# Frequency to Wavelength Calculator

*Waves:*
Periodic wave is the wave disturbance that repeats itself in time and space. If the periodic wave is sinusoidal, the shape of wave takes the form of a sine or cosine function, hence it can be called as harmonic waves. For instance an electromagnetic wave traveling in x-direction could be represented as

\(E(x,t)=E_{max}cos(kx-\omega t+\phi )\)

\(E\) is the electric field vector. The wave number is \(k = \frac{2\pi}{\lambda} \), where \( \lambda \) is the wavelength of the wave. The frequency \(\nu \) of the wave is \(\nu = \frac{\omega}{2\pi} \), \(\omega\) is the angular frequency. \( \phi \) is the phase offset.

*Wavelength \( \lambda \):* Wavelength is the amount
of distance per cycle and has dimensions of length.

*Frequency \(\nu \):* Frequency is the number of cycles per amount of time and has units of one over time
or hertz (Hz). The frequency of a wave is the inverse of the wave’s period \(t\).

Product of Frequency and wavelength is equal to the velocity of wave provided relative permittivity is unity.

## Formula

\(\lambda=\frac{c}{\nu\sqrt{\epsilon _{r}}}\)

Where: |

\(\lambda \) = Wavelength |

\(\nu \) = Frequency |

\(c \) = Velocity of Light |

\(\epsilon_{r}\) = Relative Permittivity |

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