In physics, a wave is a disturbance that travels through space and time, usually accompanied by the transfer of energy.

Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass transport. They consist, instead, of oscillations or vibrations around almost fixed locations. For example, a cork on rippling water will bob up and down, staying in about the same place while the wave itself moves onwards.

One type of wave is a mechanical wave, which propagates through a medium in which the substance of this medium is deformed. The deformation reverses itself owing to restoring forces resulting from its deformation. For example, sound waves propagate via air molecules bumping into their neighbors. This transfers some energy to these neighbors, which will cause a cascade of collisions between neighbouring molecules. When air molecules collide with their neighbors, they also bounce away from them (restoring force). This keeps the molecules from continuing to travel in the direction of the wave.

Another type of wave can travel through a vacuum, e.g. electromagnetic radiation (including visible light, ultraviolet radiation, infrared radiation, gamma rays, X-rays, and radio waves). This type of wave consists of periodic oscillations in electrical and magnetic fields.

A main distinction can be made between transverse and longitudinal waves. Transverse waves occur when a disturbance sends waves perpendicular (at right angles) to the original wave. Longitudinal waves occur when a disturbance sends waves in the same direction as the original wave.

Waves are described by a wave equation which sets out how the disturbance proceeds over time. The mathematical form of this equation varies depending on the type of wave.

General features

A single, all-encompassing definition for the term ''wave'' is not straightforward. A vibration can be defined as a ''back-and-forth'' motion around a reference value. However, a vibration is not necessarily a wave. An attempt to define the necessary and sufficient characteristics that qualify a phenomenon to be called a ''wave'' results in a fuzzy border line.

The term ''wave'' is often intuitively understood as referring to a transport of spatial disturbances that are generally not accompanied by a motion of the medium occupying this space as a whole. In a wave, the energy of a vibration is moving away from the source in the form of a disturbance within the surrounding medium . However, this notion is problematic for a standing wave (for example, a wave on a string), where energy is moving in both directions equally, or for electromagnetic / light waves in a vacuum, where the concept of medium does not apply. There are water waves on the ocean surface; light waves emitted by the Sun; microwaves used in microwave ovens; radio waves broadcast by radio stations; and sound waves generated by radio receivers, telephone handsets and living creatures (as voices).

It may appear that the description of waves is closely related to their physical origin for each specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a mechanical rather than an electromagnetic wave transfer caused by vibration. Concepts such as mass, momentum, inertia, or elasticity, become therefore crucial in describing acoustic (as distinct from optic) wave processes. This difference in origin introduces certain wave characteristics particular to the properties of the medium involved. For example, in the case of air: vortices, radiation pressure, shock waves etc.; in the case of solids: Rayleigh waves, dispersion etc.; and so on.

Other properties, however, although they are usually described in an origin-specific manner, may be generalized to all waves. For such reasons, wave theory represents a particular branch of physics that is concerned with the properties of wave processes independently from their physical origin. For example, based on the mechanical origin of acoustic waves, a moving disturbance in space–time can exist if and only if the medium involved is neither infinitely stiff nor infinitely pliable. If all the parts making up a medium were rigidly ''bound'', then they would all vibrate as one, with no delay in the transmission of the vibration and therefore no wave motion. This is impossible because it would violate general relativity. On the other hand, if all the parts were independent, then there would not be any transmission of the vibration and again, no wave motion. Although the above statements are meaningless in the case of waves that do not require a medium, they reveal a characteristic that is relevant to all waves regardless of origin: within a wave, the phase of a vibration (that is, its position within the vibration cycle) is different for adjacent points in space because the vibration reaches these points at different times.

Similarly, wave processes revealed from the study of waves other than sound waves can be significant to the understanding of sound phenomena. A relevant example is Thomas Young's principle of interference (Young, 1802, in ). This principle was first introduced in Young's study of light and, within some specific contexts (for example, scattering of sound by sound), is still a researched area in the study of sound.

Mathematical description of one-dimensional waves

Wave equation

Consider a traveling transverse wave (which may be a pulse) on a string (the medium). Consider the string to have a single spatial dimension. Consider this wave as traveling

in the $x$ direction in space. E.g., let the positive $x$ direction be to the right, and the negative $x$ direction be to the left.

with constant amplitude $u$

with constant velocity $v$, where $v$ is

*independent of wavelength (no dispersion)

independent of amplitude (linear media, not nonlinear).

with constant waveform, or shape

This wave can then be described by the two-dimensional functions

: $u(x,\; \backslash \; t)\; =\; F(x\; -\; v\; \backslash \; t)$ (waveform $F$ traveling to the right) : $u(x,\; \backslash \; t)\; =\; G(x\; +\; v\; \backslash \; t)$ (waveform $G$ traveling to the left)

or, more generally, by d'Alembert's formula:

:$u(x,t)=F(x-vt)+G(x+vt).\; \backslash ,$

representing two component waveforms $F$ and $G$ traveling through the medium in opposite directions. This wave can also be represented by the partial differential equation

:$\backslash frac\{1\}\{v^2\}\backslash frac\{\backslash partial^2\; u\}\{\backslash partial\; t^2\}=\backslash frac\{\backslash partial^2\; u\}\{\backslash partial\; x^2\}.\; \backslash ,$

General solutions are based upon Duhamel's principle.

