If a wave of a given frequency strikes a material with electrons having the same vibrational frequencies, then those electrons will absorb the energy of the wave and transform it into vibrational motion. Reflection edit main article: Reflection (physics) 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. Refraction edit main article: Refraction Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction (refraction) that results. 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.
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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 make 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 edit light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism waves exhibit common behaviors under a number of standard situations,. Transmission and media edit main articles: Rectilinear propagation, transmittance, and Transmission medium waves normally move 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 tomosynthesis of different waves at any particular point in the medium can be added. When a wave with that same natural frequency impinges upon an atom, then the electrons of that atom will be set into vibrational motion.
17 18 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. 19 20 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. 21 When a medium is nonlinear, the response to complex waves cannot be determined from a sine-wave decomposition. Plane waves edit main article: Plane wave standing waves edit main articles: Standing wave, acoustic resonance, helmholtz resonator, and Organ pipe 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 summary 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.
Displaystyle omega 2pi ffrac 2pi., The wavelength λdisplaystyle lambda of a sinusoidal waveform traveling at constant speed vdisplaystyle v is given by: 13 λvf, displaystyle lambda frac vf, where vdisplaystyle v is called the phase speed (magnitude of the phase velocity ) of the. 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. 14 summary 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. 15 due to the KramersKronig 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. 16 The sine function is periodic, so the sine wave or sinusoid has a wavelength in space and a period in time.
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. The wavelength λdisplaystyle lambda is the distance between two sequential crests or troughs (or other equivalent points generally is measured in meters. A wavenumber kdisplaystyle k, the spatial frequency of the wave in radians per unit distance (typically per meter can be associated with the wavelength by the relation k2πλ. Displaystyle kfrac 2pi lambda., The period Tdisplaystyle t is the time for one complete cycle of an oscillation of a wave. The frequency fdisplaystyle f is the number of periods per unit time (per second) and is typically measured in hertz denoted. These are related by: f1T.displaystyle ffrac., In other words, the frequency and period of a wave are reciprocals. The angular frequency ωdisplaystyle omega represents the frequency in radians per second. It is related to the frequency or period by ω2πf2πT.
The wave summary
The outline of the variation in amplitude is called the envelope of the wave. Mathematically, the modulated wave can be written in the form: 8 9 10 u(x,t)A(x,t)sin(kxωtϕ),displaystyle u(x,t)A(x,t)sin(kx-omega tphi written ), where A(x, t)displaystyle A(x, t) is the amplitude envelope of the wave, kdisplaystyle k is the wavenumber and ϕdisplaystyle phi is the phase. If the group velocity vgdisplaystyle v_g (see below) is wavelength-independent, this equation can be simplified as: 11 u(x,t)A(xvg t)sin(kxωtϕ),displaystyle u(x,t)A(x-v_g t)sin(kx-omega tphi ), 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. 11 12 Phase velocity and group velocity edit main articles: Phase velocity and Group velocity see also: Envelope (waves) Phase and group velocity There are two velocities that are associated with waves, the phase velocity and the group velocity. Phase velocity is the rate at which the phase of the wave propagates in space : any given phase of the wave (for example, the crest ) will appear to travel at the phase velocity.
The phase velocity is given in terms of the wavelength λ (lambda) and period t as vpλT. Displaystyle v_mathrm p frac lambda. A wave with the group and phase velocities going in different directions Group velocity is a property of waves that have a defined envelope, measuring propagation through space (i.e. Phase velocity) of the overall shape of the waves' amplitudes—modulation or envelope of the wave. Sinusoidal waves edit main article: Sinusoidal wave mathematically, the most basic wave is the (spatially) one-dimensional sine wave (or harmonic wave or sinusoid ) with an amplitude udisplaystyle u described by the equation: u(x,t)Asin(kxωtϕ),displaystyle u(x,t)Asin(kx-omega tphi ), where Adisplaystyle a is the maximum amplitude. In the illustration to the right, this is the maximum vertical distance between the baseline and the wave. Xdisplaystyle x is the space coordinate tdisplaystyle t is the time coordinate kdisplaystyle k is the wavenumber ωdisplaystyle omega is the angular frequency ϕdisplaystyle phi is the phase constant.
