Phase (waves) - Formula

Formula

The phase of an oscillation or wave refers to a sinusoidal function such as the following:

$\begin{align} x(t) &= A \cos( 2 \pi f t + \phi ) \\ y(t) &= A \sin( 2 \pi f t + \phi ) = A\cdot \cos\left( 2 \pi f t + \phi - \frac{\pi}{2}\right) \end{align}$

where, and are constant parameters called the amplitude, frequency, and phase of the sinusoid. These functions are periodic with period, and they are identical except for a displacement of along the axis. The term phase can refer to several different things:

It can refer to a specified reference, such as, in which case we would say the phase of is, and the phase of is .
It can refer to, in which case we would say and have the same phase but are relative to their own specific references.
In the context of communication waveforms, the time-variant angle, or its modulo value, is referred to as instantaneous phase, often just phase.

Read more about this topic: Phase (waves)

Famous quotes containing the word formula:

“But suppose, asks the student of the professor, we follow all your structural rules for writing, what about that “something else” that brings the book alive? What is the formula for that? The formula for that is not included in the curriculum.”
—Fannie Hurst (1889–1968)

“Every formula which expresses a law of nature is a hymn of praise to God.”
—Maria Mitchell (1818–1889)

“Ideals possess the strange quality that if they were completely realized they would turn into nonsense. One could easily follow a commandment such as “Thou shalt not kill” to the point of dying of starvation; and I might establish the formula that for the proper functioning of the mesh of our ideals, as in the case of a strainer, the holes are just as important as the mesh.”
—Robert Musil (1880–1942)