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Encyclopedia > Wave
Surface waves in water

Wave is the moving ripple on liquid or ocean: any of a series of ripples moving across the surface of a liquid, especially a large raised ridge of water moving across the surface of the sea. 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 of rest (e.g. Campbell & Greated, 1987: 5) or, more generally, as a variation of any physical property of a system around a reference value. However, defining the necessary and sufficient characteristics that qualify a phenomenon to be called a wave is, at least, flexible. 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). However, this notion is problematic for a standing wave (e.g. 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. Look up vibration in Wiktionary, the free dictionary. ... Look up vibration in Wiktionary, the free dictionary. ... Vibration and standing waves in a string, The fundamental and the first 6 overtones A standing wave, also known as a stationary wave, is a wave that remains in a constant position. ... Look up Vacuum in Wiktionary, the free dictionary. ...

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 (i.e. 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 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 (e.g. scattering of sound by sound), is still a researched area in the study of sound. As another example, the phenomenon of dispersion demonstrates that wave modulations behave as regular waves. When modulations propagate in media where the speed of wave propagation depends on frequency, they separate from the complex wave they belonged to and travel independently carrying energy, similarly to the rest of the frequency components of the complex wave. It is true that this separation will never happen in a non-dispersive medium such as air, where all frequencies move with the same speed. Nonetheless, the important point is that the dispersive case serves to illustrate that modulations in general and amplitude fluctuations in particular behave as waves. Dispersion provides a case where modulations are isolated from the waves that carry them and can therefore be studied more easily (assuming that the only characteristic that changes during dispersion is the modulations' velocity). In addition, systems with dispersion provide better cases for the mathematical analysis of the kinematic properties of waves (i.e. frequency, wavelength, phase and group velocities). In the case of sound waves, diffraction, absorption, reverberation, and interference are examples of phenomena that have been better understood with the aid of dispersion theory. This article is about a portion of a periodic process. ... For other uses, see Light (disambiguation). ... 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 a straight trajectory by one or more localized non-uniformities in the medium through which it passes. ... Dispersion can mean any of several things: A phenomenon that causes the separation of a wave into components of varying frequency. ... In telecommunications, modulation is the process of varying a periodic waveform, i. ... In telecommunications, modulation is the process of varying a periodic waveform, i. ... For other uses, see Frequency (disambiguation). ... For other uses, see Frequency (disambiguation). ...

To summarize, the term wave implies three general notions: vibrations in time, disturbances in space, and moving disturbances in space-time associated with the transfer/transformation of energy. Based on these notions, the following origin-specific definition may be adopted for sound waves in air (Vassilakis, 2001): "Sound-waves in air represent a transfer of vibratory energy characterized by: i) rate (frequency), ii) starting position (phase), and iii) magnitude (amplitude) of vibration. In general, amplitude can be expressed equivalently in terms of maximum displacement, velocity, or pressure relative to a reference value. Sound waves in air are manifested as alternating air-condensations and rarefactions that spread away from the vibrating source with a velocity usually not related to the velocity amplitude of the vibration. They result in pressure/density disturbance patterns in the surrounding medium, which, in general, correspond to the signal that plots the vibration of the source over time." This definition will serve as an initial operational definition of sound waves in air to which further qualifications may be added as needed. It is the one who shock us

## Characteristics

Periodic waves are characterized by crests (highs) and troughs (lows), and may usually be categorized as either longitudinal or transverse. 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. Longitudinal waves are those with vibrations parallel to the direction of the propagation of the wave; examples include most sound waves. A crest is the section of a wave that rises above an undisturbed position. ... Categories: Move to Wiktionary | Stub ... A light wave is an example of a transverse wave. ... Longitudinal waves are waves that have vibrations along or parallel to their direction of travel. ...

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

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

The reflection of a bridge in Indianapolis, Indianas Central Canal. ... For the property of metals, see refraction (metallurgy). ... The intensity pattern formed on a screen by diffraction from a square aperture Diffraction refers to various phenomena associated with wave propagation, such as the bending, spreading and interference of waves passing by an object or aperture that disrupts the wave. ... For other uses, see Interference (disambiguation). ... In linear algebra, the principle of superposition states that, for a linear system, a linear combination of solutions to the system is also a solution to the same linear system. ... Dispersion of a light beam in a prism. ... Rectilinear propagation is a wave property which states that waves propagate (move or spread out) in straight lines. ...