With constant amplitude udisplaystyle u with constant velocity vdisplaystyle v, where vdisplaystyle v is with constant waveform, or shape This wave can then be described by the two-dimensional functions u(x,t)F(xv t)displaystyle u(x,t)F(x-v t) (waveform Fdisplaystyle f traveling to the right) u(x,t)G(xv t)displaystyle u(x,t)G(xv t) (waveform Gdisplaystyle. A generalized representation of this wave can be obtained 4 as the partial differential equation 1v22ut22ux2.displaystyle frac 1v2frac partial 2upartial t2frac partial 2upartial., general solutions are based upon Duhamel's principle. 5 wave forms edit main article: waveform The form or shape of f in d'Alembert's formula involves the argument. 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). 6 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.
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. 7 Amplitude and modulation edit Amplitude modulation can be achieved through f(x,t).00*sin(2*pi/0.10 x-1.00*t) and g(x,t) the resultant is visible to improve clarity of waveform. Illustration of the envelope (the slowly varying red curve) of an amplitude-modulated wave. The fast varying blue curve is the carrier wave, which is being modulated. Main article: Amplitude modulation see also: Frequency modulation and Phase modulation The amplitude of a wave may be constant (in which case the wave is. Or continuous wave or may be modulated so as to vary with time and/or position.
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1 For example, based on the mechanical origin of acoustic waves, a moving disturbance in spacetime 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. 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. Mathematical description of one-dimensional waves edit wave equation edit main articles: wave equation and d'alembert's formula 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 wavelength λ, can be measured between any two corresponding points on a waveform Animation of two waves, the green wave moves to the right while blue wave moves to the left, the net red wave amplitude with at each point. Note that f(x,t) g(x,t) u(x,t) in the xdisplaystyle x direction in space. G., let the positive xdisplaystyle x direction be to the right, and the negative xdisplaystyle x direction be to the left.
However, this motion is problematic for a standing wave (for example, a wave on meaning a string where energy is moving in both directions equally, or for electromagnetic (e.g., light) waves in a vacuum, where the concept of medium does not apply and interaction with. There are water waves on the ocean surface; gamma waves and light waves emitted by the sun; microwaves used in microwave ovens and in radar equipment; radio waves broadcast by radio stations; and sound waves generated by radio receivers, telephone handsets and living creatures (as. 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 ; and. Other properties, however, although usually described in terms of origin, 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 of their physical origin.
creates oscillations that are perpendicular to the propagation of energy transfer, or longitudinal : the oscillations are parallel to the direction of energy propagation. While mechanical waves can be both transverse and longitudinal, all electromagnetic waves are transverse in free space. Contents General features edit 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 as a wave results in a blurred 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 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 1982,. .
Restoring forces then reverse the deformation. For example, sound waves propagate via air molecules colliding with their neighbours. When the molecules collide, they also bounce away from each other (a restoring force). This keeps the molecules from continuing to travel in the direction of the wave. Electromagnetic waves do not require a medium. Instead, they consist of periodic oscillations of electrical and magnetic fields originally generated by charged particles, and can therefore travel through diary a vacuum. These types vary in wavelength, and include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, x-rays and gamma rays. 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.
The wave (tv short 1981) - plot Summary - imdb
This article is about waves in the scientific sense. For waves on the surface of the ocean or lakes, see. For other uses, see, wave (disambiguation). Different types entry of wave with varying rectifications. In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport. Waves consist of oscillations or vibrations of a physical medium or a field, around relatively fixed locations. There are two main types of waves: mechanical and electromagnetic. Mechanical waves propagate through a physical matter, whose substance is being deformed.