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This article is about waves in the most general scientific sense. For waves in the ocean, see ocean surface wave. Ocean surface waves are Surface waves that occur on the Free surface of the Ocean. For other uses, see Wave (disambiguation).
Surface waves in water
Surface waves in water

A wave is a disturbance that propagates through space and time, usually with transference of energy. In Physics, surface wave can refer to a Mechanical wave that propagates along the interface between differing media usually two fluids with different densities Water is a common Chemical substance that is essential for the survival of all known forms of Life. Space is the extent within which Matter is physically extended and objects and Events have positions relative to one another For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός While a mechanical wave exists in a medium (which on deformation is capable of producing elastic restoring forces), waves of electromagnetic radiation (and probably gravitational radiation) can travel through vacuum, that is, without a medium. An optical medium is material through which Electromagnetic waves propagate Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. In Physics, a gravitational wave is a Fluctuation in the Curvature of Spacetime which propagates as a wave, traveling outward from This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. Waves travel and transfer energy from one point to another, often with little or no permanent displacement of the particles of the medium (that is, with little or no associated mass transport); instead there are oscillations around almost fixed positions. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός Oscillation is the repetitive variation typically in Time, of some measure about a central value (often a point of Equilibrium) or between two or more different states

Contents

Definitions

Agreeing on a single, all-encompassing definition for the term wave is non-trivial. A vibration can be defined as a back-and-forth motion around a point m around a reference value. Vibration refers to mechanical Oscillations about an equilibrium point. However, defining the necessary and sufficient characteristics that qualify a phenomenon to be called a wave is, at least, flexible. A phenomenon (from Greek φαινόμενoν, pl φαινόμενα - phenomena) is any observable occurrence The term is often understood intuitively as the transport of disturbances in space, not associated with 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 (Hall, 1980: 8). In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός Vibration refers to mechanical Oscillations about an equilibrium point. 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. A standing wave, also known as a stationary wave, is a Wave that remains in a constant position In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner.

For such reasons, wave theory represents a peculiar branch of physics that is concerned with the properties of wave processes independently from their physical origin (Ostrovsky and Potapov, 1999). Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. The peculiarity lies in the fact that this independence from physical origin is accompanied by a heavy reliance on origin when describing any 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-like transfer / transformation of vibratory energy. Acoustics is the interdisciplinary science that deals with the study of Sound, Ultrasound and Infrasound (all mechanical waves in gases liquids and solids In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός Concepts such as mass, momentum, inertia, or elasticity, become therefore crucial in describing acoustic (as opposed to optic) wave processes. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product The vis insita or innate force of matter is a power of resisting by which every body as much as in it lies endeavors to preserve in its present state whether it be of rest or of moving A material is said to be elastic if it deforms under stress (e 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. Radiation pressure is the Pressure exerted upon any surface exposed to Electromagnetic radiation. For the music album by Converter see Shock Front For the 1977 horror film see Shock Waves A shock wave (also called , in the case of solids: Rayleigh waves, dispersion, etc. Rayleigh waves, also known as the Rayleigh-Lamb Wave or "ground roll" are a type of Surface wave. , and so on).

Other properties, however, although they are usually described in an origin-specific manner, may be generalized to all waves. For example, based on the mechanical origin of acoustic waves there can be a moving disturbance in space-time 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 (or rather infinitely fast wave motion). 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 (or rather infinitely slow 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. The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0

Similarly, wave processes revealed from the study of wave phenomena with origins different from that of sound waves can be equally significant to the understanding of sound phenomena. A relevant example is Young's principle of interference (Young, 1802, in Hunt, 1978: 132). 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. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 Scattering is a general physical process whereby some forms of Radiation, such as Light, Sound or moving particles for example are forced to deviate from

Characteristics

Periodic waves are characterized by crests (highs) and troughs (lows), and may usually be categorized as either longitudinal or transverse. A crest is the point on a Wave with the greatest positive value or upward displacement in a Cycle. A crest is the point on a Wave with the greatest positive value or upward displacement in a Cycle. Transverse waves are those with vibrations perpendicular to the direction of the propagation of the wave; examples include waves on a string and electromagnetic waves. A transverse wave is a moving Wave that consists of oscillations occurring perpendicular to the direction of energy transfer Longitudinal waves are those with vibrations parallel to the direction of the propagation of the wave; examples include most sound waves. Longitudinal waves are waves that have vibrations along or parallel to their direction of travel that is waves in which the motion of the medium is in the same direction as the motion

When an object bobs up and down on a ripple in a pond, it experiences an orbital trajectory because ripples are not simple transverse sinusoidal waves.

