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