The pitch of the vibration is determined by the length of the tube and by manual modifications of the effective length of the vibrating column of air. In the case of wind instruments, sound is produced by blowing through a reed. Using different air columns for different tones, such as in the pan flute and this method is used on nearly all brass instruments. Changing the length of the air column by lengthening and/or shortening the tube using a sliding mechanism. This method is used on the trombone and the slide whistle, changing the frequency of vibration through opening or closing holes in the side of the tube. This can be done by covering the holes with fingers or pressing a key which closes the hole and this method is used in nearly all woodwind instruments. Making the column of air vibrate at different harmonics without changing the length of the column of air, almost all wind instruments use the last method, often in combination with one of the others, to extend their register. A more accurate way to determine whether an instrument is brass or woodwind is to examine how the player produces sound, in brass instruments, the players lips vibrate, causing the air within the instrument to vibrate.
For example, the saxophone is typically made of brass, but is classified as an instrument because it produces sound with a vibrating reed. In the Hornbostel-Sachs scheme of musical instrument classification, wind instruments are classed as aerophones, sound production in all wind instruments depends on the entry of air into a flow-control valve attached to a resonant chamber. The resonator is typically a long cylindrical or conical tube, open at the far end, a pulse of high pressure from the valve will travel down the tube at the speed of sound. It will be reflected from the end as a return pulse of low pressure. Under suitable conditions, the valve will reflect the pulse back, with increased energy, Reed instruments such as the clarinet or oboe have a flexible reed or reeds at the mouthpiece, forming a pressure-controlled valve. Standing waves inside the tube will be odd multiples of a quarter-wavelength, with a pressure anti-node at the mouthpiece, the reed vibrates at a rate determined by the resonator.
For Lip Reed instruments, the controls the tension in their lips so that they vibrate under the influence of the air flow through them. They adjust the vibration so that the lips are most closed, and the air flow is lowest, standing waves inside the tube will be odd multiples of a quarter-wavelength, with a pressure anti-node at the mouthpiece, and a pressure node at the open end. For Air Reed instruments, the thin grazing air sheet flowing across an opening in the pipe interacts with an edge to generate sound. The jet is generated by the player, when blowing through a thin slit, for recorders and flue organ pipes this slit is manufactured by the instrument maker and has a fixed geometry
In mathematics, a square root of a number a is a number y such that y2 = a, in other words, a number y whose square is a. For example,4 and −4 are square roots of 16 because 42 =2 =16, every nonnegative real number a has a unique nonnegative square root, called the principal square root, which is denoted by √a, where √ is called the radical sign or radix. For example, the square root of 9 is 3, denoted √9 =3. The term whose root is being considered is known as the radicand, the radicand is the number or expression underneath the radical sign, in this example 9. Every positive number a has two roots, √a, which is positive, and −√a, which is negative. Together, these two roots are denoted ± √a, although the principal square root of a positive number is only one of its two square roots, the designation the square root is often used to refer to the principal square root. For positive a, the square root can be written in exponent notation. Square roots of numbers can be discussed within the framework of complex numbers.
In Ancient India, the knowledge of theoretical and applied aspects of square and square root was at least as old as the Sulba Sutras, a method for finding very good approximations to the square roots of 2 and 3 are given in the Baudhayana Sulba Sutra. Aryabhata in the Aryabhatiya, has given a method for finding the root of numbers having many digits. It was known to the ancient Greeks that square roots of positive numbers that are not perfect squares are always irrational numbers, numbers not expressible as a ratio of two integers. This is the theorem Euclid X,9 almost certainly due to Theaetetus dating back to circa 380 BC, the particular case √2 is assumed to date back earlier to the Pythagoreans and is traditionally attributed to Hippasus. Mahāvīra, a 9th-century Indian mathematician, was the first to state that square roots of negative numbers do not exist, a symbol for square roots, written as an elaborate R, was invented by Regiomontanus. An R was used for Radix to indicate square roots in Gerolamo Cardanos Ars Magna, according to historian of mathematics D. E.
