1.
Marburg
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Marburg is a university town in the German federal state of Hesse, capital of the Marburg-Biedenkopf district. The town area spreads along the valley of the river Lahn and has a population of approximately 72,000, having been awarded town privileges in 1222, Marburg served as capital of the landgraviate of Hessen-Marburg during periods of the fifteenth to seventeenth centuries. The University of Marburg was founded in 1527 and dominates the life in the town to this day. The settlement was protected and customs were raised by a castle built during the ninth or tenth century by the Giso. Marburg has been a town since 1140, as proven by coins, from the Gisos, it fell around that time to the Landgraves of Thuringia, residing on the Wartburg above Eisenach. In 1228, the widowed princess-landgravine of Thuringia, Elizabeth of Hungary, chose Marburg as her seat, as she did not get along well with her brother-in-law. The countess dedicated her life to the sick and would become after her death in 1231, aged 24. In 1264, St Elizabeths daughter Sophie of Brabant, succeeded in winning the Landgraviate of Hessen, hitherto connected to Thuringia, Marburg was one of the capitals of Hessen from that time until about 1540. Following the first division of the landgraviate, it was the capital of Hessen-Marburg from 1485 to 1500, Hessen was one of the more powerful second-tier principalities in Germany. Its old enemy was the Archbishopric of Mainz, one of the prince-electors, after 1605, Marburg became just another provincial town, known mostly for the University of Marburg. It became a backwater for two centuries after the Thirty Years War, when it was fought over by Hessen-Darmstadt and Hesse-Kassel. The Hessian territory around Marburg lost more than two-thirds of its population, Marburg is the seat of the oldest Protestant-founded university in the world, the University of Marburg, founded in 1527. It is one of the university towns in Germany, Greifswald, Erlangen, Jena, and Tübingen, as well as the city of Gießen. In 1529, Philipp I of Hesse arranged the Marburg Colloquy, to propitiate Martin Luther, when Romanticism became the dominant cultural and artistic paradigm in Germany, Marburg became interesting once again, and many of the leaders of the movement lived, taught, or studied in Marburg. They formed a circle of friends that was of importance, especially in literature, philology, folklore. Most famous internationally, however, were the Brothers Grimm, who collected many of their fairy tales here, the original building inspiring his drawing Rapunzels Tower stands in Amönau near Marburg. Across the Lahn hills, in the area called Schwalm, the costumes of little girls included a red hood, in the Austro-Prussian War of 1866, the Prince-elector of Hessen had backed Austria. Prussia won and took the opportunity to invade and annex the Electorate of Hessen north of the Main River, however, the pro-Austrian Hesse-Darmstadt remained independent
2.
Germany
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Germany, officially the Federal Republic of Germany, is a federal parliamentary republic in central-western Europe. It includes 16 constituent states, covers an area of 357,021 square kilometres, with about 82 million inhabitants, Germany is the most populous member state of the European Union. After the United States, it is the second most popular destination in the world. Germanys capital and largest metropolis is Berlin, while its largest conurbation is the Ruhr, other major cities include Hamburg, Munich, Cologne, Frankfurt, Stuttgart, Düsseldorf and Leipzig. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity, a region named Germania was documented before 100 AD. During the Migration Period the Germanic tribes expanded southward, beginning in the 10th century, German territories formed a central part of the Holy Roman Empire. During the 16th century, northern German regions became the centre of the Protestant Reformation, in 1871, Germany became a nation state when most of the German states unified into the Prussian-dominated German Empire. After World War I and the German Revolution of 1918–1919, the Empire was replaced by the parliamentary Weimar Republic, the establishment of the national socialist dictatorship in 1933 led to World War II and the Holocaust. After a period of Allied occupation, two German states were founded, the Federal Republic of Germany and the German Democratic Republic, in 1990, the country was reunified. In the 21st century, Germany is a power and has the worlds fourth-largest economy by nominal GDP. As a global leader in industrial and technological sectors, it is both the worlds third-largest exporter and importer of goods. Germany is a country with a very high standard of living sustained by a skilled. It upholds a social security and universal health system, environmental protection. Germany was a member of the European Economic Community in 1957. It is part of the Schengen Area, and became a co-founder of the Eurozone in 1999, Germany is a member of the United Nations, NATO, the G8, the G20, and the OECD. The national military expenditure is the 9th highest in the world, the English word Germany derives from the Latin Germania, which came into use after Julius Caesar adopted it for the peoples east of the Rhine. This in turn descends from Proto-Germanic *þiudiskaz popular, derived from *þeudō, descended from Proto-Indo-European *tewtéh₂- people, the discovery of the Mauer 1 mandible shows that ancient humans were present in Germany at least 600,000 years ago. The oldest complete hunting weapons found anywhere in the world were discovered in a mine in Schöningen where three 380, 000-year-old wooden javelins were unearthed
3.
Physicist
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A physicist is a scientist who has specialized knowledge in the field of physics, the exploration of the interactions of matter and energy across the physical universe. A physicist is a scientist who specializes or works in the field of physics, physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists can also apply their knowledge towards solving real-world problems or developing new technologies, some physicists specialize in sectors outside the science of physics itself, such as engineering. The study and practice of physics is based on a ladder of discoveries. Many mathematical and physical ideas used today found their earliest expression in ancient Greek culture and Asian culture, the bulk of physics education can be said to flow from the scientific revolution in Europe, starting with the work of Galileo and Kepler in the early 1600s. New knowledge in the early 21st century includes an increase in understanding physical cosmology. The term physicist was coined by William Whewell in his 1840 book The Philosophy of the Inductive Sciences, many physicist positions require an undergraduate degree in applied physics or a related science or a Masters degree like MSc, MPhil, MPhys or MSci. In a research oriented level, students tend to specialize in a particular field, Physics students also need training in mathematics, and also in computer science and programming. For being employed as a physicist a doctoral background may be required for certain positions, undergraduate students like BSc Mechanical Engineering, BSc Electrical and Computer Engineering, BSc Applied Physics. etc. With physics orientation are chosen as research assistants with faculty members, the highest honor awarded to physicists is the Nobel Prize in Physics, awarded since 1901 by the Royal Swedish Academy of Sciences. The three major employers of career physicists are academic institutions, laboratories, and private industries, with the largest employer being the last, physicists in academia or government labs tend to have titles such as Assistants, Professors, Sr. /Jr. As per the American Institute for Physics, some 20% of new physics Ph. D. s holds jobs in engineering development programs, while 14% turn to computer software, a majority of physicists employed apply their skills and training to interdisciplinary sectors. For industry or self-employment. and also in science and programming. Hence a majority of Physics bachelors degree holders are employed in the private sector, other fields are academia, government and military service, nonprofit entities, labs and teaching
4.
Professor
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Professor is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, professor derives from Latin as a person who professes being usually an expert in arts or sciences, in much of the world, the unqualified word professor is used formally to indicate the highest academic rank, informally known as full professor. Professors conduct original research and commonly teach undergraduate, graduate, or professional courses in their fields of expertise, in universities with graduate schools, professors may mentor and supervise graduate students conducting research for a thesis or dissertation. Professors typically hold a Ph. D. another doctorate or a different terminal degree, some professors hold a masters degree or a professional degree, such as an M. D. as their highest degree. The term professor was first used in the late 14th century to one who teaches a branch of knowledge. As a title that is prefixed to a name, it dates from 1706, the hort form prof is recorded from 1838. The term professor is used with a different meaning, ne professing religion. This canting use of the word comes down from the Elizabethan period, a professor is an accomplished and recognized academic. In most Commonwealth nations, as well as northern Europe, the professor is the highest academic rank at a university. In the United States and Canada, the title of professor is also the highest rank, in these areas, professors are scholars with doctorate degrees or equivalent qualifications who teach in four-year colleges and universities. An emeritus professor is a given to selected retired professors with whom the university wishes to continue to be associated due to their stature. Emeritus professors do not receive a salary, but they are often given office or lab space, and use of libraries, labs, the term professor is also used in the titles assistant professor and associate professor, which are not considered professor-level positions in some European countries. In Australia, the associate professor is used in place of reader, ranking above senior lecturer. However, such professors usually do not undertake academic work for the granting institution, in general, the title of professor is strictly used for academic positions rather than for those holding it on honorary basis. Other roles of professorial tasks depend on the institution, its legacy, protocols, place, a professor typically earns a base salary and a range of benefits. In addition, a professor who undertakes additional roles in her institution earns additional income, some professors also earn additional income by moonlighting in other jobs, such as consulting, publishing academic or popular press books, or giving speeches or coaching executives. Some fields give professors more opportunities for outside work, the anticipated average earnings with performance-related bonuses for a German professor is €71,500. The salaries of civil servant professors in Spain are fixed in a basis, but there are some bonus related to performance and seniority
5.
University of Marburg
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The Philipp University of Marburg, was founded in 1527 by Philip I, Landgrave of Hesse as one of Germanys oldest universities, dating back to a Protestant foundation. As a state university it no longer has any religious affiliation and it was the main university of the principality of Hesse and remains a public university of that state. It now has about 25,000 students and 7,500 employees, making Marburg, a town of 72,000 inhabitants, though most subjects are grouped, the University of Marburg is not a campus university in the broader sense. About 12% of the students are international, the highest percentage in Hesse and it offers an International summer university programme every summer and has an awarded ERASMUS programme. Marburg is home to one of Germanys most traditional medical faculties, the German physicians union is called Marburger Bund. In 1609, the University of Marburg established the worlds first professorship in chemistry, in 2012 it opened the first German participative chemistry museum, called Chemicum. Its experimental course programme is aimed at encouraging people to pursue careers in science. 20 professors were expelled in 1933, among them Wilhelm Röpke who emigrated, the university is most famous for its life sciences research, but is also home to one of the few centers that conduct research on the middle east, the CNMS. The departments of psychology and geography enjoy a reputation and reached Excellence Group status in the Europe-wide CHE Excellence Ranking 2009. According to the 2012 QS Ranking, the university ranked among the top 30 German universities, the ARWU ranking which is more focused on research, ranks the university around 200, with its life sciences and social sciences department in the 151-200 range worldwide. The strong research is illustrated by its participation in several SFBs. These collaborative research centres are financed by the German Science Foundation DFG and they encourage researchers to cross the boundaries of disciplines, institutes, departments and faculties within the participating university. It retained that strength, especially in Philosophy and Theology for a time after World War II. S. S. Eliot Wilhelm Viëtor Historical detention room
6.
Christian Ludwig Gerling
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He is notable for his work on geodetics and in 1927 some 60 letters of correspondence between Gerling and Gauss on the topic were published. He is also notable as the advisor of Julius Plücker. Gerling, whose father was also called Christian Ludwig Gerling and was a pastor at the St. Jacobi church, was born in Hamburg, in 1817, he became professor of mathematics at the University of Marburg. Schaeffer C, ed. Briefwechsel zwischen Carl Friedrich Gauss und Christian Ludwig Gerling
7.
