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In general term a wave is generated by an oscillating physical quantity when the oscillation propagates following the so called wave equation.

When the oscillation starts the wave start to propagate:: in this transient situation the wavefront is the set of points that are reached by the wave at the same time. In general, due to the continuity of physical phenomena, the wavefront is a regular surface, but its shape changes in time.

The wave propagation direction in a particular point is perpendicular to the wavefront passing from that point.

The frequency spectrum of the wave is composed by all the frequencies whose power is not null (in light waves generally we call the frequency "colors" thus the frequency spectrum of a light wave is composed by all the colors that are present in the wave. If the frequency spectrum of the wave is composed by a a single powerful frequency with a set of side frequencies much less powerful, the wave is called monochromatic and the prevalent frequency is called wave frequency (a similar light wave is seen of a well specified color, for example red or green).

Each frequency that is present in a wave can be associated with a purely monochromatic wave, that is a wave constituted by that frequency only. Thus a wave can be represented as a superposition of monochromatic waves.

When the wave is created, every monochromatic wave has its own wavefront and its own velocity, that is different from frequency to frequency (that is in a light wave in air or in glass every color has a different speed). The speed of a single frequency is called phase speed and the fact that each frequency has a different speed is called wave dispersion. Sometimes there is no dispersion, that is all the frequencies have the same speed. This is the case of light in vacuum: the speed of every color of light in vacuum is generally simply called light speed.

When dispersion is present, the overall wave (composed by all the frequencies) proceeds with a collective speed that can be obtained by the frequency spectrum of the wave and by the speed of each frequency (also called dispersion relation of the wave) and that is called group speed of the wave.

The wavelength of each frequency component of the wave is obtained by dividing the speed of that frequency component by the frequency itself. In a purely periodic and monochromatic wave (that is a wave repeating itself at fixed time intervals and with a spectrum reduced to a single frequency) the wavelength is the distance in space along the propagation direction at which the wave value is the same in every moment.

The amplitude of the wave for a frequency and in a certain point is the value of the frequency spectrum in that point, that physically is the square root of the power transported by the considered frequency component of the wave through a unitary surface around the considered point. The total power that the wave transport through a given surface in space is the sum of the power transported by each individual frequency.

The phase of a frequency component of the wave in a point can be calculated by evaluating the value of that component in the initial instant (t=0), dividing by the amplitude and calculating the inverse sin of the obtained number (arcsin() ).

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