Wave forms

The form or shape of ''F'' in d'Alembert's formula involves the argument ''x − vt''. Constant values of this argument correspond to constant values of ''F'', and these constant values occur if ''x'' increases at the same rate that ''vt'' increases. That is, the wave shaped like the function ''F'' will move in the positive ''x''-direction at velocity ''v'' (and ''G'' will propagate at the same speed in the negative ''x''-direction).

In the case of a periodic function ''F'' with period ''λ'', that is, ''F''(''x + λ'' − ''vt'') = ''F''(''x '' − ''vt''), the periodicity of ''F'' in space means that a snapshot of the wave at a given time ''t'' finds the wave varying periodically in space with period ''λ'' (the wavelength of the wave). In a similar fashion, this periodicity of ''F'' implies a periodicity in time as well: ''F''(''x'' − ''v(t + T)'') = ''F''(''x '' − ''vt'') provided ''vT'' = ''λ'', so an observation of the wave at a fixed location ''x'' finds the wave undulating periodically in time with period ''T = λ''/''v''.

Amplitude and modulation

The amplitude of a wave may be constant (in which case the wave is a ''c.w.'' or ''continuous wave''), or may be ''modulated'' so as to vary with time and/or position. The outline of the variation in amplitude is called the ''envelope'' of the wave. Mathematically, the modulated wave can be written in the form:

:$u(x,\; \backslash \; t)\; =\; A(x,\; \backslash \; t)\backslash sin\; (kx\; -\; \backslash omega\; t\; +\; \backslash phi)\; \backslash \; ,$

where $A(x,\backslash \; t)$ is the amplitude envelope of the wave, $k$ is the ''wavenumber'' and $\backslash phi$ is the ''phase''. If the group velocity $v\_g$ (see below) is wavelength-independent, this equation can be simplified as:

:$u(x,\; \backslash \; t)\; =\; A(x\; -\; v\_g\; \backslash \; t)\backslash sin\; (kx\; -\; \backslash omega\; t\; +\; \backslash phi)\; \backslash \; ,$

showing that the envelope moves with the group velocity and retains its shape. Otherwise, in cases where the group velocity varies with wavelength, the pulse shape changes in a manner often described using an ''envelope equation''.

Phase velocity and group velocity

There are two velocities that are associated with waves, the phase velocity and the group velocity. To understand them, one must consider several types of waveform. For simplification, examination is restricted to one dimension.

The most basic wave (a form of plane wave) may be expressed in the form:

:$\backslash psi\; (x,\; \backslash \; t)\; =\; A\; e^\{i\; \backslash left(\; kx\; -\; \backslash omega\; t\; \backslash right)\}\; \backslash \; ,$

which can be related to the usual sine and cosine forms using Euler's formula. Rewriting the argument, $kx-\backslash omega\; t\; =\; (\backslash frac\{2\backslash pi\}\{\backslash lambda\})(x\; -\; vt)$, makes clear that this expression describes a vibration of wavelength $\backslash lambda\; =\; \backslash frac\{2\backslash pi\}\{k\}$ traveling in the ''x''-direction with a constant ''phase velocity'' $v\_p\; =\; \backslash frac\{\backslash omega\}\{k\}\backslash ,$.

The other type of wave to be considered is one with localized structure described by an envelope, which may be expressed mathematically as, for example:

:$\backslash psi\; (x,\; \backslash \; t)\; =\; \backslash int\_\{-\backslash infty\}\; ^\{\backslash infty\}\backslash \; dk\_1\; \backslash \; A(k\_1)\backslash \; e^\{i\backslash left(k\_1x\; -\; \backslash omega\; t\; \backslash right)\}\; \backslash \; ,$

where now ''A(k''₁'')'' (the integral is the inverse fourier transform of A(k1)) is a function exhibiting a sharp peak in a region of wave vectors Δ''k'' surrounding the point ''k''₁ = ''k''. In exponential form:

:$A\; =\; A\_o\; (k\_1)\; e^\; \{i\; \backslash alpha\; (k\_1)\}\; \backslash \; ,$

with ''A''_o the magnitude of ''A''. For example, a common choice for ''A''_o is a Gaussian wave packet:

:$A\_o\; (k\_1)\; =\; N\backslash \; e^\{-\backslash sigma^2\; (k\_1-k)^2\; /\; 2\}\; \backslash \; ,$

where σ determines the spread of ''k''₁-values about ''k'', and ''N'' is the amplitude of the wave.