Acoustics
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Acoustics is the interdisciplinary science that deals with the study of all 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 technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of society with the most obvious being the audio. Hearing is one of the most crucial means of survival in the animal world, 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, art, craft, science and technology have provoked one another to advance the whole, as in many other fields of knowledge. Robert Bruce Lindsays Wheel of Acoustics is a well accepted overview of the fields in acoustics. The word acoustic is derived from the Greek word ἀκουστικός, meaning of or for hearing, ready to hear and that from ἀκουστός, heard, audible, which in turn derives from the verb ἀκούω, I hear. The Latin synonym is sonic, after which the term used to be a synonym for acoustics. Frequencies above and below the range are called ultrasonic and infrasonic. If, for example, a string of a length would sound particularly harmonious with a string of twice the length. 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 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. Aristotle understood that sound consisted of compressions and rarefactions of air which falls upon, a very good expression of the nature of wave motion. The physical understanding of acoustical processes advanced rapidly during and after the Scientific Revolution, mainly Galileo Galilei but also Marin Mersenne, independently, discovered the complete laws of vibrating strings. 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 derived the relationship for wave velocity in solids, a cornerstone of physical acoustics. The eighteenth century saw advances in acoustics as mathematicians applied the new techniques of calculus to elaborate theories of sound wave propagation. 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, Underwater acoustics was used for detecting submarines in the first World War
8.
Fluid mechanics
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Fluid mechanics is a branch of physics concerned with the mechanics of fluids and the forces on them. Fluid mechanics has a range of applications, including for mechanical engineering, civil engineering, chemical engineering, geophysics, astrophysics. Fluid mechanics can be divided into fluid statics, the study of fluids at rest, and fluid dynamics, fluid mechanics, especially fluid dynamics, is an active field of research with many problems that are partly or wholly unsolved. Fluid mechanics can be complex, and can best be solved by numerical methods. A modern discipline, called computational fluid dynamics, is devoted to this approach to solving fluid mechanics problems, Particle image velocimetry, an experimental method for visualizing and analyzing fluid flow, also takes advantage of the highly visual nature of fluid flow. Inviscid flow was further analyzed by mathematicians and viscous flow was explored by a multitude of engineers including Jean Léonard Marie Poiseuille. Fluid statics or hydrostatics is the branch of mechanics that studies fluids at rest. It embraces the study of the conditions under which fluids are at rest in stable equilibrium, and is contrasted with fluid dynamics, hydrostatics is fundamental to hydraulics, the engineering of equipment for storing, transporting and using fluids. It is also relevant to some aspect of geophysics and astrophysics, to meteorology, to medicine, fluid dynamics is a subdiscipline of fluid mechanics that deals with fluid flow—the science of liquids and gases in motion. The solution to a fluid dynamics problem typically involves calculating various properties of the fluid, such as velocity, pressure, density and it has several subdisciplines itself, including aerodynamics and hydrodynamics. Some fluid-dynamical principles are used in engineering and crowd dynamics. Fluid mechanics is a subdiscipline of continuum mechanics, as illustrated in the following table, in a mechanical view, a fluid is a substance that does not support shear stress, that is why a fluid at rest has the shape of its containing vessel. A fluid at rest has no shear stress, the assumptions inherent to a fluid mechanical treatment of a physical system can be expressed in terms of mathematical equations. This can be expressed as an equation in integral form over the control volume, the continuum assumption is an idealization of continuum mechanics under which fluids can be treated as continuous, even though, on a microscopic scale, they are composed of molecules. Fluid properties can vary continuously from one element to another and are average values of the molecular properties. The continuum hypothesis can lead to results in applications like supersonic speed flows. Those problems for which the continuum hypothesis fails, can be solved using statistical mechanics, to determine whether or not the continuum hypothesis applies, the Knudsen number, defined as the ratio of the molecular mean free path to the characteristic length scale, is evaluated. Problems with Knudsen numbers below 0.1 can be evaluated using the continuum hypothesis, the Navier–Stokes equations are differential equations that describe the force balance at a given point within a fluid
9.
Meteorology
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Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not occur until the 18th century, the 19th century saw modest progress in the field after weather observation networks were formed across broad regions. Prior attempts at prediction of weather depended on historical data, Meteorological phenomena are observable weather events that are explained by the science of meteorology. Different spatial scales are used to describe and predict weather on local, regional, Meteorology, climatology, atmospheric physics, and atmospheric chemistry are sub-disciplines of the atmospheric sciences. Meteorology and hydrology compose the interdisciplinary field of hydrometeorology, the interactions between Earths atmosphere and its oceans are part of a coupled ocean-atmosphere system. Meteorology has application in diverse fields such as the military, energy production, transport, agriculture. The word meteorology is from Greek μετέωρος metéōros lofty, high and -λογία -logia -logy, varāhamihiras classical work Brihatsamhita, written about 500 AD, provides clear evidence that a deep knowledge of atmospheric processes existed even in those times. In 350 BC, Aristotle wrote Meteorology, Aristotle is considered the founder of meteorology. One of the most impressive achievements described in the Meteorology is the description of what is now known as the hydrologic cycle and they are all called swooping bolts because they swoop down upon the Earth. Lightning is sometimes smoky, and is then called smoldering lightning, sometimes it darts quickly along, at other times, it travels in crooked lines, and is called forked lightning. When it swoops down upon some object it is called swooping lightning, the Greek scientist Theophrastus compiled a book on weather forecasting, called the Book of Signs. The work of Theophrastus remained a dominant influence in the study of weather, in 25 AD, Pomponius Mela, a geographer for the Roman Empire, formalized the climatic zone system. According to Toufic Fahd, around the 9th century, Al-Dinawari wrote the Kitab al-Nabat, ptolemy wrote on the atmospheric refraction of light in the context of astronomical observations. St. Roger Bacon was the first to calculate the size of the rainbow. He stated that a rainbow summit can not appear higher than 42 degrees above the horizon, in the late 13th century and early 14th century, Kamāl al-Dīn al-Fārisī and Theodoric of Freiberg were the first to give the correct explanations for the primary rainbow phenomenon. Theoderic went further and also explained the secondary rainbow, in 1716, Edmund Halley suggested that aurorae are caused by magnetic effluvia moving along the Earths magnetic field lines. In 1441, King Sejongs son, Prince Munjong, invented the first standardized rain gauge and these were sent throughout the Joseon Dynasty of Korea as an official tool to assess land taxes based upon a farmers potential harvest. In 1450, Leone Battista Alberti developed a swinging-plate anemometer, and was known as the first anemometer, in 1607, Galileo Galilei constructed a thermoscope
10.
Standing wave
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In physics, a standing wave – also known as a stationary wave – is a wave in a medium in which each point on the axis of the wave has an associated constant amplitude. The locations at which the amplitude is minimum are called nodes, standing waves were first noticed by Michael Faraday in 1831. Faraday observed standing waves on the surface of a liquid in a vibrating container, franz Melde coined the term standing wave around 1860 and demonstrated the phenomenon in his classic experiment with vibrating strings. For waves of equal amplitude traveling in opposing directions, there is on average no net propagation of energy, as an example of the first type, under certain meteorological conditions standing waves form in the atmosphere in the lee of mountain ranges. Such waves are often exploited by glider pilots, standing waves and hydraulic jumps also form on fast flowing river rapids and tidal currents such as the Saltstraumen maelstrom. Many standing river waves are popular river surfing breaks, the effect is a series of nodes and anti-nodes at fixed points along the transmission line. The failure of the line to power at the standing wave frequency will usually result in attenuation distortion. In practice, losses in the line and other components mean that a perfect reflection. The result is a standing wave, which is a superposition of a standing wave. The degree to which the wave resembles either a standing wave or a pure traveling wave is measured by the standing wave ratio. Another example is standing waves in the ocean formed by waves with the same wave period moving in opposite directions. These may form near storm centres, or from reflection of a swell at the shore, in one dimension, two waves with the same frequency, wavelength and amplitude traveling in opposite directions will interfere and produce a standing wave or stationary wave. The reflected wave has to have the amplitude and frequency as the incoming wave. At locations which are multiples of a quarter wavelength x =. −3 λ2, − λ, − λ2,0, λ2, λ,3 λ2, called the nodes, the amplitude is always zero, whereas at locations which are odd multiples of a quarter wavelength x =. −5 λ4, −3 λ4, − λ4, λ4,3 λ4,5 λ4, called the anti-nodes, the amplitude is maximum, with a value of twice the amplitude of the original waves. The distance between two nodes or anti-nodes is λ/2. Standing waves can occur in two- or three-dimensional resonators
11.
Melde's experiment
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This experiment, a lecture-room standby, attempted to demonstrate that mechanical waves undergo interference phenomena. In the experiment, mechanical waves traveled in opposite directions form immobile points and these waves were called standing waves by Melde since the position of the nodes and loops stayed static. Standing waves were first discovered by Franz Melde, who coined the term standing wave around 1860, Melde generated parametric oscillations in a string by employing a tuning fork to periodically vary the tension at twice the resonance frequency of the string. Wave phenomena in nature have been investigated for centuries, some being some of the most controverted themes in the history of science, in the 17th century, Sir Isaac Newton described light through a corpuscular theory. The English physicist Thomas Young later contrasted Newtons theories in the 18th century, at the end of the 19th century, at the peak of the Second Industrial Revolution, the creation of electricity as the technology of the era offered a new contribution to the wave theories. This advance allowed Franz Melde to recognize the phenomena of wave interference, later, the Scottish physicist James Clerk Maxwell in his study of the wave nature of light succeeded in expressing waves and the electromagnetic spectrum in a mathematical formula. In this experiment the change in frequency produced when the tension is increased in the string – similar to the change in pitch when a string is tuned – will be measured. From this the mass per length of the string / wire can be derived. Finding the mass per length of a piece of string is also possible by using a simpler method – a ruler and some scales –
12.
Monochord
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A monochord, also known as sonometer, is an ancient musical and scientific laboratory instrument, involving one string. The term monochord is sometimes used as the class-name for any musical stringed instrument having only one string, according to the Hornbostel–Sachs system, string bows are bar zithers while monochords are traditionally board zithers. A string is fixed at both ends and stretched over a sound box, one or more movable bridges are then manipulated to demonstrate mathematical relationships among the frequencies produced. With its single string, movable bridge and graduated rule, the monochord straddled the gap between notes and numbers, intervals and ratios, sense-perception and mathematical reason, however, music, mathematics, and astronomy were inexorably linked in the monochord. For example, when a string is open it vibrates at a particular frequency. When the length of the string is halved, and plucked, it produces a pitch an octave higher, half of this length will produce a pitch two octaves higher than the original—four times the initial frequency —and so on. Standard diatonic Pythagorean tuning is easily derived starting from superparticular ratios, /n, constructed from the first four counting numbers, the mathematics involved include the multiplication table, least common multiples, and prime and composite numbers. A bichord instrument is one, having two strings in unison for each note, such as the mandolin, with two strings one can easily demonstrate how various musical intervals sound. Parts of a monochord include a tuning peg, nut, string, moveable bridge, fixed bridge, calibration marks, belly or resonating box, instruments derived from the monochord include the guqin, dan bau, koto, vina, hurdy-gurdy, and clavichord. A monopipe is the wind instrument version of a monochord, an open pipe which can produce variable pitches. End correction must be used with this method, to achieve accuracy, the monochord is mentioned in Sumerian writings, while some attribute its invention to Pythagorus. Dolge attributes the invention of the bridge to Guido of Arezzo around 1000 CE. In 1618, Robert Fludd devised a mundane monochord that linked the Ptolemaic universe to musical intervals, was it physical intuition or a Pythagorean confidence in the importance of small whole numbers. 1,5 &10, which is music that uses pitch ratios extended to higher partials beyond the standard Pythagorean tuning system. A modern playing technique used in rock as well as contemporary classical music is 3rd bridge. This technique shares the same mechanism as used on the monochord, a sonometer is a diagnostic instrument used to measure the tension, frequency or density of vibrations. They are used in medical settings to test both hearing and bone density, a sonometer, or audiometer, is used to determine hearing sensitivity, while a clinical bone sonometer measures bone density to help determine such conditions as the risk of osteoporosis. In audiology, the device is used to test for hearing loss, the audiometer measures the ability to hear sounds at frequencies normally detectable by the human ear
13.
