# Wavelength to Frequency Calculator

### Input

 Wavelength $$\lambda$$ millimetercentimetermeterkilometer Relative Permittivity $$\epsilon_{r}$$

### Output

 The Frequency is $$\nu$$ ____ GHzMHzKHzHz

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

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

 Where: $$\lambda$$ = Wavelength $$\nu$$ = Frequency $$c$$ = Velocity of light $$\epsilon_{r}$$ = Relative Permittivity

Other Related Calculator:
- Frequency to Wavelength

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