retrieved 22 May 2013.
  31. ↑ Iakovides, Stefanos A.; Iliadou, Vassiliki TH; Bizeli, Vassiliki TH; Kaprinis, Stergios G.; Fountoulakis, Konstantinos N.; Kaprinis, George S. (2004-03-29). "Psychophysiology and psychoacoustics of music: Perception of complex sound in normal subjects and psychiatric patients". Annals of General Hospital Psychiatry. 3 (1): 6. doi: 10.1186/1475-2832-3-6 . ISSN   1475-2832. PMC   400748 . PMID   15050030.
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  33. 1 2 Green, David M. (1960). "Psychoacoustics and Detection Theory". The Journal of the Acoustical Society of America. 32 (10): 1189–1203. Bibcode:1960ASAJ...32.1189G. doi:10.1121/1.1907882. ISSN   0001-4966.
  34. ↑ "Technical Committee on Speech Communication". Acoustical Society of America. Archived from the original on 2018-11-05. Retrieved 2018-11-04.
  35. ↑ "Structural Acoustics & Vibration Technical Committee". Archived from the original on 10 August 2018.
  36. ↑ Ensminger, Dale (2012). Ultrasonics: Fundamentals, Technologies, and Applications. CRC Press. pp. 1–2.
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  38. ↑ ASA Underwater Acoustics Technical Committee. "Underwater Acoustics". Archived from the original on 30 July 2013. Retrieved 22 May 2013.

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