Sine wave
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A sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. It is named after the sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time is, y = A sin = A sin where, A = the amplitude, F = the ordinary frequency, the number of oscillations that occur each second of time. ω = 2πf, the frequency, the rate of change of the function argument in units of radians per second φ = the phase. When φ is non-zero, the entire waveform appears to be shifted in time by the amount φ /ω seconds, a negative value represents a delay, and a positive value represents an advance. The sine wave is important in physics because it retains its shape when added to another sine wave of the same frequency and arbitrary phase. It is the only periodic waveform that has this property and this property leads to its importance in Fourier analysis and makes it acoustically unique. The wavenumber is related to the frequency by. K = ω v =2 π f v =2 π λ where λ is the wavelength, f is the frequency, and v is the linear speed. This equation gives a wave for a single dimension, thus the generalized equation given above gives the displacement of the wave at a position x at time t along a single line. This could, for example, be considered the value of a wave along a wire, in two or three spatial dimensions, the same equation describes a travelling plane wave if position x and wavenumber k are interpreted as vectors, and their product as a dot product. For more complex such as the height of a water wave in a pond after a stone has been dropped in. This wave pattern occurs often in nature, including wind waves, sound waves, a cosine wave is said to be sinusoidal, because cos = sin , which is also a sine wave with a phase-shift of π/2 radians. Because of this start, it is often said that the cosine function leads the sine function or the sine lags the cosine. The human ear can recognize single sine waves as sounding clear because sine waves are representations of a frequency with no harmonics. Presence of higher harmonics in addition to the fundamental causes variation in the timbre, on the other hand, if the sound contains aperiodic waves along with sine waves, then the sound will be perceived noisy as noise is characterized as being aperiodic or having a non-repetitive pattern. In 1822, French mathematician Joseph Fourier discovered that sinusoidal waves can be used as building blocks to describe and approximate any periodic waveform
14.
String vibration
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A vibration in a string is a wave. Resonance causes a string to produce a sound with constant frequency. If the length or tension of the string is correctly adjusted, vibrating strings are the basis of string instruments such as guitars, cellos, and pianos. Let Δ x be the length of a piece of string, m its mass, and μ its linear density. If the horizontal component of tension in the string is a constant, T, if both angles are small, then the tensions on either side are equal and the net horizontal force is zero. This is the equation for y, and the coefficient of the second time derivative term is equal to v −2, thus v = T μ. Once the speed of propagation is known, the frequency of the produced by the string can be calculated. The speed of propagation of a wave is equal to the wavelength λ divided by the period τ, or multiplied by the frequency f, v = λ τ = λ f. If the length of the string is L, the harmonic is the one produced by the vibration whose nodes are the two ends of the string, so L is half of the wavelength of the fundamental harmonic. Hence one obtains Mersennes laws, f = v 2 L =12 L T μ where T is the tension, μ is the linear density, and L is the length of the vibrating part of the string. This effect is called the effect, and the rate at which the string seems to vibrate is the difference between the frequency of the string and the refresh rate of the screen. The same can happen with a fluorescent lamp, at a rate that is the difference between the frequency of the string and the frequency of the alternating current. In daylight and other non-oscillating light sources, this effect does not occur and the string appears still but thicker, a similar but more controllable effect can be obtained using a stroboscope. This device allows matching the frequency of the flash lamp to the frequency of vibration of the string. In a dark room, this shows the waveform. Otherwise, one can use bending or, perhaps more easily, by adjusting the machine heads, to obtain the same, or a multiple, of the AC frequency to achieve the same effect. For example, in the case of a guitar, the 6th string pressed to the third gives a G at 97.999 Hz. A slight adjustment can alter it to 100 Hz, exactly one octave above the current frequency in Europe and most countries in Africa
15.
Parametric oscillator
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A simple example of a parametric oscillator is a child pumping a swing by periodically standing and squatting to increase the size of the swings oscillations. The childs motions vary the moment of inertia of the swing as a pendulum, the pump motions of the child must be at twice the frequency of the swings oscillations. Examples of parameters that may be varied are the resonance frequency ω. Parametric oscillators are used in areas of physics. The classical varactor parametric oscillator consists of a varactor diode connected to a resonant circuit or cavity resonator. It is driven by varying the diodes capacitance by applying a bias voltage. The circuit that varies the diodes capacitance is called the pump or driver, in microwave electronics, waveguide/YAG based parametric oscillators operate in the same fashion. Varactor parametric amplifiers have been developed as low-noise amplifiers in the radio, the advantage of a parametric amplifier is that it has much lower noise than an ordinary amplifier based on a gain device like a transistor or vacuum tube. This is because in the amplifier an reactance is varied instead of a resistance. They have been used in very low noise radio receivers in radio telescopes, Parametric resonance occurs in a mechanical system when a system is parametrically excited and oscillates at one of its resonant frequencies. Parametric excitation differs from forcing since the action appears as a time varying modification on a system parameter, michael Faraday was the first to notice oscillations of one frequency being excited by forces of double the frequency, in the crispations observed in a wine glass excited to sing. Franz Melde generated parametric oscillations in a string by employing a tuning fork to periodically vary the tension at twice the frequency of the string. Parametric oscillation was first treated as a phenomenon by Rayleigh. Parametric amplifiers were first used in 1913-1915 for radio telephony from Berlin to Vienna and Moscow, the early paramps varied inductances, but other methods have been developed since, e. g. the varactor diodes, klystron tubes, Josephson junctions and optical methods. D2 x d t 2 + β d x d t + ω2 x =0 This equation is linear in x, by assumption, the parameters ω2 and β depend only on time and do not depend on the state of the oscillator. In general, β and/or ω2 are assumed to vary periodically, without a compensating energy-loss mechanism provided by β, the oscillation amplitude grows exponentially. A familiar experience of both parametric and driven oscillation is playing on a swing and this changes moment of inertia of the swing and hence the resonance frequency, and children can quickly reach large amplitudes provided that they have some amplitude to start with. Standing and squatting at rest, however, leads nowhere and we begin by making a change of variables q = d e f e D x where D is a time integral of the damping D = d e f 12 ∫ t d τ β
16.
Tuning fork
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A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs formed from a U-shaped bar of elastic metal. It resonates at a constant pitch when set vibrating by striking it against a surface or with an object. The pitch that a tuning fork generates depends on the length. It is frequently used as a standard of pitch to tune musical instruments, the tuning fork was invented in 1711 by British musician John Shore, Sergeant Trumpeter and Lutenist to the court. A tuning fork is an acoustic resonator used in many applications to produce a fixed tone. The reason for this is that the frequency of the first overtone is about 52/22 = 25/4 = 6 1⁄4 times the fundamental. When the tuning fork is struck, little of the energy goes into the overtone modes, they die out correspondingly faster. It is easier to other instruments with this pure tone. Another reason for using the shape is that, when it vibrates in its principal mode. There is a node at the base of each prong, the fork is usually struck, and then the handle is pressed against a wooden box resonator, or a table top. Without the resonator the sound of a fork is very faint. The reason for this is that the waves produced by each fork prong are 180° out of phase with the other, so at a distance from the fork they interfere. Commercial tuning forks are normally tuned to the pitch at the factory. They can be retuned by filing material off the prongs, filing the ends of the prongs raises the pitch, while filing the inside of the base of the prongs lowers it. Tuning forks used by orchestras between 1750 and 1820 mostly had a frequency of A =423.5 Hz, although there were many forks, standard tuning forks are available that vibrate at all the musical pitches within the central octave of the piano, and other pitches. Well-known manufacturers of tuning forks include Ragg and John Walker, both of Sheffield, England, the pitch of a tuning fork varies slightly with temperature, due mainly to a slight decrease in the modulus of elasticity of steel with increasing temperature. A change in frequency of one vibration in 21,000 per °F change is typical for a tuning fork. The frequency decreases with increasing temperature, tuning forks are manufactured to have their correct pitch at a standard temperature
17.
Resonance
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In physics, resonance is a phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at a specific preferential frequency. Frequencies at which the amplitude is a relative maximum are known as the systems resonant frequencies or resonance frequencies. At resonant frequencies, small periodic driving forces have the ability to produce large amplitude oscillations, Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes. However, there are some losses from cycle to cycle, called damping, when damping is small, the resonant frequency is approximately equal to the natural frequency of the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies, resonant systems can be used to generate vibrations of a specific frequency, or pick out specific frequencies from a complex vibration containing many frequencies. Resonance occurs widely in nature, and is exploited in many manmade devices and it is the mechanism by which virtually all sine waves and vibrations are generated. Many sounds we hear, such as when hard objects of metal, glass, light and other short wavelength electromagnetic radiation is produced by resonance on an atomic scale, such as electrons in atoms. A familiar example is a swing, which acts as a pendulum. Pushing a person in a swing in time with the interval of the swing makes the swing go higher and higher. This is because the energy the swing absorbs is maximized when the match the swings natural oscillations. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings, trains, avoiding resonance disasters is a major concern in every building, tower, and bridge construction project. As a countermeasure, shock mounts can be installed to absorb resonant frequencies, the Taipei 101 building relies on a 660-tonne pendulum —a tuned mass damper—to cancel resonance. Furthermore, the structure is designed to resonate at a frequency that does not typically occur, buildings in seismic zones are often constructed to take into account the oscillating frequencies of expected ground motion. Clocks keep time by mechanical resonance in a wheel, pendulum. The cadence of runners has been hypothesized to be energetically favorable due to resonance between the energy stored in the lower limb and the mass of the runner. Acoustic resonance is a branch of mechanical resonance that is concerned with the mechanical vibrations across the range of human hearing. Like mechanical resonance, acoustic resonance can result in failure of the object at resonance. The classic example of this is breaking a glass with sound at the precise resonant frequency of the glass
18.