Smith, Aryabhatas method for finding the root was first introduced in Europe by Cataneo in 1546. According to Jeffrey A. Oaks, Arabs used the letter jīm/ĝīm, the letter jīm resembles the present square root shape. Its usage goes as far as the end of the century in the works of the Moroccan mathematician Ibn al-Yasamin. The symbol √ for the root was first used in print in 1525 in Christoph Rudolffs Coss
A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a roulette, a curve generated by a curve rolling on another curve, the cycloid has been called The Helen of Geometers as it caused frequent quarrels among 17th-century mathematicians. Historians of mathematics have proposed several candidates for the discoverer of the cycloid, mathematical historian Paul Tannery cited similar work by the Syrian philosopher Iamblichus as evidence that the curve was likely known in antiquity. Galileo Galileis name was put forward at the end of the 19th century, in this work, Bovelles mistakes the arch traced by a rolling wheel as part of a larger circle with a radius 120% larger than the smaller wheel. Galileo originated the term cycloid and was the first to make a study of the curve. He discovered the ratio was roughly 3,1 but incorrectly concluded the ratio was an irrational fraction, around 1628, Gilles Persone de Roberval likely learned of the quadrature problem from Père Marin Mersenne and effected the quadrature in 1634 by using Cavalieris Theorem.
However, this work was not published until 1693, constructing the tangent of the cycloid dates to August 1638 when Mersenne received unique methods from Roberval, Pierre de Fermat and René Descartes. Mersenne passed these results along to Galileo, who gave them to his students Torricelli and Viviana and this result and others were published by Torricelli in 1644, which is the first printed work on the cycloid. This led to Roberval charging Torricelli with plagiarism, with the cut short by Torricellis early death in 1647. In 1658, Blaise Pascal had given up mathematics for theology but, while suffering from a toothache and his toothache disappeared, and he took this as a heavenly sign to proceed with his research. Eight days he had completed his essay and, to publicize the results, Pascal proposed three questions relating to the center of gravity and volume of the cycloid, with the winner or winners to receive prizes of 20 and 40 Spanish doubloons. Pascal and Senator Carcavy were the judges, and neither of the two submissions were judged to be adequate.
While the contest was ongoing, Christopher Wren sent Pascal a proposal for a proof of the rectification of the cycloid, wallis published Wrens proof in Walliss Tractus Duo, giving Wren priority for the first published proof. In 1686, Gottfried Wilhelm Leibniz used analytic geometry to describe the curve with a single equation, in 1696, Johann Bernoulli posed the brachistochrone problem, the solution of which is a cycloid. For given t, the centre lies at x = rt. Solving for t and replacing, the Cartesian equation is found to be, an equation for the cycloid of the form y = f with a closed-form expression for the right-hand side is not possible. When y is viewed as a function of x, the cycloid is differentiable everywhere except at the cusps, the map from t to is a differentiable curve or parametric curve of class C∞ and the singularity where the derivative is 0 is an ordinary cusp. A cycloid segment from one cusp to the next is called an arch of the cycloid, the first arch of the cycloid consists of points such that 0 ≤ t ≤2 π
Joseph Sauveur was a French mathematician and physicist. He was a professor of mathematics and in 1696 became a member of the French Academy of Sciences, Joseph Sauveur was the son of a provincial notary. At seventeen, his uncle agreed to finance his studies in philosophy, however, discovered Euclid and turned to anatomy and botany. He soon met Cordemoy, reader to the son of Louis XIV, despite his handicap, Joseph promptly began teaching mathematics to the Dauphines pages and to a number of princes, among them Eugene of Savoy. By 1680, he was something of a pet at court, in 1681, Sauveur did the mathematical calculations for a waterworks project for the Grand Condés estate at Chantilly, working with Edmé Mariotte, the father of French hydraulics. Condé became very fond of Sauveur and severely reprimanded anyone who laughed at the speech impediment. Condé would invite Saveur to stay at Chantilly and it was there that Sauveur did his work on hydrostatics. During the summer of 1689, Sauveur was chosen to be the science and mathematics teacher for the Duke of Chartres, Louis XIVs nephew.
For the prince, he drew up a manuscript outlining the elements of geometry and, in collaboration with Marshal Vauban, another of the princes teachers was Étienne Loulié, a musician engaged to teach him the elements of musical theory and notation. Loulié and Sauveur joined forces to show the prince how mathematics, remnants of this joint course have survived in Sauveurs manuscript treatise on the theory of music, and in Louliés Éléments. In the years followed, Sauveur taught mathematics to various princes of the royal family. Circa 1694, Sauveur began working with Loulié on the science of sound, as Fontenelle put it, Sauveur laid out a vast plan that amounted to the discovery of an unknown country, and that created for him a personal empire, the study of acoustical sound. But, as Fontenelle pointed out, He had neither a voice nor hearing and he was reduced to borrowing the voice and the ear of someone else. And in return he gave hitherto unknown demonstrations to musicians, the Duke of Chartres did everything he could to make the undertaking successful.
