Definition:Periodic Wave
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Definition
A periodic wave is a wave which is propagated without change of shape whose wave profile is a periodic function.
Wavelength
Let $\phi$ be a periodic wave expressed as:
- $\forall x, t \in \R: \map \phi {x, t} = \map f {x - c t}$
The wavelength $\lambda$ of $\phi$ is the period of the wave profile of $\phi$.
Period
Let $\phi$ be a periodic wave expressed as:
- $\forall x, t \in \R: \map \phi {x, t} = \map f {x - c t}$
The period $\tau$ of $\phi$ is the time taken for one complete wavelength of $\phi$ to pass an arbitrary point on the $x$-axis.
Frequency
Let $\phi$ be a periodic wave expressed as:
- $\forall x, t \in \R: \map \phi {x, t} = \map f {x - c t}$
The frequency $\nu$ of $\phi$ is the number of complete wavelengths of $\phi$ to pass an arbitrary point in unit time.
Wave Number
Let $\phi$ be a periodic wave expressed as:
- $\forall x, t \in \R: \map \phi {x, t} = \map f {x - c t}$
The wave number $k$ of $\phi$ is the number of complete wavelengths of $\phi$ per unit distance along the $x$-axis.
Also see
- Results about periodic waves can be found here.
Sources
- 1955: C.A. Coulson: Waves (7th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Equation of Wave Motion: $\S 3$