Frequency
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Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as frequency, which emphasizes the contrast to spatial frequency. The period is the duration of time of one cycle in a repeating event, for example, if a newborn babys heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as vibrations, audio signals, radio waves. For cyclical processes, such as rotation, oscillations, or waves, in physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by the Greek letter ν or ν. For a simple motion, the relation between the frequency and the period T is given by f =1 T. The SI unit of frequency is the hertz, named after the German physicist Heinrich Hertz, a previous name for this unit was cycles per second. The SI unit for period is the second, a traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. As a matter of convenience, longer and slower waves, such as ocean surface waves, short and fast waves, like audio and radio, are usually described by their frequency instead of period. Spatial frequency is analogous to temporal frequency, but the axis is replaced by one or more spatial displacement axes. Y = sin = sin d θ d x = k Wavenumber, in the case of more than one spatial dimension, wavenumber is a vector quantity. For periodic waves in nondispersive media, frequency has a relationship to the wavelength. Even in dispersive media, the frequency f of a wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave. In the special case of electromagnetic waves moving through a vacuum, then v = c, where c is the speed of light in a vacuum, and this expression becomes, f = c λ. When waves from a monochrome source travel from one medium to another, their remains the same—only their wavelength. For example, if 71 events occur within 15 seconds the frequency is, the latter method introduces a random error into the count of between zero and one count, so on average half a count. This is called gating error and causes an error in the calculated frequency of Δf = 1/, or a fractional error of Δf / f = 1/ where Tm is the timing interval. This error decreases with frequency, so it is a problem at low frequencies where the number of counts N is small, an older method of measuring the frequency of rotating or vibrating objects is to use a stroboscope
19.
Landsmannschaft (Studentenverbindung)
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A Landsmannschaft is a German fraternity of several fraternity forms called Studentenverbindung. The older forms of Landsmannschaften were part of corporations and are aligned with the beginnings of universities in medieval times of the 12th and 13th centuries. The newer forms of Landsmannschaften are a kind of reform corps, students joined groups in regards to region in order to have protection as well as support in being heard in their interests. Landsmannschaften formerly had the character of guilds and they were loosely organized bodies of students from the same region or nation naturally enough drawn together by their longings for companionship. A good example is the Mosellanerlandsmannschaft of the University of Jena and it contained members from the Rhineland, Palatinate, Swabia, and Alsace. By 1786, this code had grown to 86 paragraphs, Nations in Finnish universities Nations in Swedish universities Sudetendeutsche Landsmannschaft Homepage of Landsmannschaft Ulmia Tübingen
20.
Academy of Sciences Leopoldina
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The Leopoldina is the national academy of Germany. Historically it was known under the German name Deutsche Akademie der Naturforscher Leopoldina until 2007, the Leopoldina is located in Halle. Founded in 1652, the Leopoldina claims to be the oldest continuously existing learned society in the world. The Leopoldina was founded in the city of Schweinfurt on 1 January 1652 under the Latin name Academia Naturae Curiosorum, the four founding members were physicians, namely Johann Laurentius Bausch, first president of the society, Johann Michael Fehr, Georg Balthasar Metzger, and Georg Balthasar Wohlfarth. In 1677, Leopold I, emperor of the Holy Roman Empire, recognised the society, P. 7–8, At first, the society conducted its business by correspondence and was located wherever the president was working. It was not permanently located in Halle until 1878 and did not meet regularly until 1924, pp. 8–9 When Adolf Hitler became Germanys chancellor in 1933, the Leopoldina started to exclude its Jewish members. Albert Einstein was one of the first victims, more than 70 followed until 1938, eight of them were murdered by the Nazis. At the end of World War II, the city of Halle, and hence the building of the academy, became part of East Germany, however, the Leopoldina successfully resisted these attempts and continued to think of itself as an institution for the whole of Germany. In 1991, after German reunification, the Leopoldina was granted the status of a non-profit organisation and it is funded jointly by the German government and the government of the state of Saxony-Anhalt. As the German Academy of Sciences, it is a counterpart to the rights and responsibilities of institutions such as Britains Royal Society and the United States National Academy of Science. The Leopoldina is the first and foremost academic society in Germany to advise the German government on a variety of scientific matters, the Leopoldina gives conferences and lectures and continues to publish the Ephemeriden under the name Nova Acta Leopoldina. It issues various medals and awards, offers grants and scholarships, the Academy also maintains a library and an archive and it also researches its own history and publishes another journal, Acta Historica Leopoldina devoted to this subject. The election to membership of the Leopoldina is the highest academic honour awarded by an institution in Germany, as of early 2014, a total of 169 Nobel prize laureates are fellows of the Leopoldina
21.
World's Columbian Exposition
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The Worlds Columbian Exposition was a worlds fair held in Chicago in 1893 to celebrate the 400th anniversary of Christopher Columbuss arrival in the New World in 1492. The centerpiece of the Fair, the water pool, represented the long voyage Columbus took to the New World. Chicago bested New York City, Washington, D. C. the Exposition was an influential social and cultural event and had a profound effect on architecture, sanitation, the arts, Chicagos self-image, and American industrial optimism. The layout of the Chicago Columbian Exposition was, in part, designed by John Wellborn Root, Daniel Burnham, Frederick Law Olmsted. It was the prototype of what Burnham and his colleagues thought a city should be and it was designed to follow Beaux Arts principles of design, namely French neoclassical architecture principles based on symmetry, balance, and splendor. The color of the generally used to cover the buildings facades gave the fairgrounds its nickname. Many prominent architects designed its 14 great buildings, artists and musicians were featured in exhibits and many also made depictions and works of art inspired by the exposition. The exposition covered more than 600 acres, featuring nearly 200 new buildings of predominantly neoclassical architecture, canals and lagoons, more than 27 million people attended the exposition during its six-month run. Dedication ceremonies for the fair were held on October 21,1892, the fair continued until October 30,1893. On October 9,1893, the day designated as Chicago Day, the debt for the fair was soon paid off with a check for $1.5 million. Chicago has commemorated the fair one of the stars on its municipal flag. Schwab, Chicago railroad and manufacturing magnate John Whitfield Bunn, and Connecticut banking, insurance, the fair was planned in the early 1890s during the Gilded Age of rapid industrial growth, immigration, and class tension. Worlds fairs, such as Londons 1851 Crystal Palace Exhibition, had been successful in Europe as a way to bring together societies fragmented along class lines, the first American attempt at a worlds fair in Philadelphia in 1876, drew crowds but was a financial failure. Nonetheless, ideas about distinguishing the 400th anniversary of Columbus landing started in the late 1880s. Civic leaders in St. Louis, New York City, Washington DC and Chicago expressed an interest in hosting a fair to generate profits, boost real estate values, Congress was called on to decide the location. What finally persuaded Congress was Chicago banker Lyman Gage, who raised several million dollars in a 24-hour period, over. The exposition corporation and national exposition commission settled on Jackson Park, Daniel H. Burnham was selected as director of works, and George R. Davis as director-general. Burnham emphasized architecture and sculpture as central to the fair and assembled the periods top talent to design the buildings, the temporary buildings were designed in an ornate Neoclassical style and painted white, resulting in the fair site being referred to as the “White City”
22.
Ernst Chladni
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Ernst Florens Friedrich Chladni was a German physicist and musician. His most important work, for which he is labeled the father of acoustics, included research on vibrating plates. He also undertook pioneering work in the study of meteorites and so is regarded by some as the father of meteoritics. Although Chladni was born in Wittenberg in Saxony, his family originated from Kremnica, then part of the Kingdom of Hungary, Chladni has therefore been identified as German, Hungarian and Slovak. Chladni came from an family of academics and learned men. Chladnis great-grandfather, the Lutheran clergyman Georg Chladni, had left Kremnica in 1673 during the Counter Reformation, Chladnis grandfather, Martin Chladni, was also a Lutheran theologian and, in 1710, became professor of theology at the University of Wittenberg. He was dean of the faculty in 1720–1721 and later became the universitys rector. Chaldnis uncle, Justus Georg Chladni, was a law professor at the university, another uncle, Johann Martin Chladni, was a theologian, a historian and a professor at the University of Erlangen and the University of Leipzig. Chladnis father, Ernst Martin Chladni, was a law professor and rector of the University of Wittenberg and he had joined the law faculty there in 1746. Chladnis mother was Johanna Sophia and he was an only child and his father disapproved of his sons interest in science and insisted that Chladni become a lawyer. Chladni studied law and philosophy in Wittenberg and Leipzig, obtaining a law degree from the University of Leipzig in 1782 and that same year, his father died and he turned to physics in earnest. One of Chladnis best-known achievements was inventing a technique to show the modes of vibration of a rigid surface. When resonating, a plate or membrane is divided into regions that vibrate in opposite directions, Chladni repeated the pioneering experiments of Robert Hooke who, on July 8,1680, had observed the nodal patterns associated with the vibrations of glass plates. Hooke ran a bow along the edge of a plate covered with flour. Chladnis technique, first published in 1787 in his book Entdeckungen über die Theorie des Klanges, the plate was bowed until it reached resonance, when the vibration causes the sand to move and concentrate along the nodal lines where the surface is still, outlining the nodal lines. The patterns formed by these lines are what are now called Chladni figures, similar nodal patterns can also be found by assembling microscale materials on Faraday waves. When Chladni showed the technique in Paris, Napoleon set a prize for the best mathematical explanation, sophie Germains answer, although rejected due to flaws, was the only entry with the correct approach. Variations of this technique are still used in the design and construction of acoustic instruments such as violins, guitars
23.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
24.
Acoustical engineering
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Acoustical engineering is the branch of engineering dealing with sound and vibration. It is the application of acoustics, the science of sound and vibration, Acoustical engineers are typically concerned with the design, analysis and control of sound. One goal of engineering can be the reduction of unwanted noise. Unwanted noise can have significant impacts on animal and human health and well-being, reduce attainment by pupils in schools, acoustic engineers usually possess a bachelors degree or higher qualification in acoustics, physics or another engineering discipline. Practicing as an acoustic engineer usually requires a degree with significant scientific. Acoustic engineers might work in consultancy, specializing in particular fields, such as architectural acoustics. Acousticians are also involved in researching and understanding sound scientifically, some positions, such as faculty require a Doctor of Philosophy. In most countries, a degree in acoustics can represent the first step towards professional certification, after completing a certified degree program the engineer must satisfy a range of requirements before being certified. Once certified, the engineer is designated the title of Chartered Engineer, the listed subdisciplines are loosely based on the PACS coding used by the Acoustical Society of America. Aeroacoustics is concerned with how noise is generated by the movement of air, for instance via turbulence, aeroacoustics plays an important role in understanding how noise is generated by aircraft and wind turbines, as well as exploring how wind musical instruments work. Audio signal processing is the manipulation of audio signals using analog. Perceptual coding in MP3 and Opus, and to understand the content of the signal, audio engineers develop and use audio signal processing algorithms. Architectural acoustics is the science and engineering of achieving a good sound within a building, architectural acoustic design is usually done by acoustic consultants. Bioacoustics usually concerns the study of sound production and hearing in animals. This branch of acoustic engineering deals with the design of headphones, microphones, loudspeakers, sound systems, sound reproduction, environmental acoustics work is usually done by acoustic consultants or those working in environmental health. Recent research work has put an emphasis on soundscapes, the positive use of sound. Musical acoustics is concerned with researching and describing the physics of music, noise control is a set of strategies to reduce noise pollution by reducing noise at its source, by inhibiting sound propagation using noise barriers or similar, or by the use of ear protection. Control at the source is the most cost-effective way of providing noise control, noise control engineering applied to cars and trucks is known as noise, vibration, and harshness
25.
