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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.
Learn what a sinusoidal function is, how to graph it, and how to write its equation in the form y = A·sin (B (x-C)) + D. See examples of sinusoidal graphs with different parameters and how to find them.
30 Δεκ 2020 · Learn about the simplest kind of wave, a transverse sinusoidal wave in a one-dimensional string, and its equation. Find out how to describe the wave in terms of amplitude, frequency, phase, wavelength, and speed.
Finding the characteristics of a sinusoidal wave. To find the amplitude, wavelength, period, and frequency of a sinusoidal wave, write down the wave function in the form \(y(x, t)=A \sin (k x-\omega t+\phi)\). The amplitude can be read straight from the equation and is equal to \(A\).
Equation for Sinusoidal Wave: The general equation for a sinusoidal wave is y(t) = A sin(ωt + φ). Here, y(t) is the wave value at any given time t, A is the amplitude, ω is the angular frequency, and φ is the phase of the wave.
Sinusoidal Functions. Sinusoidal functions (or sinusoid ∿) are based on the sine or cosine functions. y = A ⋅sin(ωx+ϕ) y = A ⋅ sin (ω x + ϕ) y = A ⋅cos(ωx+ ϕ) y = A ⋅ cos (ω x + ϕ) where A is the amplitude, ω (omega) is the angular frequency (radians per second), and φ (phi) is the phase shift. A,ω,ϕ ∈ R A, ω, ϕ ∈ R.
22 Μαΐ 2022 · The sine wave is the simplest wave that may be created. It represents the motion of a simple vector rotating at a constant speed, such as the vertical displacement of the second hand of a clock. An example is shown in Figure \(\PageIndex{1}\).