The exponential function inside the integral for ψ oscillates rapidly with its argument, say φ(''k''₁), and where it varies rapidly, the exponentials cancel each other out, interfere destructively, contributing little to ψ. However, an exception occurs at the location where the argument φ of the exponential varies slowly. (This observation is the basis for the method of stationary phase for evaluation of such integrals.) The condition for φ to vary slowly is that its rate of change with ''k''₁ be small; this rate of variation is:

:$\backslash left\; .\; \backslash frac\{d\; \backslash varphi\; \}\{d\; k\_1\}\; \backslash right\; |\; \_\{k\_1\; =\; k\; \}\; =\; x\; -\; t\; \backslash left\; .\; \backslash frac\{d\; \backslash omega\}\{dk\_1\}\backslash right\; |\; \_\{k\_1\; =\; k\; \}\; +\backslash left\; .\; \backslash frac\{d\; \backslash alpha\}\{d\; k\_1\}\backslash right\; |\; \_\{k\_1\; =\; k\; \}\; \backslash \; ,$

where the evaluation is made at ''k''₁ = ''k'' because ''A(k''₁'')'' is centered there. This result shows that the position ''x'' where the phase changes slowly, the position where ψ is appreciable, moves with time at a speed called the ''group velocity'':

:$v\_g\; =\; \backslash frac\{d\; \backslash omega\}\{dk\}\; \backslash \; .$

The group velocity therefore depends upon the dispersion relation connecting ω and ''k''. For example, in quantum mechanics the energy of a particle represented as a wave packet is ''E'' = ħω = (ħ''k'')²/(2''m''). Consequently, for that wave situation, the group velocity is

:$v\_g\; =\; \backslash frac\; \{\backslash hbar\; k\}\{m\}\; \backslash \; ,$

showing that the velocity of a localized particle in quantum mechanics is its group velocity. Because the group velocity varies with ''k'', the shape of the wave packet broadens with time, and the particle becomes less localized. In other words, the velocity of the constituent waves of the wave packet travel at a rate that varies with their wavelength, so some move faster than others, and they cannot maintain the same interference pattern as the wave propagates.

Sinusoidal waves

Mathematically, the most basic wave is the (spatially) one-dimensional sine wave (or ''harmonic wave'' or ''sinusoid'') with an amplitude $u$ described by the equation:

:$u(x,\; \backslash \; t)=\; A\; \backslash sin\; (kx\; -\; \backslash omega\; t\; +\; \backslash phi)\; \backslash \; ,$

where

$A$ is the maximum amplitude of the wave, maximum distance from the highest point of the disturbance in the medium (the crest) to the equilibrium point during one wave cycle. In the illustration to the right, this is the maximum vertical distance between the baseline and the wave.

$x$ is the space coordinate

$t$ is the time coordinate

$k$ is the wavenumber

$\backslash omega$ is the angular frequency

$\backslash phi$ is the phase.

The units of the amplitude depend on the type of wave. Transverse mechanical waves (e.g., a wave on a string) have an amplitude expressed as a distance (e.g., meters), longitudinal mechanical waves (e.g., sound waves) use units of pressure (e.g., pascals), and electromagnetic waves (a form of transverse vacuum wave) express the amplitude in terms of its electric field (e.g., volts/meter).

The wavelength $\backslash lambda$ is the distance between two sequential crests or troughs (or other equivalent points), generally is measured in meters. A wavenumber $k$, the spatial frequency of the wave in radians per unit distance (typically per meter), can be associated with the wavelength by the relation

:$k\; =\; \backslash frac\{2\; \backslash pi\}\{\backslash lambda\}.\; \backslash ,$

The period $T$ is the time for one complete cycle of an oscillation of a wave. The frequency $f$ is the number of periods per unit time (per second) and is typically measured in hertz. These are related by:

:$f=\backslash frac\{1\}\{T\}.\; \backslash ,$

In other words, the frequency and period of a wave are reciprocals.

The angular frequency $\backslash omega$ represents the frequency in radians per second. It is related to the frequency or period by

:$\backslash omega\; =\; 2\; \backslash pi\; f\; =\; \backslash frac\{2\; \backslash pi\}\{T\}.\; \backslash ,$

The wavelength $\backslash lambda$ of a sinusoidal waveform traveling at constant speed $v$ is given by: :$\backslash lambda\; =\; \backslash frac\{v\}\{f\},$

where $v$ is called the phase speed (magnitude of the phase velocity) of the wave and $f$ is the wave's frequency.

Wavelength can be a useful concept even if the wave is not periodic in space. For example, in an ocean wave approaching shore, the incoming wave undulates with a varying ''local'' wavelength that depends in part on the depth of the sea floor compared to the wave height. The analysis of the wave can be based upon comparison of the local wavelength with the local water depth.

Although arbitrary wave shapes will propagate unchanged in lossless linear time-invariant systems, in the presence of dispersion the sine wave is the unique shape that will propagate unchanged but for phase and amplitude, making it easy to analyze. Due to the Kramers–Kronig relations, a linear medium with dispersion also exhibits loss, so the sine wave propagating in a dispersive medium is attenuated in certain frequency ranges that depend upon the medium. The sine function is periodic, so the sine wave or sinusoid has a wavelength in space and a period in time.

The sinusoid is defined for all times and distances, whereas in physical situations we usually deal with waves that exist for a limited span in space and duration in time. Fortunately, an arbitrary wave shape can be decomposed into an infinite set of sinusoidal waves by the use of Fourier analysis. As a result, the simple case of a single sinusoidal wave can be applied to more general cases. In particular, many media are linear, or nearly so, so the calculation of arbitrary wave behavior can be found by adding up responses to individual sinusoidal waves using the superposition principle to find the solution for a general waveform. When a medium is nonlinear, the response to complex waves cannot be determined from a sine-wave decomposition.

Plane waves

Standing waves

A standing wave, also known as a ''stationary wave'', is a wave that remains in a constant position. 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.