A = In deep water. B = In shallow water. The elliptical movement of a surface particle becomes flatter with decreasing depth. 1 = Progression of wave 2 = Crest 3 = Trough
A = In deep water.
B = In shallow water. The elliptical movement of a surface particle becomes flatter with decreasing depth.
1 = Progression of wave
2 = Crest
3 = Trough

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. In Physics and Engineering, a ripple tank is a shallow glass tank of water used in schools and colleges to demonstrate the basic properties of Waves It

All waves have common behavior under a number of standard situations. All waves can experience the following:

Polarization

Main article: Polarization

A wave is polarized, if it can only oscillate in one direction. Reflection is the change in direction of a Wave front at an interface between two different media so that the wave front returns into the medium from which Refraction is the change in direction of a Wave due to a change in its Speed. Diffraction is normally taken to refer to various phenomena which occur when a wave encounters an obstacle In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. In physics interference is the addition ( superposition) of two or more Waves that result in a new wave pattern In Physics and Systems theory, the superposition principle, also known as superposition property, states that for all Linear systems In Optics, dispersion is the phenomenon in which the Phase velocity of a wave depends on its frequency Rectilinear propagation is a Wave property which states that waves propagate (move or spread out in straight Polarization ( ''Brit'' polarisation) is a property of Waves that describes the orientation of their oscillations Polarization ( ''Brit'' polarisation) is a property of Waves that describes the orientation of their oscillations 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, because for these waves the direction of oscillation is along the direction of travel. A wave can be polarized by using a polarizing filter.

Examples

An ocean surface wave crashing into rocks
An ocean surface wave crashing into rocks

Examples of waves include:

Mathematical description

A wave with constant amplitude.
A wave with constant amplitude.
Illustration of a wave (the fast varying blue curve) and its envelope (the slower varying red curve).
Illustration of a wave (the fast varying blue curve) and its envelope (the slower varying red curve).

From a mathematical point of view, the most primitive or fundamental wave is harmonic (sinusoidal) wave which is described by the equation f(x,t) = Asin(ωt − kx)), where A is the amplitude of a wave - a measure of the maximum disturbance in the medium during one wave cycle (the maximum distance from the highest point of the crest to the equilibrium). In Acoustics and Telecommunication, the harmonic of a Wave is a component Frequency of the signal that is an Integer Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system In the illustration to the right, this is the maximum vertical distance between the baseline and the wave. The units of the amplitude depend on the type of wave — waves on a string have an amplitude expressed as a distance (meters), sound waves as pressure (pascals) and electromagnetic waves as the amplitude of the electric field (volts/meter). In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can The amplitude may be constant (in which case the wave is a c. w. or continuous wave), or may vary with time and/or position. A continuous wave or continuous waveform ( CW) is an Electromagnetic wave of constant Amplitude and Frequency; and in Mathematical The form of the variation of amplitude is called the envelope of the wave.

The wavelength (denoted as λ) is the distance between two sequential crests (or troughs). In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. This generally is measured in meters; it is also commonly measured in nanometers for the optical part of the electromagnetic spectrum. The electromagnetic (EM spectrum is the range of all possible Electromagnetic radiation frequencies

A wavenumber k can be associated with the wavelength by the relation

k = \frac{2 \pi}{\lambda}. \,
Waves can be represented by simple harmonic motion.
Waves can be represented by simple harmonic motion. Wavenumber in most physical sciences is a Wave property inversely related to Wavelength, having SI units of reciprocal meters Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped.

The period T is the time for one complete cycle for an oscillation of a wave. Frequency is a measure of the number of occurrences of a repeating event per unit Time. The frequency f (also frequently denoted as ν) is how many periods per unit time (for example one second) and is measured in hertz. Frequency is a measure of the number of occurrences of a repeating event per unit Time. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second. These are related by:

f=\frac{1}{T}. \,

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

The angular frequency ω represents the frequency in terms of radians per second. Do not confuse with Angular velocity In Physics (specifically Mechanics and Electrical engineering) angular frequency It is related to the frequency by

\omega = 2 \pi f = \frac{2 \pi}{T}. \,

There are two velocities that are associated with waves. The first is the phase velocity, which gives the rate at which the wave propagates, is given by

v_p = \frac{\omega}{k} = {\lambda}f.