### Polarization

Main article: Polarization

A wave is polarized if it can only oscillate in one direction. 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.Linked with Optical Isomerism In electrodynamics, polarization (also spelled polarisation) is the property of electromagnetic waves, such as light, that describes the direction of their transverse electric field. ... This article treats polarization in electrodynamics. ...

### Examples

An ocean surface wave crashing into rocks

Examples of waves include: Image File history File linksMetadata Download high-resolution version (1704x2272, 2026 KB) Author: Earth Network Editor Use: Image in public domain (requested to not be used for harmful purposes) Source: Digital camera, Taken in Cornwall. ... Image File history File linksMetadata Download high-resolution version (1704x2272, 2026 KB) Author: Earth Network Editor Use: Image in public domain (requested to not be used for harmful purposes) Source: Digital camera, Taken in Cornwall. ...

## Mathematical description

From mathematical point of view most primitive (or fundamental) wave is harmonic (sinusoidal) wave which is described by the equation f(x,t) = Asin(wt-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 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). 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. The form of the variation of amplitude is called the envelope of the wave. moved over from meta File links The following pages link to this file: Wave Amplitude Categories: GFDL images ... This article is about the components of sound. ... It has been suggested that pulse amplitude be merged into this article or section. ... 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. ... A continuous wave (CW) is an electromagnetic wave of constant amplitude and frequency. ...

The wavelength (denoted as λ) is the distance between two sequential crests (or troughs). This generally has the unit of meters; it is also commonly measured in nanometers for the optical part of the electromagnetic spectrum. For other uses, see Wavelength (disambiguation). ... Legend Î³ = Gamma rays HX = Hard X-rays SX = Soft X-Rays EUV = Extreme ultraviolet NUV = Near ultraviolet Visible light NIR = Near infrared MIR = Moderate infrared FIR = Far infrared Radio waves EHF = Extremely high frequency (Microwaves) SHF = Super high frequency (Microwaves) UHF = Ultra high frequency VHF = Very high frequency HF = High...

A wavenumber k can be associated with the wavelength by the relation Wavenumber in most physical sciences is a wave property inversely related to wavelength, having SI units of reciprocal meters (mâˆ’1). ...

$k = frac{2 pi}{lambda}. ,$
Waves can be represented by simple harmonic motion.

The period T is the time for one complete cycle for an oscillation of a wave. The frequency f (also frequently denoted as ν) is how many periods per unit time (for example one second) and is measured in hertz. These are related by: Image File history File links Simple_harmonic_motion_animation. ... Image File history File links Simple_harmonic_motion_animation. ... Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. ... Periodicity is the quality of occurring at regular intervals (e. ... For other uses, see Frequency (disambiguation). ... This article is about the SI unit of frequency. ...

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

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. It is related to the frequency by It has been suggested that this article or section be merged into Angular velocity. ...

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

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 The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ...

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

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

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

### 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 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 travelling 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 The wave equation is an important partial differential equation that describes the propagation of a variety of waves, such as sound waves, light waves and water waves. ... Visualization of airflow into a duct modelled using the Navier-Stokes equations, a set of partial differential equations. ...

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

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 vector calculus, the Laplace operator or Laplacian is a differential operator equal to the sum of all the unmixed second partial derivatives of a dependent variable. ...

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 Jean le Rond dAlembert, pastel by Maurice Quentin de la Tour Jean Le Rond dAlembert (November 16, 1717 &#8211; October 29, 1783) was a French mathematician, mechanician, physicist and philosopher. ...

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

This can be viewed as two pulses travelling 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 behaviour 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. For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ...

### Traveling waves

Simple wave or traveling wave, also sometimes called 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 velocity vp of this wave is given by This article is about a portion of a periodic process. ... The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ...

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

where λ is the wavelength of the wave. For other uses, see Wavelength (disambiguation). ...

### Standing wave

Main article: standing wave Vibration and standing waves in a string, The fundamental and the first 6 overtones A standing wave, also known as a stationary wave, is a wave that remains in a constant position. ...

Standing wave in stationary medium. 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. 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. Animation of a standing wave. ... A standing wave. ... For other uses, see Interference (disambiguation). ...