The ''sum'' of two counter-propagating waves (of equal amplitude and frequency) creates a ''standing wave''. Standing waves commonly arise when a boundary blocks further propagation of the wave, thus causing wave reflection, and therefore introducing a counter-propagating wave. For example when a violin string is displaced, transverse waves propagate out to where the string is held in place at the bridge and the nut, where the waves are reflected back. At the bridge and nut, the two opposed waves are in antiphase and cancel each other, producing a node. Halfway between two nodes there is an antinode, where the two counter-propagating waves ''enhance'' each other maximally. There is no net propagation of energy over time.

Physical properties

Waves exhibit common behaviors under a number of standard situations, e.g.,

Transmission and media

Waves normally move in in a straight line (i.e. rectilinearly) through a ''transmission medium''. Such media can be classified into one or more of the following categories:

A ''bounded medium'' if it is finite in extent, otherwise an ''unbounded medium''

A ''linear medium'' if the amplitudes of different waves at any particular point in the medium can be added

A ''uniform medium'' or ''homogeneous medium'' if its physical properties are unchanged at different locations in space

An ''anisotropic medium'' if one or more of its physical properties differ in one or more directions

An ''isotropic medium'' if its physical properties are the ''same'' in all directions

Absorption

Reflection

When a wave strikes a reflective surface, it changes direction, such that the angle made by the incident wave and line normal to the surface equals the angle made by the reflected wave and the same normal line.

Interference

Waves that encounter each other combine through superposition to create a new wave called an interference pattern. Important interference patterns occur for waves that are in phase.

Refraction

Refraction is the phenomenon of a wave changing its speed. Mathematically, this means that the size of the phase velocity changes. Typically, refraction occurs when a wave passes from one medium into another. The amount by which a wave is refracted by a material is given by the refractive index of the material. The directions of incidence and refraction are related to the refractive indices of the two materials by Snell's law.

Diffraction

A wave exhibits diffraction when it encounters an obstacle that bends the wave or when it spreads after emerging from an opening. Diffraction effects are more pronounced when the size of the obstacle or opening is comparable to the wavelength of the wave.

Polarization

A wave is polarized if it oscillates in one direction or plane. A wave can be polarized by the use of a polarizing filter. The polarization of a transverse wave describes the direction of oscillation in the plane perpendicular to the direction of travel.

Longitudinal waves such as sound waves do not exhibit polarization. For these waves the direction of oscillation is along the direction of travel.

Dispersion

A wave undergoes dispersion when either the phase velocity or the group velocity depends on the wave frequency. Dispersion is most easily seen by letting white light pass through a prism, the result of which is to produce the spectrum of colours of the rainbow. Isaac Newton performed experiments with light and prisms, presenting his findings in the ''Opticks'' (1704) that white light consists of several colours and that these colours cannot be decomposed any further.

Mechanical waves

Waves on strings

The speed of a wave traveling along a vibrating string ('' v '') is directly proportional to the square root of the tension of the string ('' T '') over the linear mass density ('' μ ''):

:$v=\backslash sqrt\{\backslash frac\{T\}\{\backslash mu\}\},\; \backslash ,$

where the linear density ''μ'' is the mass per unit length of the string.

Acoustic waves

Acoustic or sound waves travel at speed given by

:$v=\backslash sqrt\{\backslash frac\{B\}\{\backslash rho\_0\}\},\; \backslash ,$

or the square root of the adiabatic bulk modulus divided by the ambient fluid density (see speed of sound).

Water waves

Ripples on the surface of a pond are actually a combination of transverse and longitudinal waves; therefore, the points on the surface follow orbital paths.

Sound—a mechanical wave that propagates through gases, liquids, solids and plasmas;

Inertial waves, which occur in rotating fluids and are restored by the Coriolis effect;

Ocean surface waves, which are perturbations that propagate through water.

Seismic waves

Shock waves

Other

Waves of traffic, that is, propagation of different densities of motor vehicles, and so forth, which can be modeled as kinematic waves

Metachronal wave refers to the appearance of a traveling wave produced by coordinated sequential actions.

Electromagnetic waves

(radio, micro, infrared, visible, uv)

An electromagnetic wave consists of two waves that are oscillations of the electric and magnetic fields. An electromagnetic wave travels in a direction that is at right angles to the oscillation direction of both fields. In the 19th century, James Clerk Maxwell showed that, in vacuum, the electric and magnetic fields satisfy the wave equation both with speed equal to that of the speed of light. From this emerged the idea that light is an electromagnetic wave. Electromagnetic waves can have different frequencies (and thus wavelengths), giving rise to various types of radiation such as radio waves, microwaves, infrared, visible light, ultraviolet and X-rays.

Quantum mechanical waves

The Schrödinger equation describes the wave-like behavior of particles in quantum mechanics. Solutions of this equation are wave functions which can be used to describe the probability density of a particle. Quantum mechanics also describes particle properties that other waves, such as light and sound, have on the atomic scale and below.

thumb|A propagating wave packet; in general, the ''envelope'' of the wave packet moves at a different speed than the constituent waves.

de Broglie waves

Louis de Broglie postulated that all particles with momentum have a wavelength

:$\backslash lambda\; =\; \backslash frac\{h\}\{p\},$

where ''h'' is Planck's constant, and ''p'' is the magnitude of the momentum of the particle. This hypothesis was at the basis of quantum mechanics. Nowadays, this wavelength is called the de Broglie wavelength. For example, the electrons in a CRT display have a de Broglie wavelength of about 10⁻¹³ m.'''

