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A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine function. In mechanics , as a linear motion over time, this is simple harmonic motion ; as rotation , it corresponds to uniform circular motion .
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
A sphere rotating around an axis. Points farther from the axis move faster, satisfying ω = v / r.. In physics, angular frequency (symbol ω), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function (for example, in oscillations and waves).
with T the wave period (the reciprocal of the frequency f, T=1/f). So in deep water the phase speed increases with the wavelength, and with the period. Since the phase speed satisfies c p = λ/T = λf, wavelength and period (or frequency) are related. For instance in deep water:
where is the speed of the wave, the fundamental frequency can be found in terms of the speed of the wave and the length of the pipe: f 0 = v 4 L {\displaystyle f_{0}={\frac {v}{4L}}} If the ends of the same pipe are now both closed or both opened, the wavelength of the fundamental harmonic becomes 2 L {\displaystyle 2L} .
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 ...
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 ...