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For an incident wave traveling from one medium (where the wave speed is c 1) to another medium (where the wave speed is c 2), one part of the wave will transmit into the second medium, while another part reflects back into the other direction and stays in the first medium. The amplitude of the transmitted wave and the reflected wave can be ...
The additivity of the forward and backward wavelets coinciding at the site of measurement at a particular time can be combined algebraically with the water-hammer equations to calculate the magnitudes of the two wavelets [2] = This method assumes that the wave speed is constant. In general, the wave speed is a function of the pressure.
For a monochromatic propagating electromagnetic wave, such as a plane wave or a Gaussian beam, if E is the complex amplitude of the electric field, then the time-averaged energy density of the wave, travelling in a non-magnetic material, is given by: = | |, and the local intensity is obtained by multiplying this expression by the wave velocity
[2] [3] [4] It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time (ordinary frequency) or radians per unit time (angular frequency). In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space.
Wave speed is a wave property, which may refer to absolute value of: . phase velocity, the velocity at which a wave phase propagates at a certain frequency; group velocity, the propagation velocity for the envelope of wave groups and often of wave energy, different from the phase velocity for dispersive waves
t is time, ψ is a function of r and t describing the disturbance describing the wave (for example, for an ocean wave, ψ would be the excess height of the water, or for a sound wave, ψ would be the excess air pressure). A is the amplitude of the wave (the peak magnitude of the oscillation), φ is a phase offset,
Since the amplitude to travel from x to y after a time t + t ' can be considered in two steps, the propagator obeys the composition identity, (;) (; ′) = (; + ′) , which can be interpreted as follows: the amplitude to travel from x to z in time t + t ' is the sum of the amplitude to travel from x to y in time t, multiplied by the amplitude ...
A wave packet has an envelope that describes the overall amplitude of the wave; within the envelope, the distance between adjacent peaks or troughs is sometimes called a local wavelength. [21] [22] An example is shown in the figure. In general, the envelope of the wave packet moves at a speed different from the constituent waves. [23]