A wave representing such a particle traveling in the ''k''-direction is expressed by the wave function:

:$\backslash psi\; (\backslash mathbf\{r\},\; \backslash \; t=0)\; =A\backslash \; e^\{i\backslash mathbf\{k\; \backslash cdot\; r\}\}\; \backslash \; ,$

where the wavelength is determined by the wave vector k as:

:$\backslash lambda\; =\; \backslash frac\; \{2\; \backslash pi\}\{k\}\; \backslash \; ,$

and the momentum by:

:$\backslash mathbf\; p\; =\; \backslash hbar\; \backslash mathbf\{k\}\; \backslash \; .$

However, a wave like this with definite wavelength is not localized in space, and so cannot represent a particle localized in space. To localize a particle, de Broglie proposed a superposition of different wavelengths ranging around a central value in a wave packet, a waveform often used in quantum mechanics to describe the wave function of a particle. In a wave packet, the wavelength of the particle is not precise, and the local wavelength deviates on either side of the main wavelength value.

In representing the wave function of a localized particle, the wave packet is often taken to have a Gaussian shape and is called a ''Gaussian wave packet''. Gaussian wave packets also are used to analyze water waves.

For example, a Gaussian wavefunction ψ might take the form:

:$\backslash psi(x,\backslash \; t=0)\; =\; A\backslash \; \backslash exp\; \backslash left(\; -\backslash frac\{x^2\}\{2\backslash sigma^2\}\; +\; i\; k\_0\; x\; \backslash right)\; \backslash \; ,$

at some initial time ''t'' = 0, where the central wavelength is related to the central wave vector ''k''₀ as λ₀ = 2π / ''k''₀. It is well known from the theory of Fourier analysis, or from the Heisenberg uncertainty principle (in the case of quantum mechanics) that a narrow range of wavelengths is necessary to produce a localized wave packet, and the more localized the envelope, the larger the spread in required wavelengths. The Fourier transform of a Gaussian is itself a Gaussian. Given the Gaussian:

:$f(x)\; =\; e^\{-x^2\; /\; (2\backslash sigma^2)\}\; \backslash \; ,$

the Fourier transform is:

:$\backslash tilde\{\; f\}\; (k)\; =\; \backslash sigma\; e^\{-\backslash sigma^2\; k^2\; /\; 2\}\; \backslash \; .$

The Gaussian in space therefore is made up of waves:

:$f(x)\; =\; \backslash frac\{1\}\{\backslash sqrt\{2\; \backslash pi\}\}\; \backslash int\_\{-\backslash infty\}^\{\backslash infty\}\; \backslash \; \backslash tilde\{f\}\; (k)\; e^\{ikx\}\; \backslash \; dk\; \backslash \; ;$

that is, a number of waves of wavelengths λ such that ''k''λ = 2 π.

The parameter σ decides the spatial spread of the Gaussian along the ''x''-axis, while the Fourier transform shows a spread in wave vector ''k'' determined by 1/σ. That is, the smaller the extent in space, the larger the extent in ''k'', and hence in λ = 2π/''k''.

Gravitational waves

Researchers believe that gravitational waves also travel through space, although gravitational waves have never been directly detected. Not to be confused with gravity waves, gravitational waves are disturbances in the curvature of spacetime, predicted by Einstein's theory of general relativity.

WKB method

In a nonuniform medium, in which the wavenumber ''k'' can depend on the location as well as the frequency, the phase term ''kx'' is typically replaced by the integral of ''k''(''x'')''dx'', according to the WKB method. Such nonuniform traveling waves are common in many physical problems, including the mechanics of the cochlea and waves on hanging ropes.

References

See also

Sources

Campbell, M. and Greated, C. (1987). ''The Musician’s Guide to Acoustics''. New York: Schirmer Books.

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Vassilakis, P.N. (2001). ''Perceptual and Physical Properties of Amplitude Fluctuation and their Musical Significance''. Doctoral Dissertation. University of California, Los Angeles.

External links

Interactive Visual Representation of Waves

Science Aid: Wave properties—Concise guide aimed at teens

Simulation of diffraction of water wave passing through a gap

Simulation of interference of water waves

Simulation of longitudinal traveling wave

Simulation of stationary wave on a string

Simulation of transverse traveling wave

Sounds Amazing—AS and A-Level learning resource for sound and waves

chapter from an online textbook

Simulation of waves on a string

of longitudinal and transverse mechanical wave

MIT OpenCourseWare 8.03: Vibrations and Waves Free, independent study course with video lectures, assignments, lecture notes and exams.

Category:Fundamental physics concepts Category:Partial differential equations

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Byron Coley is an American music critic who wrote prominently for ''Forced Exposure'' magazine in the 1980s, starting with their fifth issue until the magazine ceased publication in 1993. Prior to Forced Exposure, he wrote for NY Rocker, Boston Rock, and Take It! magazine. Coley is one of the first writers to have extensively documented indie rock from its inception to the present day. Coley was a contributing writer to ''Spin'' in the 1980s and '90s, and currently writes for the Wire and Arthur magazine with Thurston Moore. He also runs Ecstatic Yod, a record label and shop based in Florence, Massachusetts.

