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Sine Wave
A SINE WAVE or SINUSOID is a mathematical curve that describes a smooth repetitive oscillation . A sine wave is a continuous wave . It is named after the function 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 (t) is: y ( t ) = A sin ( 2 f t + ) = A sin ( t + ) {displaystyle y(t)=Asin(2pi ft+varphi )=Asin(omega t+varphi )} where: * A = the amplitude , the peak deviation of the function from zero. * f = the ordinary frequency , the number of oscillations (cycles) that occur each second of time. * ω = 2πf, the angular frequency , the rate of change of the function argument in units of radians per second* {displaystyle varphi } = the phase , specifies (in radians) where in its cycle the oscillation is at t = 0
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Timbre
In music , TIMBRE (/ˈtæmbər/ TAM-bər , also known as TONE COLOR or TONE QUALITY from psychoacoustics ), is the perceived sound quality of a musical note , sound, or tone. Timbre
Timbre
distinguishes different types of sound production, such as choir voices and musical instruments , such as string instruments , wind instruments , and percussion instruments. It also enables listeners to distinguish different instruments in the same category (e.g. an oboe and a clarinet ). The physical characteristics of sound that determine the perception of timbre include spectrum and envelope . Singers and instrumental musicians can change the timbre of the music they are singing/playing by using different singing or playing techniques
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Musical Note
In music , the term NOTE has three primary meanings: * A sign used in musical notation to represent the relative duration and pitch of a sound (♪, ♫); * A pitched sound itself. * A pitch class .Notes are the building blocks of much written music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis . The term note can be used in both generic and specific senses: one might say either "the piece ' Happy Birthday to You
Happy Birthday to You
' begins with two notes having the same pitch", or "the piece begins with two repetitions of the same note". In the former case, one uses note to refer to a specific musical event; in the latter, one uses the term to refer to a class of events sharing the same pitch
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Harmonics
A HARMONIC is any member of the harmonic series , a divergent infinite series. Its name derives from the concept of overtones , or harmonics in musical instruments : the wavelengths of the overtones of a vibrating string or a column of air (as with a tuba ) are derived from the string's (or air column's) fundamental wavelength. Every term of the series (i.e., the higher harmonics) after the first is the "harmonic 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
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Ear
The EAR is the organ of hearing and, in mammals, balance . In mammals, the ear is usually described as having three parts—the outer ear , middle ear and the inner ear . The outer ear consists of the pinna and the ear canal . Since the outer ear is the only visible portion of the ear in most animals, the word "ear" often refers to the external part alone. The middle ear includes the tympanic cavity and the three ossicles . The inner ear sits in the bony labyrinth , and contains structures which are key to several senses: the semicircular canals , which enable balance and eye tracking when moving; the utricle and saccule , which enable balance when stationary; and the cochlea , which enables hearing. The ears of vertebrates are placed somewhat symmetrically on either side of the head, an arrangement that aids sound localisation
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Dot Product
In mathematics , the DOT PRODUCT or SCALAR PRODUCT is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors ) and returns a single number. In Euclidean geometry , the dot product of the Cartesian coordinates of two vectors is widely used and often called INNER PRODUCT (or rarely PROJECTION PRODUCT); see also inner product space . Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. In modern geometry , Euclidean spaces are often defined by using vector spaces
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Head Start (positioning)
In positioning , a 'head start" is a start in advance of the starting position of others in competition, or simply toward the finish line or desired outcome. Depending on the situation, a head start may be inherent, obtained by special privilege, earned through one's accomplishments, or granted mercifully by an opponent. While not guaranteeing success, a head start will increase such chances. CONTENTS* 1 In sports * 1.1 In baseball * 2 In traffic * 3 In achieving a goal * 4 See also * 5 References IN SPORTSIn competitive sports, such as a race , a head start refers to a start ahead of other competitors, allowing a shorter distance to the finish line. The idea of a head start may seem unfair. But in some cases, a head start is an advantage that may be earned by one more of the competitors. Also, adults who are racing against children may provide children with a head start, knowing the children are slower, and wanting to allow them a chance to win
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Noise (acoustic)
NOISE is unwanted sound judged to be unpleasant, loud or disruptive to hearing. From a physics standpoint, noise is indistinguishable from sound, as both are vibrations through a medium, such as air or water. The difference arises when the brain receives and perceives a sound. In experimental sciences , noise can refer to any random fluctuations of data that hinders perception of an expected signal. Acoustic noise is any sound in the acoustic domain, either deliberate (e.g., music or speech) or unintended. In contrast, noise in electronics may not be audible to the human ear and may require instruments for detection. In audio engineering , noise can refer to the unwanted residual electronic noise signal that gives rise to acoustic noise heard as a hiss. This signal noise is commonly measured using A-weighting or ITU-R 468 weighting