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 two opposed waves each cancel the wave propagation of the other. This effect is known as interference. There is no net propagation of energy. For the Anne Rice novel, see Violin (novel). ... A Violin Bridge blank and finished bridge 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 of the instrument in order to transfer the sound to the surrounding air balls. ... The nut of a string instrument is a small strip or block of hard material forming a transition between the strings playing length and the tuning machines on the headstock, or the tuning pegs in the pegbox at the upper end of the fingerboard. ... For other uses, see Interference (disambiguation). ...

Also see: Acoustic resonance, Helmholtz resonator, and organ pipe Acoustic resonance is an important consideration for instrument builders as most acoustic instruments use resonators, such as the strings and body of a violin, the length of tube in a flute, and the shape of a drum membrane. ... A brass, spherical Helmholtz resonator based on his original design, from around 1890-1900. ... The choir division of the organ at St. ...

### 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): A vibration in a string is a wave. ... Tension is a reaction force applied by a stretched string (rope or a similar object) on the objects which stretch it. ... The linear density of a one-dimensional object is calculated as the mass per unit length of the object. ...

$v=sqrt{frac{T}{mu}} ,$

## Transmission medium

Main article: Transmission medium

The medium that carries a wave is called a transmission medium. It can be classified into one or more of the following categories: A transmission medium is any material substance, such as fiber-optic cable, twisted-wire pair, coaxial cable, dielectric-slab waveguide, water, or air, that can be used for the propagation of signals, usually in the form of modulated radio, light, or acoustic waves, from one point to another. ...

• A linear medium if the amplitudes of different waves at any particular point in the medium can be added.
• A bounded medium if it is finite in extent, otherwise an unbounded medium.
• A uniform medium if its physical properties are unchanged at different locations in space.
• An isotropic medium if its physical properties are the same in different directions.

A transmission medium is any material substance, such as fiber-optic cable, twisted-wire pair, coaxial cable, dielectric-slab waveguide, water, or air, that can be used for the propagation of signals, usually in the form of modulated radio, light, or acoustic waves, from one point to another. ... This is a list of wave topics, by Wikipedia page. ... A capillary wave is a wave travelling along a meniscus, whose dynamics are dominated by the effects of surface tension. ... A source of waves moving to the left. ... The group velocity of a wave is the velocity with which the variations in the shape of the waves amplitude (known as the modulation or envelope of the wave) propagate through space. ... The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ... Wikibooks has more about this subject: School science how-to 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. ... Vibration and standing waves in a string, The fundamental and the first 6 overtones A standing wave, also known as a stationary wave, is a wave that remains in a constant position. ... Stadium crowd performing the wave at the Confederations Cup 2005 in Frankfurt A packed crowd in a stadium does the wave (in some places outside of North America known as the Mexican wave) when a wave is created in the crowd by successive groups of spectators briefly standing and raising... The Ocean Waves, see I Can Hear the Sea Ocean waves Ocean surface waves are surface waves that occur in the upper layer of the ocean. ... The Draupner wave, a single giant wave measured on New Years Day 1995, finally confirmed the existence of freak waves, which had previously been considered near-mythical Rogue waves, also known as freak waves, or extreme waves, are relatively large and spontaneous ocean surface waves which are a threat... Output from a shallow water equation model of water in a bathtub. ... Hans Jenny created this image during his studies of cymatics. ... Reaction-diffusion systems are systems characterized by having two or more diffusible reactants. ... A beat wave is the product of two waves with slightly different frequencies added together. ...

## Sources

• Campbell, M. and Greated, C. (1987). The Musician’s Guide to Acoustics. New York: Schirmer Books.
• French, A.P. (1971). Vibrations and Waves (M.I.T. Introductory physics series). Nelson Thornes. ISBN 0-393-09936-9.
• Hall, D. E. (1980). Musical Acoustics: An Introduction. Belmont, California: Wadsworth Publishing Company.
• Hunt, F. V. (1978). Origins in Acoustics. New York: Acoustical Society of America Press, (1992).
• Ostrovsky, L. A. and Potapov, A. S. (1999). Modulated Waves, Theory and Applications. Baltimore: The Johns Hopkins University Press.
• Vassilakis, P.N. (2001). Perceptual and Physical Properties of Amplitude Fluctuation and their Musical Significance. Doctoral Dissertation. University of California, Los Angeles.

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