Coley has contributed liner notes to albums by The Flesh Eaters, Borbetomagus, Sonic Youth, Dinosaur Jr., Big Boys, Yo La Tengo, John Fahey, Steffen Basho-Junghans, Flaherty/Corsano duo, and numerous others. He has also appeared in documentaries about musical artists Half Japanese, Minutemen, Jandek, and The Holy Modal Rounders, in each extolling the genius of the subject matter. When he wrote The Flesh Eaters' entry in the Spin Alternative Record Guide, Coley stated that he considers "A Minute to Pray, A Second to Die" the best rock album ever recorded. For the 2007 Deluxe Edition of Sonic Youth's ''Daydream Nation'', he contributed to the liner notes with a reflective essay on the legendary album.

Coley is also a published poet and occasionally gives public readings of his (and others') works. He also wrote a biography of Chuck Norris that was published in 1986. He also published a quickie bio of Mötley Crüe under the pseudonym "Billy Dwight" (an in-joke).

In 2010, Coley became involved with Feeding Tube Records in Northampton, Massachusetts, a record store where he sells rare items from his personal collection.

In 2011, Coley published the first collection of his reviews, "C'est la guerre : Early Writings 1978-1983" in a bilingual edition put out by Montreal publisher L'Oie de Cravan.

References

Category:American music critics Category:Living people

Coordinates	3°58′2.96″N122°35′40.92″N
name	Thurston Moore
background	solo_singer
birth name	Thurston Joseph Moore
alias	Mirror, Fred Cracklin
born	July 25, 1958Coral Gables, Florida, U.S.
instrument	Vocals, guitar, bass, harmonica, synthesizer, piano, saxophone
genre	Alternative rock, noise rock, experimental rock, no wave
occupation	Singer, Guitarist, Songwriter, Consultant, Record producer
years active	1978–present
label	GeffenSSTEcstatic Peace!Father YodLo RecordingsDestructive Industries Arts & Crafts México
associated acts	Sonic YouthCiccone YouthThe CoachmenMirror/DashEven WorseDream/Aktion UnitBark HazeDim StarsNorthampton Wools
notable instruments	Fender JazzmasterFender JaguarFender Telecaster Deluxe }}

Thurston Joseph Moore (born July 25, 1958) is an American musician best known as a singer, songwriter and guitarist of Sonic Youth. He has also participated in many solo and group collaborations outside of Sonic Youth, as well as running the Ecstatic Peace! record label. Moore was ranked 34th in Rolling Stone's 2004 edition of the "100 Greatest Guitarists of All Time."

Early years

Moore was born in Coral Gables, Florida, but was raised in Bethel, Connecticut. Although he enrolled at Western Connecticut State University, he instead moved to New York City to join the burgeoning post-punk/no wave music scenes. At the beginning of his time in New York, he lived in an apartment below Dan Graham, eventually befriending him, sometimes using records from Graham's collection for mix tapes.

Once in the city, Moore was briefly a member of the hardcore punk band Even Worse, featuring future ''The Big Takeover'' editor (and future Springhouse drummer) Jack Rabid. After exiting the band, Moore and Lee Ranaldo learned experimental guitar techniques in Glenn Branca's "guitar orchestras."

Sonic Youth

Moore and Ranaldo soon formed Sonic Youth, serving as the band's guitarists, with Moore on lead vocals. The band signed to Neutral Records, then to Homestead Records, and then to SST Records.

In 1984, Moore married Sonic Youth bassist/vocalist Kim Gordon. The pair have a daughter, Coco Hayley Gordon Moore (born 1 July 1994). They currently reside in Northampton, Massachusetts.

He and Ranaldo make extensive use of unusual guitar tunings, often heavily modifying their instruments to provide unusual timbres and drones. They are known for bringing upwards of fifty guitars to every live gig, using some guitars for one song only. In 2004, ''Rolling Stone'' magazine ranked Moore and Ranaldo the 33rd and 34th ''Greatest Guitarists of All Time''.

Work outside of Sonic Youth

In addition to his work with Sonic Youth, Moore has also released albums as a solo artist. He and Gordon released a few songs as Mirror/Dash, a reference to their respective nicknames. ("Mirror" being an alliterative pun on "Moore," and "Dash" being a pun on Flash Gordon.) The two also established Protest records together but the project has since lapsed.

Moore has collaborated with scores of musicians, including Maryanne Amacher, Lydia Lunch, DJ Spooky, William Hooker, Daniel Carter, Christian Marclay, Mike Watt, Loren Mazzacane Connors, Tom Surgal, William Winant, Nels Cline, Cock E.S.P., WRONG, Daniel Castro, Glenn Branca, Yamantaka Eye, Chris Corsano and My Cat is an Alien. Most of his solo/duo collaborations have been instrumental, and are generally improvised and/or noise based.