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Time Series
A TIME SERIES is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides , counts of sunspots , and the daily closing value of the Dow Jones Industrial Average
Dow Jones Industrial Average
. Time
Time
series are very frequently plotted via line charts . Time
Time
series are used in statistics , signal processing , pattern recognition , econometrics , mathematical finance , weather forecasting , intelligent transport and trajectory forecasting, earthquake prediction , electroencephalography , control engineering , astronomy , communications engineering , and largely in any domain of applied science and engineering which involves temporal measurements
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Helmholtz Equation
In mathematics, the HELMHOLTZ EQUATION, named for Hermann von Helmholtz , is the partial differential equation 2 A + k 2 A = 0 {displaystyle nabla ^{2}A+k^{2}A=0} where ∇2 is the Laplacian , k is the wavenumber , and A is the amplitude . CONTENTS * 1 Motivation and uses * 2 Solving the Helmholtz equation
Helmholtz equation
using separation of variables * 2.1 Vibrating membrane * 2.2 Three-dimensional solutions * 3 Paraxial approximation * 4 Inhomogeneous Helmholtz equation
Helmholtz equation
* 5 Notes * 6 See also * 7 References * 8 External links MOTIVATION AND USESThe Helmholtz equation
Helmholtz equation
often arises in the study of physical problems involving partial differential equations (PDEs) in both space and time
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Instantaneous Phase
INSTANTANEOUS PHASE and INSTANTANEOUS FREQUENCY are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (or "local phase" or simply "phase") of a complex-valued function s(t), is the real-valued function: ( t ) = arg { s ( t ) } , {displaystyle phi (t)=arg{s(t)},} where ARG is the complex argument function . And for a real-valued function s(t), it is determined from the function's analytic representation , sa(t): ( t ) = arg { s a ( t ) } = arg { s ( t ) + j s ( t ) } . {displaystyle {begin{aligned}phi (t)&=arg{s_{mathrm {a} }(t)}\ width:25.79ex; height:6.176ex;" alt="{displaystyle {begin{aligned}phi (t)&=arg{s_{mathrm {a} }(t)}\"> Instantaneous phase vs time
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Harmonic Series (mathematics)
In mathematics , the HARMONIC SERIES is the divergent infinite series : n = 1 1 n = 1 + 1 2 + 1 3 + 1 4 + 1 5 + {displaystyle sum _{n=1}^{infty }{frac {1}{n}}=1+{frac {1}{2}}+{frac {1}{3}}+{frac {1}{4}}+{frac {1}{5}}+cdots } Its name derives from the concept of overtones , or harmonics in music : the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's fundamental wavelength . Every term of the series after the first is the harmonic mean of the neighboring terms; the phrase harmonic mean likewise derives from music
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Tension (physics)
In physics , TENSION describes the pulling force transmitted axially by means of a string, cable, chain, or similar one-dimensional continuous object, or by each end of a rod, truss member, or similar three-dimensional object; tension can also be described as the action-reaction pair of forces acting at each end of said elements. Tension is the opposite of compression . At the atomic level, when atoms or molecules are pulled apart from each other and gain potential energy with a restoring force still existing, the restoring force creates what is also called tension. Each end of a string or rod under such tension will pull on the object it is attached to, to restore the string/rod to its relaxed length. In physics, tension, as a transmitted force, as an action-reaction pair of forces, or as a restoring force, is a force and has the units of force measured in newtons (or sometimes pounds-force )
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Standing Wave
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 , and the locations where the amplitude is maximum are called antinodes . Standing waves were first noticed by Michael Faraday
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" (German: stehende Welle or Stehwelle) around 1860 and demonstrated the phenomenon in his classic experiment with vibrating strings. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions
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Wave Number
In the physical sciences , the WAVENUMBER (also WAVE NUMBER) is the spatial frequency of a wave , either in cycles per unit distance or radians per unit distance. It can be envisaged as the number of waves that exist over a specified distance (analogous to frequency being the number of cycles or radians per unit time). In multidimensional systems , the wavenumber is the magnitude of the wave vector . The space of wave vectors is called reciprocal space . Wave
Wave
numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction
X-ray diffraction
, neutron diffraction , and elementary particle physics. For quantum mechanical waves, wavenumber multiplied by Planck\'s constant is the canonical momentum . Wavenumber
Wavenumber
can be used to specify quantities other than spatial frequency
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Light
LIGHT is electromagnetic radiation within a certain portion of the electromagnetic spectrum . The word usually refers to VISIBLE LIGHT, which is visible to the human eye and is responsible for the sense of sight . Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), or 4.00 × 10−7 to 7.00 × 10−7 m, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths). This wavelength means a frequency range of roughly 430–750 terahertz (THz). The main source of light on Earth
Earth
is the Sun
Sun
. Sunlight
Sunlight
provides the energy that green plants use to create sugars mostly in the form of starches, which release energy into the living things that digest them. This process of photosynthesis provides virtually all the energy used by living things
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