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| ] ] ] ] | |||
| A '''wave''' is a disturbance that propagates. Apart from ], which can travel through vacuum, waves have a medium through which they travel and can transfer energy from one place to another without any of the particles of the medium being displaced permanently. Instead, any particular point ] around a fixed position. | |||
| == Examples of waves == | |||
| *Sea-waves, which are perturbations that propagate through water (see also ] and ]). | |||
| *] - a mechanical wave that propagates through air, liquid or solids, and is of a frequency detected by the ]. Similar are ]s in ]s, of which there are the S, P and L kinds. | |||
| *], ], ]s, etc. make up ]. In this case propagation is possible without a medium, through vacuum. | |||
| == Characteristic properties == | |||
| All waves have common behaviour under a number of standard situations. All waves can experience the following: | |||
| *] - when a wave turns back from the direction it was travelling, due to hitting a reflective material. | |||
| *] - the change of direction of waves due to them entering a new medium. | |||
| *] - the spreading out of waves, for example when they travel through a small slit. | |||
| *] - the addition of two waves that come in to contact with each other. | |||
| *] - the splitting up of a wave up depending on frequency. | |||
| == Transverse and longitudinal waves == | |||
| ]s are those with vibrations perpendicular to the wave's direction of travel; examples include ]s on the surface of a pond, waves on a string and electromagnetic waves. ]s are those with vibrations along the wave's direction of travel; examples include sound waves. | |||
| === Polarization === | |||
| Transverse waves can be ]. Unpolarised waves can oscillate in any direction in the plane perpendicular to the direction of travel, while polarized waves oscillate in only one direction perpendicular to the line of travel. | |||
| == Physical description of a wave == | |||
| ] | |||
| Waves can be described using a number of standard variables including: ], ], ] and ]. | |||
| The ] of a wave is the measure of the magnitude of the maximum disturbance in the medium during one wave cycle, and is measured in units depending on the type of wave. For examples, 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 ] (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. | |||
| The period (''T'') is the time for one complete cycle for an oscillation of a wave. The frequency (''F'') is how many periods per unit time (for example one second) and is measured in ]. These are related by: | |||
| :<math>f=\frac{1}{T}</math>. | |||
| When waves are expressed mathematically, the '']'' (''ω'', radians/second) is often used; it is related to the frequency ''f'' by: | |||
| :<math>f=\frac{\omega}{2 \pi}</math>. | |||
| === Travelling waves === | |||
| Waves that remain in one place are called ''standing waves'' - eg vibrations on a violin string. | |||
| Waves that are moving are called ''travelling waves'', and have a disturbance that varies both with time ''t'' and distance ''z''. This can be expressed mathematically as: | |||
| <math>y=A(z,t) \cos (\omega t - kz + \phi)</math>, | |||
| where ''A''(''z'',''t'') is the amplitude envelope of the wave, ''k'' is the ''wave number'' and ''φ'' is the '']''. The velocity ''v'' of this wave is given by: | |||
| <math>v=\frac{\omega}{k}= \lambda f</math>, | |||
| where ''λ'' is the '']'' of the wave. | |||
| === The wave equation === | |||
| In the most general sense, not all waves are sinusoidal. One example of a non-sinusoidal wave is a pulse that travels down a rope resting on the ground. In the most general case, any function of x, y, z, and t that is a non-trivial solution to the ] is a wave. The ] is a differential equation which describes a harmonic wave passing through a certain medium. The equation has different forms depending on how the wave is transmitted, and on what medium. | |||
| The ] describes the wave-like behaviour of particles in ]. Solutions of this equation are ]s which can be used to describe the probability density of a particle. | |||
| == See also == | |||
| *] | |||
| *] | |||
| *] | |||