Architectural acoustics
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Architectural acoustics is the science and engineering of achieving a good sound within a building and is a branch of acoustical engineering. Architectural acoustic design is usually done by acoustic consultants and this science analyzes noise transmission from building exterior envelope to interior and vice versa. The main noise paths are roofs, eaves, walls, windows, door, sufficient control ensures space functionality and is often required based on building use and local municipal codes. An example would be providing a design for a home which is to be constructed close to a high volume roadway, or under the flight path of a major airport. The science of limiting and/or controlling noise transmission from one building space to another to ensure space functionality, the typical sound paths are ceilings, room partitions, acoustic ceiling panels, doors, windows, flanking, ducting and other penetrations. Technical solutions depend on the source of the noise and the path of acoustic transmission, an example would be providing suitable party wall design in an apartment complex to minimize the mutual disturbance due to noise by residents in adjacent apartments. This is the science of controlling a rooms surfaces based on sound absorbing and reflecting properties, excessive reverberation time, which can be calculated, can lead to poor speech intelligibility. Sound reflections create standing waves that produce natural resonances that can be heard as a pleasant sensation or an annoying one, reflective surfaces can be angled and coordinated to provide good coverage of sound for a listener in a concert hall or music recital space. To illustrate this concept consider the difference between a large office meeting room or lecture theater and a traditional classroom with all hard surfaces. Interior building surfaces can be constructed of different materials and finishes. Ideal acoustical panels are those without a face or finish material that interferes with the acoustical infill or substrate, fabric covered panels are one way to heighten acoustical absorption. Perforated metal shows also sound absorbing qualities, finish material is used to cover over the acoustical substrate. Mineral fiber board, or Micore, is a commonly used acoustical substrate, finish materials often consist of fabric, wood or acoustical tile. Fabric can be wrapped around substrates to create what is referred to as a pre-fabricated panel, prefabricated panels are limited to the size of the substrate ranging from 2 by 4 feet to 4 by 10 feet. Fabric retained in a perimeter track system, is referred to as on-site acoustical wall panels. This is constructed by framing the perimeter track into shape, infilling the acoustical substrate, on-site wall panels can be constructed to accommodate door frames, baseboard, or any other intrusion. Large panels can be created on walls and ceilings with this method, wood finishes can consist of punched or routed slots and provide a natural look to the interior space, although acoustical absorption may not be great. There are three ways to improve workplace acoustics and solve workplace sound problems – the ABCs, inadequate control may lead to elevated sound levels within the space which can be annoying and reduce speech intelligibility
26.
Reverberation
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Reverberation, in psychoacoustics and acoustics, is the persistence of sound after a sound is produced. This is most noticeable when the sound source stops but the reflections continue, decreasing in amplitude, until they reach zero amplitude. In comparison to an echo that is a minimum of 50 to 100 ms after the initial sound. As time passes, the amplitude of the reflections is reduced until it is reduced to zero, Reverberation is not limited to indoor spaces as it exists in forests and other outdoor environments where reflection exists. Reverberation occurs naturally when a person sings, talks or plays an instrument acoustically in a hall or performance space with sound-reflective surfaces. The sound of reverberation is often added to the vocals of singers in live sound systems. The time it takes for a signal to drop by 60 dB is the reverberation time, RT60 is the time required for reflections of a direct sound to decay 60 dB. Reverberation time is stated as a single value, if measured as a wide band signal, however, being frequency dependent. Being frequency dependent, the time measured in narrow bands will differ depending on the frequency band being measured. For precision, it is important to know what ranges of frequencies are being described by a time measurement. In the late 19th century, Wallace Clement Sabine started experiments at Harvard University to investigate the impact of absorption on the reverberation time. Using a portable wind chest and organ pipes as a sound source and he found that the reverberation time is proportional to room dimensions and inversely proportional to the amount of absorption present. The optimum reverberation time for a space in which music is played depends on the type of music that is to be played in the space, rooms used for speech typically need a shorter reverberation time so that speech can be understood more clearly. If the reflected sound from one syllable is still heard when the syllable is spoken. Cat, Cab, and Cap may all sound very similar, if on the other hand the reverberation time is too short, tonal balance and loudness may suffer. Reverberation effects are used in studios to add depth to sounds. Reverberation changes the perceived spectral structure of a sound, but does not alter the pitch, basic factors that affect a rooms reverberation time include the size and shape of the enclosure as well as the materials used in the construction of the room. Every object placed within the enclosure can also affect this time, including people
27.
Soundproofing
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Soundproofing is any means of reducing the sound pressure with respect to a specified sound source and receptor. Two distinct soundproofing problems may need to be considered when designing acoustic treatments - to improve the sound within a room, acoustic quieting, noise mitigation, and noise control can be used to limit unwanted noise. Soundproofing can suppress unwanted indirect sound waves such as reflections that cause echoes and resonances that cause reverberation, soundproofing can reduce the transmission of unwanted direct sound waves from the source to an involuntary listener through the use of distance and intervening objects in the sound path. The energy density of sound waves decreases as they spread out, in a normal three-dimensional setting, with a point source and point receptor, the intensity of sound waves will be attenuated according to the inverse square of the distance from the source. Damping means to reduce resonance in the room, by absorption or redirection, absorption will reduce the overall sound level, whereas redirection makes unwanted sound harmless or even beneficial by reducing coherence. Damping can reduce the acoustic resonance in the air, or mechanical resonance in the structure of the room itself or things in the room. Absorbing sound spontaneously converts part of the energy to a very small amount of heat in the intervening object. There are several ways in which a material can absorb sound, the choice of sound absorbing material will be determined by the frequency distribution of noise to be absorbed and the acoustic absorption profile required. Porous absorbers, typically open cell rubber foams or melamine sponges, porous open cell foams are highly effective noise absorbers across a broad range of medium-high frequencies. Performance is less impressive at low frequencies, unlike porous absorbers, resonant absorbers are most effective at low-medium frequencies and the absorption of resonant absorbers is always matched to a narrow frequency range. In an outdoor environment such as engineering, embankments or panelling are often used to reflect sound upwards into the sky. If a specular reflection from a flat surface is giving a problematic echo then an acoustic diffuser may be applied to the surface. It will scatter sound in all directions and this is effective to eliminate pockets of noise in a room. A room within a room is one method of isolating sound, most vibration / sound transfer from a room to the outside occurs through mechanical means. The vibration passes directly through the brick, woodwork and other structural elements. When it meets with an element such as a wall, ceiling, floor or window, which acts as a sounding board, a mechanical transmission is much faster, more efficient and may be more readily amplified than an airborne transmission of the same initial strength. The use of foam and other absorbent means is less effective against this transmitted vibration. The user is advised to break the connection between the room contains the noise source and the outside world
28.
String resonance
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String resonance occurs on string instruments. Strings or parts of strings may resonate at their fundamental or overtone frequencies when other strings are sounded, for example, an A string at 440 Hz will cause an E string at 330 Hz to resonate, because they share an overtone of 1320 Hz. Electric guitars can have string trees near the tuning pegs to mute this type of reverberation, the string length behind the bridge also must be as short as possible to prevent the resonance. String resonance is a factor in the timbre of a string instrument, tailed bridge guitars like the Fender Jaguar differ in timbre from guitars with short bridges, because of their floating bridge. The Japanese Koto is also an example of an instrument with occurring string resonance, sometimes string resonance is used in the construction of the instrument, like for instance the Sympathetic strings in many Eastern instruments. In the octave duplex piano by Hoerr of Toronto, each note had four strings, the following table shows the created resonating overtones on the koto for various positions on a stopped string
29.
Spectrogram
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A spectrogram is a visual representation of the spectrum of frequencies in a sound or other signal as they vary with time or some other variable. Spectrograms are sometimes called spectral waterfalls, voiceprints, or voicegrams, spectrograms can be used to identify spoken words phonetically, and to analyse the various calls of animals. They are used extensively in the development of the fields of music, sonar, radar, the frequency and amplitude axes can be either linear or logarithmic, depending on what the graph is being used for. Audio would usually be represented with a logarithmic amplitude axis, and frequency would be linear to emphasize harmonic relationships, or logarithmic to emphasize musical, tonal relationships. Spectrograms are usually created in one of two ways, approximated as a filterbank that results from a series of filters, or calculated from the time signal using the Fourier transform. These two methods actually form two different time–frequency representations, but are equivalent under some conditions, creating a spectrogram using the FFT is a digital process. Digitally sampled data, in the domain, is broken up into chunks, which usually overlap. Each chunk then corresponds to a line in the image. These spectrums or time plots are laid side by side to form the image or a three-dimensional surface, or slightly overlapped in various ways. Early analog spectrograms were applied to a range of areas including the study of bird calls, with current research continuing using modern digital equipment. Contemporary use of the spectrogram is especially useful for studying frequency modulation in animal calls. Specifically, the characteristics of FM chirps, broadband clicks. By reversing the process of producing a spectrogram, it is possible to create a signal whose spectrogram is an arbitrary image and this technique can be used to hide a picture in a piece of audio and has been employed by several electronic music artists. See Audio timescale-pitch modification and Phase vocoder, spectrograms can be used to analyze the results of passing a test signal through a signal processor such as a filter in order to check its performance. The Analysis & Resynthesis Sound Spectrograph is an example of a program that attempts to do this. The Pattern Playback was a speech synthesizer, designed at Haskins Laboratories in the late 1940s. In fact, there is some information in the spectrogram. The size and shape of the window can be varied
30.