The second is the group velocity, which gives the velocity at which variations in the shape of the wave's amplitude propagate through space. The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space The group velocity of a Wave is the Velocity with which the variations in the shape of the wave's amplitude (known as the modulation or envelope This is the rate at which information can be transmitted by the wave. It is given by

v_g = \frac{\partial \omega}{\partial k}. \,

The wave equation

Main article: Wave equation

The wave equation is a differential equation that describes the evolution of a harmonic wave over time. The wave equation is an important second-order linear Partial differential equation that describes the propagation of a variety of Waves such as Sound waves A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the The equation has slightly different forms depending on how the wave is transmitted, and the medium it is traveling through. Considering a one-dimensional wave that is traveling down a rope along the x-axis with velocity v and amplitude u (which generally depends on both x and t), the wave equation is

\frac{1}{v^2}\frac{\partial^2 u}{\partial t^2}=\frac{\partial^2 u}{\partial x^2}. \,

In three dimensions, this becomes

\frac{1}{v^2}\frac{\partial^2 u}{\partial t^2} = \nabla^2 u. \,

where \nabla^2 is the Laplacian. In Mathematics and Physics, the Laplace operator or Laplacian, denoted by \Delta\  or \nabla^2  and named after

The velocity v will depend on both the type of wave and the medium through which it is being transmitted.

A general solution for the wave equation in one dimension was given by d'Alembert. It is

u(x,t)=F(x-vt)+G(x+vt). \,

This can be viewed as two pulses traveling down the rope in opposite directions; F in the +x direction, and G in the −x direction. If we substitute for x above, replacing it with directions x, y, z, we then can describe a wave propagating in three dimensions.

The Schrödinger equation describes the wave-like behavior of particles in quantum mechanics. In Physics, especially Quantum mechanics, the Schrödinger equation is an equation that describes how the Quantum state of a Physical system Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Solutions of this equation are wave functions which can be used to describe the probability density of a particle. A wave function or wavefunction is a mathematical tool used in Quantum mechanics to describe any physical system Quantum mechanics also describes particle properties that other waves, such as light and sound, have on the atomic scale and below.

Traveling waves

Simple wave or a traveling wave, also sometimes called a progressive wave is a disturbance that varies both with time t and distance z in the following way:

y(z,t) = A(z, t)\sin (kz - \omega t + \phi), \,

where A(z,t) is the amplitude envelope of the wave, k is the wave number and φ is the phase. The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 The phase velocity vp of this wave is given by

v_p = \frac{\omega}{k}= \lambda f, \,

where λ is the wavelength of the wave. The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency.

Standing wave

Main article: standing wave
Standing wave in stationary medium. The red dots represent the wave nodes
Standing wave in stationary medium. A standing wave, also known as a stationary wave, is a Wave that remains in a constant position The red dots represent the wave nodes

A standing wave, also known as a stationary wave, is a wave that remains in a constant position. A node is a point along a Standing wave where the wave has minimal Amplitude. 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. In physics interference is the addition ( superposition) of two or more Waves that result in a new wave pattern

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, longitudinal waves propagate out to where the string is held in place at the bridge and the "nut", where upon the waves are reflected back. The violin is a bowed String instrument with four strings usually tuned in Perfect fifths It is the smallest and highest-pitched member A bridge is a device for supporting the strings on a Stringed instrument and transmitting the Vibration of those strings to some other structural component The nut of a String instrument is a small piece of hard material which supports the strings at the end closest to the Headstock or scroll. At the bridge and nut, the two opposed waves are in antiphase and cancel each other, producing a node. The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 A node is a point along a Standing wave where the wave has minimal Amplitude. Halfway between two nodes there is an antinode, where the two counter-propagating waves enhance each other maximally. A node is a point along a Standing wave where the wave has minimal Amplitude. There is on average no net propagation of energy. In Mathematics, an average, or central tendency of a Data set refers to a measure of the "middle" or " expected " value of

Also see: Acoustic resonance, Helmholtz resonator, and organ pipe

Propagation through strings

The speed of a wave traveling along a vibrating string (v) is directly proportional to the square root of the tension (T) over the linear density (μ):

v=\sqrt{\frac{T}{\mu}}. \,

Transmission medium

Main article: Transmission medium

The medium that carries a wave is called a transmission medium. Acoustic resonance is the tendency of an acoustic system to absorb more energy when the Frequency of its oscillations matches the system's natural frequency of vibration Helmholtz resonance is the phenomenon of air Resonance in a cavity An organ pipe is a sound-producing element of the Pipe organ that resonates at a specific pitch when pressurized air (commonly referred to as wind A Vibration in a string is a Wave. Usually a vibrating string produces a Sound whose Frequency in most cases is constant In Physics String Tension is the magnitude of the pulling force exerted by a string cable chain or similar object on another object Linear density, linear mass density or linear mass is a measure of Mass per unit of Length, and it is a characteristic of strings or other one-dimensional A transmission medium' (plural transmission media) is a material substance ( Solid, Liquid or Gas) which can propagate It can be classified into one or more of the following categories:

See also

Sources

External links

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