In the early 1990s, Moore formed the side band Dim Stars, featuring punk legend Richard Hell of the Voidoids. Moore performed solo on the side stage of the 1993 Lollapalooza tour. Additionally, Moore also contributed guitar work and backing vocals on "Crush With Eyeliner," which appeared on R.E.M.'s ''Monster'' LP.

Since 2004, Moore has recorded and performed with the all-star noise collective To Live and Shave in L.A., the lineup of which also features Andrew W.K.. He recorded with the band at Sonic Youth's former studio in Manhattan, and later performed with them at the George W. Bush "anti-inaugural" Noise Against Fascism concert in Washington, D.C., named in reference to Sonic Youth's 1992 song "Youth Against Fascism." Moore curated the "Nightmare Before Christmas" weekend of the All Tomorrow's Parties music festival in December 2006.

Moore directed the music video for Pavement's song "Here," from ''Slanted and Enchanted''. Foot is a collaboration between Don Fleming, Jim Dunbar and Thurston Moore.

On June 21, 2007, Moore revealed to ''Spin Magazine'' that he would be releasing a solo album titled ''Trees Outside The Academy''. The album was recorded at J Mascis' studio in Amherst, Massachusetts. The album is made up of mostly acoustic material and features Sonic Youth drummer Steve Shelley and violinist Samara Lubelski. The album also features collaborations between Mascis and Charalambides' Christina Carter, who performs a duet with Moore on the track, "Honest James." The album was released on September 18, 2007, on Moore's label Ecstatic Peace.

On September 24, 2008, Pitchfork Media reported that Thurston was working on a song with former Be Your Own Pet vocalist Jemina Pearl, a cover of the Ramones song "Sheena Is a Punk Rocker." The song was recorded for the teenage drama Gossip Girl and was featured in the episode "There Might Be Blood".

Since 2008, Moore has provided narration for a variety of documentaries on the National Geographic Channel. His work includes ''Inside: Straight Edge'' and the ''Hard Time'' series about life in prison.

Work on film soundtracks

In 1994, Moore teamed up with Greg Dulli of The Afghan Whigs, Don Fleming of Gumball, Mike Mills of R.E.M., and Dave Grohl of Nirvana/Foo Fighters, to form the Backbeat Band, which recorded the soundtrack album to the movie ''Backbeat''.

In 1998 Moore played on the soundtrack of the film ''Velvet Goldmine'' as a member of ''Wylde Ratttz'', along with The Stooges' Ron Asheton, his Sonic Youth bandmate Steve Shelley, Minutemen's Mike Watt, Gumball's Don Fleming, Mark Arm of Mudhoney and Jim Dunbar.

Moore also composed original music for the films:

''Heavy'' (1995)

''Bully'' (2001)

''Manic'' (2001)

''Extra Action and Extra Hardcore'' (2008)

In 2007, Moore also appeared with noise/improv constellation "Original Silence" featuring Norwegian drummer Paal Nilssen-Love (The thing, Atomic, Scorch Trio), guitarist Terrie Ex (The Ex), Jim O'Rourke (Sonic Youth, Wilco, Illusion of Safety), saxophonist Mats Gustafsson and bassist Massimo Pupillo (Zu). The group released the live album "The First Original Silence" in 2007, on Oslo (Norway) label SmallTown Superjazz, and a second album "The Second Original Silence" in 2008.

Record label and writings

Moore and other Sonic Youth members published the irreverent music zine ''Sonic Life''. Moore runs the record label Ecstatic Peace!. Beginning in 1993, this label jointly released records with rock critic Byron Coley's label, Father Yod, as Ecstatic Yod Records.

Moore reviews new music in ''Arthur Magazine'' in a column written jointly with Byron Coley. He manages the website Protest Records, named for its protest against United States' invasions in the Middle East. Moore was the editor/overseer of the 2005 book ''Mix Tape: The Art of Cassette Culture''. He published a highly influential list of collectible free jazz records in Grand Royal magazine.

Equipment

Moore is known for using a large selection of Fender guitars during gigs. Most of the time he plays a Jazzmaster through many different types of amps among which Vox AC30, Peaveys and Fenders are present. He also plays a Jaguar and (less often) a heavily modified Fender Duo-Sonic with three single-coil pickups.

Since Ranaldo and Moore, together with Elvis Costello, J. Mascis, and Kevin Shields, are known for being key figures in the popularization and resurrection of the Fender Jazzmaster, in 2009 Fender introduced a Lee Ranaldo signature edition of a Sapphire Blue Transparent version featuring two Fender Wide Range humbucking pickups and a Forest Green transparent finish for Moore, equipped with a pair of Seymour Duncan Antiquity II Jazzmaster single-coil pickups).