Psychoacoustics
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Psychoacoustics is the scientific study of sound perception. More specifically, it is the branch of science studying the psychological and physiological responses associated with sound and it can be further categorized as a branch of psychophysics. Psychoacoustics received its name from a field within psychology—i. e, recognition science—which deals with all kinds of human perceptions. It is a field of many areas, including psychology, acoustics, electronic engineering, physics, biology, physiology. These nerve pulses then travel to the brain where they are perceived, the inner ear, for example, does significant signal processing in converting sound waveforms into neural stimuli, so certain differences between waveforms may be imperceptible. Data compression techniques, such as MP3, make use of this fact, in addition, the ear has a nonlinear response to sounds of different intensity levels, this nonlinear response is called loudness. Telephone networks and audio noise reduction systems make use of this fact by nonlinearly compressing data samples before transmission, another effect of the ears nonlinear response is that sounds that are close in frequency produce phantom beat notes, or intermodulation distortion products. The expression that one hears what one wants to hear may pertain in such discussions, the human ear can nominally hear sounds in the range 20 Hz to 20,000 Hz. The upper limit tends to decrease with age, most adults are unable to hear above 16 kHz, the lowest frequency that has been identified as a musical tone is 12 Hz under ideal laboratory conditions. Tones between 4 and 16 Hz can be perceived via the sense of touch. Frequency resolution of the ear is 3.6 Hz within the octave of 1000 –2000 Hz and that is, changes in pitch larger than 3.6 Hz can be perceived in a clinical setting. However, even smaller pitch differences can be perceived through other means, for example, the interference of two pitches can often be heard as a repetitive variation in volume of the tone. This amplitude modulation occurs with a equal to the difference in frequencies of the two tones and is known as beating. The semitone scale used in Western musical notation is not a frequency scale. The intensity range of sounds is enormous. Human ear drums are sensitive to variations in the sound pressure, for this reason, sound pressure level is also measured logarithmically, with all pressures referenced to 20 µPa. The lower limit of audibility is defined as 0 dB. The upper limit is more a question of the limit where the ear will be harmed or with the potential to cause noise-induced hearing loss
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Bark scale
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The Bark scale is a psychoacoustical scale proposed by Eberhard Zwicker in 1961. Above about 500 Hz this scale is more or less equal to a logarithmic frequency axis, below 500 Hz the Bark scale becomes more and more linear. The scale ranges from 1 to 24 and corresponds to the first 24 critical bands of hearing and it is related to, but somewhat less popular than, the mel scale, a perceptual scale of pitches judged by listeners to be equal in distance from one another. Since the direct measurements of the bands are subject to error. In all these phenomena, the band seems to play an important role. Thus the important attribute of the Bark scale is the width of the band at any given frequency. OR f = 600*sinh Luminosity function, which describes the average sensitivity of the eye to light of different wavelengths. Fletcher–Munson curves Equivalent rectangular bandwidth, the ERB scale Critical bands Smith and Abel - Bark and ERB Bilinear Transforms Auditory scales of frequency representation
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Combination tone
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A combination tone is a psychoacoustic phenomenon of an additional tone or tones that are artificially perceived when two real tones are sounded at the same time. Their discovery is credited to the violinist Giuseppe Tartini and so are also called Tartini tones, combination tones are heard when two pure tones, differing in frequency by about 50 cycles per second or more, sound together at sufficient intensity. Combination tones can also be produced electronically by combining two signals in a circuit that has nonlinear distortion, such as a subject to clipping or a ring modulator. One way a difference tone can be heard is when two tones with fairly complete sets of harmonics make a just fifth and this can be explained as an example of the missing fundamental phenomenon. If f is the fundamental frequency, then 2 f would be the frequency of the lower tone. Since a fifth corresponds to a ratio of 2,3. When both tones are sounded, there are components with frequencies of 2 f,3 f,4 f,6 f,8 f,9 f, the missing fundamental is heard because so many of these components refer to it. The specific phenomenon that Tartini discovered was physical, sum and difference tones are thought to be caused sometimes by the non-linearity of the inner ear. This causes intermodulation distortion of the frequencies which enter the ear. They are combined linearly, generating relatively faint components with frequencies equal to the sums and differences of whole multiples of the original frequencies. Any components which are heard are usually lower, with the most commonly heard frequency being just the tone, f 2 − f 1. However, experiments show evidence that even when using headphones providing a single pure tone to each ear separately, since the peculiar, non-linear physics of the ear doesnt come into play in this case, it is thought that this must be a separate, neural phenomenon. Heinz Bohlen proposed what is now known as the Bohlen–Pierce scale on the basis of combination tones, a resultant tone is produced when any two loud and sustained musical sounds are heard at the same time. In pipe organs, this is done by having two pipes, one pipe of the note being played, and another related, typically at its fifth. The result is a pitch at a common subharmonic of the pitches played and this effect is useful especially in the lowest ranks of the pipe organ where cost or space could prohibit having a rank of such low pitch. For example, a 64 pipe would be costly and take up at least 32 of space for each pipe, using a resultant tone for such low pitches would eliminate the cost and space factor, but would not sound as full as a true 64 pipe. This effect is most often used in the lowest octave of the organ only and it can vary from highly effective to disappointing depending on several factors, primarily the skill of the organ voicer, and the acoustics of the room the instrument is installed in. Uses combination tones for pitch recognition, if certain intervals are played in double-stop, the program can display its Tartini-tone
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Equal-loudness contour
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An equal-loudness contour is a measure of sound pressure, over the frequency spectrum, for which a listener perceives a constant loudness when presented with pure steady tones. The unit of measurement for loudness levels is the phon, and is arrived at by reference to equal-loudness contours, Equal-loudness contours are often referred to as Fletcher-Munson curves, after the earliest researchers, but those studies have been superseded and incorporated into newer standards. The definitive curves are defined in the international standard ISO226,2003. The human auditory system is sensitive to frequencies from about 20 Hz to a maximum of around 22,000 Hz, although the upper hearing limit decreases with age. Within this range, the ear is most sensitive between 2 and 5 kHz, largely due to the resonance of the ear canal and the transfer function of the ossicles of the middle ear. Fletcher and Munson first measured equal-loudness contours using headphones, in their study, test subjects listened to pure tones at various frequencies and over 10 dB increments in stimulus intensity. For each frequency and intensity, the listener also listened to a tone at 1000 Hz. Fletcher and Munson adjusted the reference tone until the listener perceived that it was the same loudness as the test tone, loudness, being a psychological quantity, is difficult to measure, so Fletcher and Munson averaged their results over many test subjects to derive reasonable averages. The lowest equal-loudness contour represents the quietest audible tone—the absolute threshold of hearing, the highest contour is the threshold of pain. Churcher and King carried out a second determination in 1937, but their results and Fletcher, in 1956 Robinson and Dadson produced a new experimental determination that they believed was more accurate. It became the basis for a standard that was considered definitive until 2003, perceived discrepancies between early and more recent determinations led the International Organization for Standardization to revise the standard curves in ISO226. They did this in response to recommendations in a study coordinated by the Research Institute of Electrical Communication, Tohoku University, the study produced new curves by combining the results of several studies—by researchers in Japan, Germany, Denmark, UK, and USA. This has resulted in the recent acceptance of a new set of curves standardized as ISO226,2003, Equal-loudness curves derived using headphones are valid only for the special case of what is called side-presentation, which is not how we normally hear. Real-life sounds arrive as planar wavefronts, if from a distant source. Off-centre sounds result in increased head masking at one ear, and subtle changes in the effect of the pinna and this combined effect of head-masking and pinna reflection is quantified in a set of curves in three-dimensional space referred to as head-related transfer functions. Frontal presentation is now regarded as preferable when deriving equal-loudness contours, the Robinson-Dadson determination used loudspeakers, and for a long time the difference from the Fletcher-Munson curves was explained partly on the basis that the latter used headphones. However, the ISO report actually lists the latter as using compensated headphones, good headphones, well sealed to the ear, provide a flat low-frequency pressure response to the ear canal, with low distortion even at high intensities. At low frequencies the ear is purely pressure-sensitive, and the cavity formed between headphones and ear is too small to introduce modifying resonances
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Mel scale
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The mel scale, named by Stevens, Volkmann, and Newman in 1937, is a perceptual scale of pitches judged by listeners to be equal in distance from one another. The reference point between this scale and normal frequency measurement is defined by assigning a perceptual pitch of 1000 mels to a 1000 Hz tone,40 dB above the listeners threshold, above about 500 Hz, increasingly large intervals are judged by listeners to produce equal pitch increments. As a result, four octaves on the scale above 500 Hz are judged to comprise about two octaves on the mel scale. The name mel comes from the melody to indicate that the scale is based on pitch comparisons. A popular formula to convert f hertz into m mels is, more curves soon followed in Fletcher and Munsons 1937 and Fletchers 1938 and Stevens 1937 and Stevens and Volkmanns 1940 papers using a variety of experimental methods and analysis approaches. Above 7 kHz, however, the situation is reversed, the break frequency is the only free parameter in the usual form of the formula.8 Hz, and the cochlear frequency–place map of Greenwood uses 165.3 Hz. Other functional forms for the mel scale have been explored by Umesh et al, table of contents for Stevens et al. paper Handbook for Acoustic Ecology Bark scale Mel-frequency cepstrum Fletcher–Munson curves
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Missing fundamental
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For example, when a note has a pitch of 100 Hz, it will consist of frequency components that are integer multiples of that value. However, smaller loudspeakers may not produce low frequencies, and so in our example, nevertheless, a pitch corresponding to the fundamental may still be heard. A low pitch can sometimes be heard there is no apparent source or component of that frequency. This perception is due to the brain interpreting repetition patterns that are present and it was once thought that this effect was because the missing fundamental was replaced by distortions introduced by the physics of the ear. It is now accepted that the brain processes the information present in the overtones to calculate the fundamental frequency. The precise way in which it does so is still a matter of debate, however, it has long been noted that any neural mechanisms which may accomplish a delay have not been found. Autocorrelation can thus be considered, at best, an incomplete model, the pitch of the missing fundamental, usually at the greatest common divisor of the frequencies present, is not, however, always perceived. This was done by asking subjects to judge the direction of motion of two complexes in succession, on-line sound examples comparing pure and complex tones and complexes with missing fundamentals can be found here. Timpani produce inharmonic overtones, but are constructed and tuned to produce near-harmonic overtones to a missing fundamental. Hit in the way, the fundamental note of a timpani is very weak in relation to its second through fifth harmonic overtones. A timpani might be tuned to produce sound most strongly at 200,302,398, a violins lowest air and body resonances generally fall between 250 Hz and 300 Hz. In these cases, the string vibration has no discernable effect on the bridge, instead, the bridge is excited by changes in string tension. On these instruments, listeners hear the first harmonic as the lowest note, electric guitars are not like this, the fundamental frequency of each string is heard because the lateral string movement excites the electric pickups underneath the vibrating string. Most common telephones cannot reproduce sounds lower than 300 Hz, but a voice has a fundamental frequency approximately 150 Hz. Because of the fundamental effect, the fundamental frequencies of male voices are still perceived as their pitches over the telephone. The missing fundamental phenomenon is used electronically by some pro audio manufacturers to allow systems to seem to produce notes that are lower in pitch than they are capable of reproducing. In a hardware unit or a software plugin, a crossover filter is set at a low frequency above which the sound system is capable of safely reproducing tones. Musical signal content above the part of the crossover filter is sent to the main output which is amplified by the sound system
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Pitch (music)