This pushed him all the way to the music of the ancient Greeks and Romans, the Arabs, the Turks, Sauveur is known principally for his detailed studies on acoustics. Indeed, he has credited with coining the term acoustique. He created a measure of intervals concerning the octave, demi-heptaméride, 1/602 part of an octave, 1/2 of an eptaméride. Decaméride, 1/3010 part of an octave, 1/10 of an eptaméride Also 1/55 of an octave would become known as a Sauveur comma
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, walls, 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, windows, flanking 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 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
A monochord, 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 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 and ratios, sense-perception and mathematical reason, music 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, string, moveable bridge, fixed bridge, calibration marks, belly or resonating box, instruments derived from the monochord include the guqin, dan bau, 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
Sir James Hopwood Jeans OM FRS was an English physicist and mathematician. Born in Ormskirk, the son of William Tulloch Jeans, Jeans was educated at Merchant Taylors School, Wilsons Grammar School and Trinity College, Cambridge. He told them that he could not guarantee that they would come out higher than fifteenth in the list of wranglers, but he understood that they would never regret it. They accepted his advice, and went to R. R. Webb, Walker accordingly took Jeans himself, and the result was a triumph. Jeans was bracketed second wrangler with J. F. Cameron. R. W. H. T. Hudson was Senior Wrangler and G. H, Jeans was elected Fellow of Trinity College in October 1901, and taught at Cambridge, but went to Princeton University in 1904 as a professor of applied mathematics. He returned to Cambridge in 1910 and he made important contributions in many areas of physics, including quantum theory, the theory of radiation and stellar evolution. This theory is not accepted today, along with Arthur Eddington, is a founder of British cosmology.
In 1928 Jeans was the first to conjecture a steady state cosmology based on a continuous creation of matter in the universe. This theory fell out of favour when the 1965 discovery of the microwave background was widely interpreted as the tell-tale signature of the Big Bang. His scientific reputation is grounded in the monographs The Dynamical Theory of Gases, Theoretical Mechanics and these books made Jeans fairly well known as an expositor of the revolutionary scientific discoveries of his day, especially in relativity and physical cosmology. In 1939, the Journal of the British Astronomical Association reported that Jeans was going to stand as a candidate for parliament for the Cambridge University constituency, the election, expected to take place in 1939 or 1940 did not take place until 1945, and without his involvement. He wrote the book Physics and Philosophy where he explores the different views on reality from two different perspectives and philosophy, on his religious views, Jeans was an agnostic Freemason.
Jeans married twice, first to the American poet Charlotte Tiffany Mitchell in 1907, one of Jeans major discoveries, named Jeans length, is a critical radius of an interstellar cloud in space. It depends on the temperature, and density of the cloud, Jeans helped to discover the Rayleigh–Jeans law, which relates the energy density of black-body radiation to the temperature of the emission source. F =8 π c k B T λ4 Jeans is credited with calculating the rate of escape from a planet due to kinetic energy of the gas molecules. The stream of knowledge is heading towards a non-mechanical reality, the Universe begins to more like a great thought than like a great machine. Mind no longer appears to be an intruder into the realm of matter. We ought rather hail it as the creator and governor of the realm of matter and he replied, I incline to the idealistic theory that consciousness is fundamental, and that the material universe is derivative from consciousness, not consciousness from the material universe
A musical instrument is an instrument created or adapted to make musical sounds. In principle, any object that produces sound can be a musical instrument—it is through purpose that the object becomes a musical instrument, the history of musical instruments dates to the beginnings of human culture. Early musical instruments may have used for ritual, such as a trumpet to signal success on the hunt. Cultures eventually developed composition and performance of melodies for entertainment, Musical instruments evolved in step with changing applications. The date and origin of the first device considered an instrument is disputed. The oldest object that some refer to as a musical instrument. Some consensus dates early flutes to about 37,000 years ago, many early musical instruments were made from animal skins, bone and other non-durable materials. Musical instruments developed independently in many populated regions of the world, contact among civilizations caused rapid spread and adaptation of most instruments in places far from their origin.