Solo discography and collaborations

; Solo albums:

''Psychic Hearts'' (1995, Geffen Records)

''Trees Outside the Academy'' (2007, Ecstatic Peace)

''Demolished Thoughts'' (2011, Matador Records) (UK chart peak: #119)

; Other:

''Root'' - Remix Project (1998, Lo Recordings)

''Solo Acoustic Volume Five'' - Part of the VDSQ (Vin Du Select Qualitite) acoustic guitar series (2011)

; Limited Edition Noise, experimental, drone projects:

2006 - ''Flipped Out Bride 12'''' (2006, Blossoming Noise), Limited Edition of 500 blue marbled vinyl

2006 - ''Free / Love EP'' (2006, Blossoming Noise), Limited Edition of 90 Cassettes only

2007 - ''Black Weeds - White Death'' (2007, Meudiademorte), Limited Edition of 200 Cassettes only

2008 - Sensitive / Lethal

2008 - ''Blindfold' (Destructive Industries), Limited Edition of 200 Cassettes only

2008 - ''Built For Lovin'' (Lost Treasures of the Underworld), Limited Edition of 500 vinyl only

2010 - Suicide Notes For Acoustic Guitar EP

; Collaborations:

1988 - Barefoot In The Head [with Jim Sauter & Don Dietrich]

1993 - Shamballa [With William Hooker & Elliott Sharp]

1995 - Klangfarbenmelodie & the Colorist Strikes Primitive [with Tom Surgal]

1996 - Pillow Wand [with Nels Cline]

1996 - ''Piece For Yvonne Rainer'' [with Yoshimi & Mark Ibold (Sunship)]

1997 - ''MMMR'' [with Loren Mazzacane Connors, Jean-Marc Montera & Lee Ranaldo (Numero Zero Audio)

2000 - New York - Ystad [Thurston Moore, Lee Ranaldo, Steve Shelley, Mats Gustafsson]

2001 - Three Incredible Ideas [Thurston Moore / Walter Prati / Giancarlo Schiaffini]

1998 - Foot [with Don Fleming & Jim Dunbar]

1999 - The Promise [With Evan Parker & Walter Prati]

; Free Improvisation Albums:

2007 - The Roadhouse Session Vol.1 [Thurston Moore / Chris Corsano / Paul Flaherty / Wally Shoup 4tet]

2008 - Untitled [Paul Flaherty / Thurston Moore / Bill Nace]

; Live Albums:

1996 - ''Piece for Jetsun Dolma'' [a live improvisation with Tom Surgal and William Winant at Festival International de Musique Actuelle de Victoriaville (Les Disques VICTO)]

; Albums with Sonic Youth:

See Sonic Youth discography

; Albums with Diskaholics Anonymous Trio [Jim O'Rourke, Mats Gustafsson, Thurston Moore]:

2001 - Diskaholics Anonymous Trio

2006 - Weapons Of Ass Destruction (Recorded in 2002)

; Albums with Original Silence:

2007 - The First Original Silence (Recorded live in concert on sept. 30 2005 at Teatro Ariosto, Reggio Emilia, Italy)

2008 - The Second Original Silence (Recorded Live In Concert on September 28, 2005 at Brancaleone, Rome)

; Early work with Glenn Branca:

1981 - ''Symphony No. 1'' "Tonal Plexus" (w/Glenn Branca, Lee Ranaldo, Anne DeMarinis & others)

1982 - ''Symphony No. 2'' "The Peak Of The Sacred"

1983 - ''Symphony No. 3'' "Gloria" - Music for the first 127 intervals of the harmonic series

; Early work with the Coachmen:

1979 -Failure to Thrive

; Singles:

"Sputnik" 7" (1997) Thurston Moore and Don Fleming on one side, Pete Kember aka Sonic Boom on the other. Gilltery vinyl.

"Wonderful Witches" single (2007)

1995 - The Church Should Be For The Outcasts, Not A Church That Casts People Out (7") [As Male Slut]

; Split LPs:

From The Earth To The Spheres (2004, split with My Cat Is An Alien)

''Thrash Sabbatical'' (2008, Deathbomb Arc, four-way split 12" + 2x7" w/ Men Who Can't Love, Barrabarracuda, Kevin Shields)

''Mature, Lonely + Out of Control/Alternative Hair Styles'' (2008, Nihilist Records, split LP with Graham Moore)

; Album appearances:

1992 - ''Do You Wanna Dance'' (by Dim Stars)

1994 - ''Monster'' (by R.E.M.)

1997 - ''Legend Of The Blood Yeti'' (by XIII Ghosts & Derek Bailey)

1998 - ''Velvet Goldmine - Music From The Original Motion Picture'' ("T.V. Eye" with the Wylde Ratttz)

2002 - ''Kapotte Muziek'' - #12 in Kapotte Muziek series (Korm Plastics)

2006 - The Voloptulist [The New Blockaders, with Thurston Moore (track 1) / Jim O'Rourke (track 2)]

2007 - ''Touch The Iceberg'' (by Owl Xounds Exploding Galaxy)

References

External links

Sonic Youth.com - Official website

Official Myspace page for "Kill Your Idols", a documentary about the Cinema of Transgression featuring Thurston Moore

Ecstatic Peace! Records.

''Spike'' magazine interview.

Writings by Thurston on 2003 NYC power blackout.

Thurston Moore's "Skrewer Boy" published on the Tellus Audio Cassette Magazine @ Ubuweb

Pichfork article Working with Jemina

Category:1958 births Category:Living people Category:Sonic Youth members Category:American rock guitarists Category:American male singers Category:American rock singers Category:Songwriters from Florida Category:American indie rock musicians Category:American experimental musicians Category:Musicians from Florida Category:People from Miami, Florida Category:Noise musicians Category:Ecstatic Peace! artists Category:People from Coral Gables, Florida

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