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Signal velocity is usually equal to group velocity (the speed of a short "pulse" or of a wave-packet's middle or "envelope"). However, in a few special cases (e.g., media designed to amplify the front-most parts of a pulse and then attenuate the back section of the pulse), group velocity can exceed the speed of light in vacuum, while the signal ...
The attenuation in the signal of ground motion intensity plays an important role in the assessment of possible strong groundshaking. A seismic wave loses energy as it propagates through the earth (seismic attenuation). This phenomenon is tied into the dispersion of the seismic energy with the distance. There are two types of dissipated energy:
An electromagnetic wave propagating in the +z-direction is conventionally described by the equation: (,) = [()], where E 0 is a vector in the x-y plane, with the units of an electric field (the vector is in general a complex vector, to allow for all possible polarizations and phases);
In the above formula, P is measured in units of power, such as watts (W) or milliwatts (mW), and the signal-to-noise ratio is a pure number. However, when the signal and noise are measured in volts (V) or amperes (A), which are measures of amplitude, [note 1] they must first be squared to obtain a quantity proportional to power, as shown below:
It is also used in equation (4) of the 2005 NASA's report [3] in an application of satellite tracking. The assumption of the refraction index varying with the latitude is not strictly compatible with the notion of layers. However the variation of the index is very small, this point is usually ignored in practice.
Attenuation constant can be defined by the amplitude ratio | A 0 A x | = e α x {\displaystyle \left|{\frac {A_{0}}{A_{x}}}\right|=e^{\alpha x}} The propagation constant per unit length is defined as the natural logarithm of the ratio of the sending end current or voltage to the receiving end current or voltage, divided by the distance x involved:
In physics, the acoustic wave equation is a second-order partial differential equation that governs the propagation of acoustic waves through a material medium resp. a standing wavefield. The equation describes the evolution of acoustic pressure p or particle velocity u as a function of position x and time t. A simplified (scalar) form of the ...
In acoustics, Stokes's law of sound attenuation is a formula for the attenuation of sound in a Newtonian fluid, such as water or air, due to the fluid's viscosity.It states that the amplitude of a plane wave decreases exponentially with distance traveled, at a rate α given by = where η is the dynamic viscosity coefficient of the fluid, ω is the sound's angular frequency, ρ is the fluid ...