Definition:Out of Phase

Definition

Let $\phi_1$ and $\phi_2$ be a harmonic waves expressed in wave number and frequency form as:

\(\ds \forall x, t \in \R: \, \)

\(\ds \map {\phi_1} {x, t}\)

\(=\)

\(\ds a \map \cos {2 \pi \paren {k x - \nu t} }\)

\(\ds \map {\phi_2} {x, t}\)

\(=\)

\(\ds a \map \cos {2 \pi \paren {k x - \nu t} + \epsilon}\)

Let the phase $\epsilon$ be such that $\epsilon \in \set {2 n + 1 \pi: n \in \Z}$.

Then $\phi_1$ and $\phi_2$ are described as being out of phase.

Sources

• 1955: C.A. Coulson: Waves (7th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Equation of Wave Motion: $\S 3$