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Pitch can be determined only in sounds that have a frequency that is clear and stable enough to distinguish from noise. Pitch is a major attribute of musical tones, along with duration, loudness. Pitch may be quantified as a frequency, but pitch is not a purely objective physical property, Pitch is an auditory sensation in which a listener assigns musical tones to relative positions on a musical scale based primarily on their perception of the frequency of vibration. Pitch is closely related to frequency, but the two are not equivalent, frequency is an objective, scientific attribute that can be measured. Pitch is each persons subjective perception of a wave, which cannot be directly measured. However, this not necessarily mean that most people wont agree on which notes are higher and lower. Sound waves themselves do not have pitch, but their oscillations can be measured to obtain a frequency and it takes a sentient mind to map the internal quality of pitch. However, pitches are usually associated with, and thus quantified as frequencies in cycles per second, or hertz, by comparing sounds with pure tones, Complex and aperiodic sound waves can often be assigned a pitch by this method. According to the American National Standards Institute, pitch is the attribute of sound according to which sounds can be ordered on a scale from low to high. That is, high pitch means very rapid oscillation, and low pitch corresponds to slower oscillation, despite that, the idiom relating vertical height to sound pitch is shared by most languages. At least in English, it is just one of many deep conceptual metaphors that involve up/down, the exact etymological history of the musical sense of high and low pitch is still unclear. There is evidence that humans do actually perceive that the source of a sound is slightly higher or lower in vertical space when the frequency is increased or reduced. The pitch of tones can be ambiguous, meaning that two or more different pitches can be perceived, depending upon the observer. In a situation like this, the percept at 200 Hz is commonly referred to as the missing fundamental, Pitch depends to a lesser degree on the sound pressure level of the tone, especially at frequencies below 1,000 Hz and above 2,000 Hz. The pitch of lower tones gets lower as sound pressure increases, for instance, a tone of 200 Hz that is very loud seems one semitone lower in pitch than if it is just barely audible. Above 2,000 Hz, the pitch gets higher as the sound gets louder, theories of pitch perception try to explain how the physical sound and specific physiology of the auditory system work together to yield the experience of pitch. In general, pitch perception theories can be divided into place coding, place theory holds that the perception of pitch is determined by the place of maximum excitation on the basilar membrane. However, a purely place-based theory cannot account for the accuracy of pitch perception in the low, temporal theories offer an alternative that appeals to the temporal structure of action potentials, mostly the phase-locking and mode-locking of action potentials to frequencies in a stimulus
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Beat (acoustics)
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In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies. When tuning instruments that can produce sustained tones, beats can readily be recognized, tuning two tones to a unison will present a peculiar effect, when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively, as the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. It can be proven that the envelope of the maxima and minima form a wave frequency is half the difference between the frequencies of the two original waves. Instead, it is perceived as a variation in the amplitude of the first term in the expression above. It can be said that the lower frequency cosine term is an envelope for the higher frequency one, the frequency of the modulation is f1 + f2/2, that is, the average of the two frequencies. It can be noted that every second burst in the pattern is inverted. Each peak is replaced by a trough and vice versa, however, because the human ear is not sensitive to the phase of a sound, only its amplitude or intensity, only the magnitude of the envelope is heard. A physical interpretation is that when cos =1 the two waves are in phase and they interfere constructively, when it is zero, they are out of phase and interfere destructively. Beats occur also in more complex sounds, or in sounds of different volumes, beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the harmonic of the bass note beats with the second harmonic of the other note. Musicians commonly use interference beats to objectively check tuning at the unison, perfect fifth, piano and organ tuners even use a method involving counting beats, aiming at a particular number for a specific interval. The composer Alvin Lucier has written many pieces that feature interference beats as their main focus, composer Phill Niblocks music is entirely based on beating caused by microtonal differences. Binaural beats are heard when the right ear listens to a different tone than the left ear. Here, the tones do not interfere physically, but are summed by the brain in the olivary nucleus and this effect is related to the brains ability to locate sounds in three dimensions. Combination tone Gamelan tuning Heterodyne Consonance and dissonance Moiré pattern, a form of interference that generates new frequencies
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Formant
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A formant, as defined by James Jeans, is a harmonic of a note that is augmented by a resonance. The speech researcher Gunnar Fant defines formants as the peaks of the sound spectrum |P|. In speech science and phonetics, however, a formant is also used to mean an acoustic resonance of the human vocal tract. Thus, in phonetics, formant can mean either a resonance or the maximum that the resonance produces. A room can be said to have formants characteristic of that room, due to the way sound reflects from its walls. Room formants of this nature reinforce themselves by emphasizing specific frequencies and absorbing others, as exploited, for example, Formants are distinctive frequency components of the acoustic signal produced by speech or singing. The information that humans require to distinguish speech sounds can be represented purely quantitatively by specifying peaks in the amplitude/frequency spectrum. Most of these formants are produced by tube and chamber resonance, the formant with the lowest frequency is called F1, the second F2, and the third F3. Most often the two first formants, F1 and F2, are enough to disambiguate the vowel, an interactive demonstration of this can be found here. Nasal consonants usually have an additional formant around 2500 Hz, the liquid usually has an extra formant at 1500 Hz, whereas the English r sound is distinguished by a very low third formant. Plosives modify the placement of formants in the surrounding vowels, the time course of these changes in vowel formant frequencies are referred to as formant transitions. If the fundamental frequency of the vibration is higher than a resonance frequency of the system. This is most apparent in the example of opera singers. Spectrograms are used to visualise formants, the first two formants are important in determining the quality of vowels, and are frequently said to correspond to the open/close and front/back dimensions. As can be seen in Fig.1, vowels will almost always have four or more distinguishable formants, sometimes there are more than six. An example of how the vowels of a language or dialect may be plotted on a traditional auditory vowel chart, many writers have addressed the problem of finding an optimal alignment of the positions of vowels on formant plots with those on the conventional vowel quadrilateral. Two alternatives to the Mel scale are the Bark scale and the ERB-rate scale, a comparison of these three scales is shown by Hayward, p.141, and formant plots based on the Hertz scale and on the Bark scale are compared on p.153. Another strategy for improving formant plots that has widely adopted is to plot on the horizontal axis not the value of F2
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Fundamental frequency
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The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the frequency is the lowest frequency sinusoidal in the sum. In some contexts, the fundamental is usually abbreviated as f0, in other contexts, it is more common to abbreviate it as f1, the first harmonic. All sinusoidal and many non-sinusoidal waveforms are periodic, which is to say they repeat exactly over time. The period of a waveform is the T for which the equation is true. This means that this equation and a definition of the values over any interval of length T is all that is required to describe the waveform completely. Every waveform may be described using any multiple of this period, there exists a smallest period over which the function may be described completely and this period is the fundamental period. The fundamental frequency is defined as its reciprocal, f 0 =1 T Since the period is measured in units of time, when the time units are seconds, the frequency is in s −1, also known as Hertz. For a tube of length L with one end closed and the end open the wavelength of the fundamental harmonic is 4 L. If the ends of the tube are now both closed or both opened as in the last two animations, the wavelength of the fundamental harmonic becomes 2 L. By the same method as above, the frequency is found to be f 0 = v 2 L. At 20 °C the speed of sound in air is 343 m/s and this speed is temperature dependent and does increase at a rate of 0.6 m/s for each degree Celsius increase in temperature. The fundamental may be created by vibration over the length of a string or air column. The fundamental is one of the harmonics, a harmonic is any member of the harmonic series, an ideal set of frequencies that are positive integer multiples of a common fundamental frequency. The reason a fundamental is also considered a harmonic is because it is 1 times itself, the fundamental is the frequency at which the entire wave vibrates. Overtones are other components present at frequencies above the fundamental. All of the components that make up the total waveform, including the fundamental
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Spectral density
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The power spectrum S x x of a time series x describes the distribution of power into frequency components composing that signal. According to Fourier analysis any physical signal can be decomposed into a number of discrete frequencies, the statistical average of a certain signal or sort of signal as analyzed in terms of its frequency content, is called its spectrum. When the energy of the signal is concentrated around a time interval, especially if its total energy is finite. More commonly used is the spectral density, which applies to signals existing over all time. The power spectral density then refers to the energy distribution that would be found per unit time. Summation or integration of the spectral components yields the total power or variance, identical to what would be obtained by integrating x 2 over the time domain, the spectrum of a physical process x often contains essential information about the nature of x. For instance, the pitch and timbre of an instrument are immediately determined from a spectral analysis. The color of a source is determined by the spectrum of the electromagnetic waves electric field E as it fluctuates at an extremely high frequency. Obtaining a spectrum from time series such as these involves the Fourier transform, however this article concentrates on situations in which the time series is known or directly measured. The power spectrum is important in signal processing and in the statistical study of stochastic processes, as well as in many other branches of physics. Typically the process is a function of time but one can similarly discuss data in the domain being decomposed in terms of spatial frequency. Any signal that can be represented as an amplitude that varies in time has a frequency spectrum. This includes familiar entities such as light, musical notes, radio/TV. When these signals are viewed in the form of a frequency spectrum, in some cases the frequency spectrum may include a distinct peak corresponding to a sine wave component. And additionally there may be corresponding to harmonics of a fundamental peak. In physics, the signal might be a wave, such as an electromagnetic wave, the power spectral density of the signal describes the power present in the signal as a function of frequency, per unit frequency. Power spectral density is expressed in watts per hertz. When a signal is defined in terms only of a voltage, for instance, in this case power is simply reckoned in terms of the square of the signal, as this would always be proportional to the actual power delivered by that signal into a given impedance
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Harmonic
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A harmonic is any member of the harmonic series, the divergent infinite series. Every term of the series after the first is the mean of the neighboring terms. The phrase harmonic mean likewise derives from music, the term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. It is typically applied to repeating signals, such as sinusoidal waves, a harmonic of such a wave is a wave with a frequency that is a positive integer multiple of the frequency of the original wave, known as the fundamental frequency. The original wave is called the 1st harmonic, the following harmonics are known as higher harmonics. As all harmonics are periodic at the frequency, the sum of harmonics is also periodic at that frequency. On strings, harmonics that are bowed have a glassy, pure tone, harmonics may also be called overtones, partials or upper partials. In some music contexts, the harmonic, overtone and partial are used fairly interchangeably. Most acoustic instruments emit complex tones containing many individual partials, rather, a musical note is perceived as one sound, the quality or timbre of that sound being a result of the relative strengths of the individual partials. Oscillators that produce harmonic partials behave somewhat like one-dimensional resonators, and are long and thin. Wind instruments whose air column is open at one end, such as trumpets and clarinets. However they only produce partials matching the odd harmonics, at least in theory, the reality of acoustic instruments is such that none of them behaves as perfectly as the somewhat simplified theoretical models would predict. Partials whose frequencies are not integer multiples of the fundamental are referred to as inharmonic partials, antique singing bowls are known for producing multiple harmonic partials or multiphonics. An overtone is any partial higher than the lowest partial in a compound tone, the relative strengths and frequency relationships of the component partials determine the timbre of an instrument. This chart demonstrates how the three types of names are counted, In many musical instruments, it is possible to play the upper harmonics without the note being present. In a simple case this has the effect of making the note go up in pitch by an octave, in some cases it also changes the timbre of the note. This is part of the method of obtaining higher notes in wind instruments. The extended technique of playing multiphonics also produces harmonics, on string instruments it is possible to produce very pure sounding notes, called harmonics or flageolets by string players, which have an eerie quality, as well as being high in pitch
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Harmonic series (music)
