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Tracing the y component of a circle while going around the circle results in a sine wave (red). Tracing the x component results in a cosine wave (blue). Both waves are sinusoids of the same frequency but different phases. A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine ...
A sinusoidal plane wave could be a suitable model for a sound wave within a volume of air that is small compared to the distance of the source (provided that there are no echos from nearly objects). In that case, F ( x → , t ) {\displaystyle F({\vec {x}},t)\,} would be a scalar field, the deviation of air pressure at point x → ...
This sinusoidal model can be fit using nonlinear least squares; to obtain a good fit, routines may require good starting values for the unknown parameters. Fitting a model with a single sinusoid is a special case of spectral density estimation and least-squares spectral analysis .
Taflove and Umashankar developed the first FDTD electromagnetic wave scattering models computing sinusoidal steady-state near-fields, far-fields, and radar cross-section for two- and three-dimensional structures. [14] [15] 1984: Liao et al reported an improved ABC based upon space-time extrapolation of the field adjacent to the outer grid ...
The corresponding time-domain function for a sinusoidal exponential chirp is the sine of the phase in radians: = [+ ( ())] As was the case for the Linear Chirp, the instantaneous frequency of the Exponential Chirp consists of the fundamental frequency f ( t ) = f 0 k t T {\displaystyle f(t)=f_{0}k^{\frac {t}{T}}} accompanied by ...
Sinusoidal plane-wave solutions are particular solutions to the wave equation. The general solution of the electromagnetic wave equation in homogeneous, linear, time-independent media can be written as a linear superposition of plane-waves of different frequencies and polarizations .
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 .
By extension, in signal processing a single-frequency tone or pure tone is a purely sinusoidal signal (e.g., a voltage). A pure tone has the property – unique among real-valued wave shapes – that its wave shape is unchanged by linear time-invariant systems ; that is, only the phase and amplitude change between such a system's pure-tone ...