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Learn what a sinusoidal function is, how to graph it, and how to write its equation. See examples of sinusoidal functions with different amplitudes, periods, phases and shifts.
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.
30 Δεκ 2020 · Combining the dependencies on space and time in a single expression, we can write for the sinusoidal wave: \[u(x, t)=A \cos (k x-\omega t) \label{9.1}\] Figure \(\PageIndex{1}\): Two basic types of waves.
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 \(A\).
A sinusoid is periodic, meaning it repeats at regular intervals. y(t) = y(t + T) y (t) = y (t + T) For example, at times t 1 and t 1 + T, the sinusoidal wave takes the same value, y (t 1) = y (t 1 + T) = -A. This holds for any multiple of T, meaning y (t 1) = y (t 1 + kT) = -A where k = 1, 2, 3, and so on.
In physics, a sinusoidal plane wave is a special case of plane wave: a field whose value varies as a sinusoidal function of time and of the distance from some fixed plane. It is also called a monochromatic plane wave, with constant frequency (as in monochromatic radiation).
Let sine enter your mental toolbox (Hrm, I need a formula to make smooth changes... Eventually, we'll understand the foundations intuitively ( e , pi , radians , imaginaries , sine...) and they can be mixed into a scrumptious math salad.