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A harmonic series is the sequence of sounds where the base frequency of each sound is an integer multiple of the lowest base frequency. Pitched musical instruments are based on an approximate harmonic oscillator such as a string or a column of air. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves, interaction with the surrounding air causes audible sound waves, which travel away from the instrument. Because of the spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency. The musical timbre of a tone from such an instrument is determined by the relative strengths of each harmonic. A complex tone can be described as a combination of many simple periodic waves or partials, each with its own frequency of vibration, amplitude, a partial is any of the sine waves of which a complex tone is composed. A harmonic is any member of the series, an ideal set of frequencies that are positive integer multiples of a common fundamental frequency. The fundamental is also considered a harmonic because it is 1 times itself, a harmonic partial is any real partial component of a complex tone that matches an ideal harmonic. An inharmonic partial is any partial that does not match an ideal harmonic, Inharmonicity is a measure of the deviation of a partial from the closest ideal harmonic, typically measured in cents for each partial. Unpitched, or indefinite-pitched instruments, such as cymbals, gongs, or tam-tams make sounds that are rich in inharmonic partials, an overtone is any partial except the lowest partial. The term overtone does not imply harmonicity or inharmonicity and has no special meaning other than to exclude the fundamental. It is the relative strengths of the different overtones that gives an instrument its particular timbre, some electronic instruments, such as synthesizers, can play a pure frequency with no overtones. Synthesizers can also combine pure frequencies into more complex tones, such as to other instruments. Certain flutes and ocarinas are very nearly without overtones, in most pitched musical instruments, the fundamental is accompanied by other, higher-frequency harmonics. Thus shorter-wavelength, higher-frequency waves occur with varying prominence and give each instrument its characteristic tone quality, the fact that a string is fixed at each end means that the longest allowed wavelength on the string is twice the length of the string. Other allowed wavelengths are 1/2, 1/3, 1/4, 1/5, 1/6, theoretically, these shorter wavelengths correspond to vibrations at frequencies that are 2,3,4,5,6, etc. times the fundamental frequency. Physical characteristics of the vibrating medium and/or the resonator it vibrates against often alter these frequencies, the harmonic series is an arithmetic series. In terms of frequency, the difference between consecutive harmonics is therefore constant and equal to the fundamental, but because human ears respond to sound nonlinearly, higher harmonics are perceived as closer together than lower ones
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Inharmonicity
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In music, inharmonicity is the degree to which the frequencies of overtones depart from whole multiples of the fundamental frequency. Acoustically, a note perceived to have a distinct pitch in fact contains a variety of additional overtones. Many percussion instruments, such as cymbals, tam-tams, and chimes, create complex, any departure from this ideal harmonic series is known as inharmonicity. The less elastic the strings are, the more inharmonicity they exhibit, Music harmony and intonation depends strongly on the harmonicity of tones. An ideal, homogeneous, infinitesimally thin or infinitely flexible string or column of air has exactly harmonic modes of vibration. In any real musical instrument, the resonant body that produces the music tone—typically a string, wire, or column of air—deviates from this ideal and has some small or large amount of inharmonicity. For instance, a thick string behaves less as an ideal string and more like a cylinder. For this reason, a single tone played by a string instrument, brass instrument. The inharmonicity of a string depends on its characteristics, such as tension, stiffness. For instance, a string under low tension exhibits a high degree of inharmonicity. A wound string generally exhibits less inharmonicity than the equivalent solid string, in 1943, Schuck and Young were the first scientists to measure the spectral inharmonicity in piano tones. They found that the spectral partials in piano tones are progressively stretched—that is to say, in 1962, research by Harvey Fletcher and his collaborators indicated that the spectral inharmonicity is important for tones to sound piano-like. They proposed that inharmonicity is responsible for the warmth property common to real piano tones, according to their research synthesized piano tones sounded more natural when some inharmonicity was introduced. In general, electronic instruments that duplicate acoustic instruments must duplicate both the inharmonicity and the resulting stretched tuning of the original instruments. When pianos are tuned by piano tuners, the technician sometimes listens for the sound of beating when two notes are played together, and tunes to the point that minimizes roughness between tones. Piano tuners must deal with the inharmonicity of piano strings, which is present in different amounts in all of the ranges of the instrument, the result is that octaves are tuned slightly wider than the harmonic 2,1 ratio. Because of the problem of inharmonicity, electronic piano tuning devices used by piano technicians are not designed to tune according to a harmonic series. Rather, the use various means to duplicate the stretched octaves
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Mersenne's laws
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Mersennes laws are laws describing the frequency of oscillation of a stretched string or monochord, useful in musical tuning and musical instrument construction. The equation was first proposed by French mathematician and music theorist Marin Mersenne in his 1637 work Traité de lharmonie universelle. Mersennes laws govern the construction and operation of string instruments, pianos, harps, lower strings are thicker, thus having a greater mass per unit length. Higher-pitched strings typically are thinner, have higher tension, and may be shorter and this result does not differ substantially from Galileos, yet it is rightly known as Mersennes law, because Mersenne physically proved their truth through experiments. Mersenne investigated and refined these relationships by experiment but did not himself originate them, though his theories are correct, his measurements are not very exact, and his calculations where greatly improved by Joseph Sauveur through the use of acoustic beats and metronomes. These laws are derived from Mersennes equation 22, f 0 = ν λ =12 L F μ. The formula for the frequency is, f 0 =12 L F μ. Beat Cycloid Long-string instrument Mersenne conjectures Overtone Standing wave
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Overtone
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An overtone is any frequency greater than the fundamental frequency of a sound. Using the model of Fourier analysis, the fundamental and the overtones together are called partials, harmonics, or more precisely, harmonic partials, are partials whose frequencies are integer multiples of the fundamental. These overlapping terms are used when discussing the acoustic behavior of musical instruments. The model of Fourier analysis provides for the inclusion of inharmonic partials, when a resonant system such as a blown pipe or plucked string is excited, a number of overtones may be produced along with the fundamental tone. In simple cases, such as for most musical instruments, the frequencies of these tones are the same as the harmonics. Examples of exceptions include the drum, – a timpani whose first overtone is about 1.6 times its fundamental resonance frequency, gongs and cymbals. The human vocal tract is able to produce highly variable amplitudes of the overtones, called formants, most oscillators, from a guitar string to a flute, will naturally vibrate at a series of distinct frequencies known as normal modes. The lowest normal mode frequency is known as the fundamental frequency, often, when an oscillator is excited by, for example, plucking a guitar string, it will oscillate at several of its modal frequencies at the same time. So when a note is played, this gives the sensation of hearing other frequencies above the lowest frequency, timbre is the quality that gives the listener the ability to distinguish between the sound of different instruments. The timbre of an instrument is determined by which overtones it emphasizes and that is to say, the relative volumes of these overtones to each other determines the specific flavor or color of sound of that family of instruments. The intensity of each of these overtones is rarely constant for the duration of a note, over time, different overtones may decay at different rates, causing the relative intensity of each overtone to rise or fall independent of the overall volume of the sound. A carefully trained ear can hear these changes even in a single note and this is why the timbre of a note may be perceived differently when played staccato or legato. A driven non-linear oscillator, such as the folds, a blown wind instrument, or a bowed violin string will oscillate in a periodic. This generates the impression of sound at integer multiple frequencies of the known as harmonics, or more precisely. Thus, in music, overtones are often called harmonics, depending upon how the string is plucked or bowed, different overtones can be emphasized. However, some overtones in some instruments may not be of an integer multiplication of the fundamental frequency. High quality instruments are built in such a manner that their individual notes do not create disharmonious overtones. This is illustrated by the following, Consider a guitar string and this dead length actually varies from string to string, being more pronounced with thicker and/or stiffer strings
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Acoustic resonance
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Acoustic resonance is a phenomenon where acoustic systems amplify sound waves whose frequency matches one of its own natural frequencies of vibration. An acoustically resonant object usually has more than one resonance frequency and it will easily vibrate at those frequencies, and vibrate less strongly at other frequencies. It will pick out its resonance frequency from a complex excitation, in effect, it is filtering out all frequencies other than its resonance. Acoustic resonance is also important for hearing, for example, resonance of a stiff structural element, called the basilar membrane within the cochlea of the inner ear allows hair cells on the membrane to detect sound. Like mechanical resonance, acoustic resonance can result in failure of the vibrator. The classic example of this is breaking a glass with sound at the precise resonant frequency of the glass. In musical instruments, strings under tension, as in lutes, harps, guitars, pianos, violins and so forth, have resonant frequencies directly related to the mass, length, and tension of the string. The wavelength that will create the first resonance on the string is equal to twice the length of the string, higher resonances correspond to wavelengths that are integer divisions of the fundamental wavelength. The corresponding frequencies are related to the v of a wave traveling down the string by the equation f = n v 2 L where L is the length of the string. Higher tension and shorter lengths increase the resonant frequencies, when the string is excited with an impulsive function, the string vibrates at all the frequencies present in the impulse. Those frequencies that are not one of the resonances are quickly filtered out—they are attenuated—and all that is left is the vibrations that we hear as a musical note. String resonance occurs on string instruments, strings or parts of strings may resonate at their fundamental or overtone frequencies when other strings are sounded. For example, an A string at 440 Hz will cause an E string at 330 Hz to resonate, the resonance of a tube of air is related to the length of the tube, its shape, and whether it has closed or open ends. Musically useful tube shapes are conical and cylindrical, a pipe that is closed at one end is said to be stopped while an open pipe is open at both ends. Modern orchestral flutes behave as open pipes, clarinets and lip-reed instruments behave as closed cylindrical pipes, and saxophones, oboes. Vibrating air columns also have resonances at harmonics, like strings, an open tube is a tube in which both ends are open. The tube resonates at many frequencies or notes and its lowest resonance occurs at the same frequency as a closed tube of half its length. An open tube will resonate if there is a displacement antinode at each open end and these displacement antinodes are places where there is a maximum movement of air in and out of the ends of the tube
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Node (physics)
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A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the length of the vibrating string. The opposite of a node is an anti-node, a point where the amplitude of the wave is a maximum. These occur midway between the nodes, standing waves result when two sinusoidal wave trains of the same frequency are moving in opposite directions in the same space and interfere with each other. In a standing wave the nodes are a series of locations at equally spaced intervals where the amplitude is zero. At these points the two waves add with opposite phase and cancel each other out and they occur at intervals of half a wavelength. Midway between each pair of nodes are locations where the amplitude is maximum, at these points the two waves add with the same phase and reinforce each other. In cases where the two opposite wave trains are not the amplitude, they do not cancel perfectly, so the amplitude of the standing wave at the nodes is not zero. This occurs when the reflection at the boundary is imperfect and this is indicated by a finite standing wave ratio, the ratio of the amplitude of the wave at the antinode to the amplitude at the node. These can be visible by sprinkling sand on the surface. In transmission lines a voltage node is a current antinode, in this type the derivative of the waves amplitude is forced to zero at the boundary. So there is a maximum at the boundary, the first node occurs a quarter wavelength from the end. A sound wave consists of alternating cycles of compression and expansion of the wave medium, during compression, the molecules of the medium are forced together, resulting in the increased pressure and density. During expansion the molecules are forced apart, resulting in the decreased pressure, the number of nodes in a specified length is directly proportional to the frequency of the wave. Occasionally on a guitar, violin, or other stringed instrument, when the finger is placed on top of the string at a certain point, but does not push the string all the way down to the fretboard, a third node is created and a harmonic is sounded. During normal play when the frets are used, the harmonics are always present, with the artificial node method, the overtone is louder and the fundamental tone is quieter. If the finger is placed at the midpoint of the string, the first overtone is heard, when two additional nodes divide the string into thirds, this creates an octave and a perfect fifth