By the Middle Ages, instruments from Mesopotamia were in maritime Southeast Asia, development in the Americas occurred at a slower pace, but cultures of North and South America shared musical instruments. By 1400, musical instrument development slowed in areas and was dominated by the Occident. Musical instrument classification is a discipline in its own right, Instruments can be classified by their effective range, their material composition, their size, etc. However, the most common method, Hornbostel-Sachs, uses the means by which they produce sound. The academic study of instruments is called organology. Once humans moved from making sounds with their bodies—for example, by using objects to create music from sounds. Primitive instruments were designed to emulate natural sounds, and their purpose was ritual rather than entertainment. The concept of melody and the pursuit of musical composition were unknown to early players of musical instruments. A player sounding a flute to signal the start of a hunt does so without thought of the notion of making music.
Musical instruments are constructed in an array of styles and shapes
String instruments, stringed instruments, or chordophones are musical instruments that produce sound from vibrating strings when the performer plays or sounds the strings in some manner. Musicians play some string instruments by plucking the strings with their fingers or a plectrum—and others by hitting the strings with a wooden hammer or by rubbing the strings with a bow. In some keyboard instruments, such as the harpsichord or piano, with bowed instruments, the player rubs the strings with a horsehair bow, causing them to vibrate. With a hurdy-gurdy, the musician operates a wheel that rubs the strings. Bowed instruments include the string instruments of the Classical music orchestra. All of the string instruments can be plucked with the fingers. Some types of string instrument are mainly plucked, such as the harp, in the Hornbostel-Sachs scheme of musical instrument classification, used in organology, string instruments are called chordophones. Other examples include the sitar, banjo, ukulele, in most string instruments, the vibrations are transmitted to the body of the instrument, which often incorporates some sort of hollow or enclosed area.
The body of the instrument vibrates, along with the air inside it, the vibration of the body of the instrument and the enclosed hollow or chamber make the vibration of the string more audible to the performer and audience. The body of most string instruments is hollow, however—such as electric guitar and other instruments that rely on electronic amplification—may have a solid wood body. Archaeological digs have identified some of the earliest stringed instruments in Ancient Mesopotamian sites, like the lyres of Ur, the development of lyre instruments required the technology to create a tuning mechanism to tighten and loosen the string tension. During the medieval era, instrument development varied from country to country, Middle Eastern rebecs represented breakthroughs in terms of shape and strings, with a half a pear shape using three strings. Early versions of the violin and fiddle, by comparison, emerged in Europe through instruments such as the gittern, a four stringed precursor to the guitar and these instruments typically used catgut and other materials, including silk, for their strings.
String instrument design refined during the Renaissance and into the Baroque period of musical history and guitars became more consistent in design, and were roughly similar to what we use in the 2000s. At the same time, the 19th century guitar became more associated with six string models. In big bands of the 1920s, the guitar played backing chords. The development of guitar amplifiers, which contained a power amplifier, the development of the electric guitar provided guitarists with an instrument that was built to connect to guitar amplifiers. Electric guitars have magnetic pickups, volume control knobs and an output jack, in the 1960s, more powerful guitar amplifiers were developed, called stacks
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The term vibration is used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current power, the simplest mechanical oscillating system is a weight attached to a linear spring subject to only weight and tension. Such a system may be approximated on an air table or ice surface, the system is in an equilibrium state when the spring is static. If the system is displaced from the equilibrium, there is a net restoring force on the mass, tending to bring it back to equilibrium. However, in moving the back to the equilibrium position, it has acquired momentum which keeps it moving beyond that position. If a constant force such as gravity is added to the system, the time taken for an oscillation to occur is often referred to as the oscillatory period. All real-world oscillator systems are thermodynamically irreversible and this means there are dissipative processes such as friction or electrical resistance which continually convert some of the energy stored in the oscillator into heat in the environment.
Thus, oscillations tend to decay with time there is some net source of energy into the system. The simplest description of this process can be illustrated by oscillation decay of the harmonic oscillator. In addition, a system may be subject to some external force. In this case the oscillation is said to be driven, some systems can be excited by energy transfer from the environment. This transfer typically occurs where systems are embedded in some fluid flow, at sufficiently large displacements, the stiffness of the wing dominates to provide the restoring force that enables an oscillation. The harmonic oscillator and the systems it models have a degree of freedom. More complicated systems have more degrees of freedom, for two masses and three springs. In such cases, the behavior of each variable influences that of the others and this leads to a coupling of the oscillations of the individual degrees of freedom. For example, two pendulum clocks mounted on a wall will tend to synchronise. This phenomenon was first observed by Christiaan Huygens in 1665, more special cases are the coupled oscillators where energy alternates between two forms of oscillation
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, 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 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