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The number of waves that moves a fixed point in unit time is known as frequency.

$f\mathit{=}\frac{\mathit{1}}{\mathit{T}}or\frac{\mathit{蝇}}{\mathit{2}\mathit{蟺}}$

Where, Time period in seconds and is angular frequency in .

The frequency, wavelength, and speed of light of any wave are related by the wavelength-frequency relationship.

The wavelength-frequency relationship is:

$c=位f$

Where, c is the speed of light which is equal to $3脳{10}^8\mathrm{m}/\mathrm{s}$, is the wavelength and f is the frequency.

The wavelength is inversely proportional to the frequency.

$位=\frac{c}{f}or\frac{v}{f}$

Where, v is velocity of wave in .

The relation between wave number and wavelength is:

$k=\frac{2蟺}{位}$

Where, k is wavenumber in .

The formula used to determine the amplitude of electric and magnetic fields of the wave are:

$$\begin{gathered} E_{max}=\sqrt{\frac{2l}{{蔚}_{0}c}} \\ {B}_{max}=\frac{E_{max}}{c} \end{gathered}$$

The equations of sinusoidal electromagnetic wave for electric and magnetic field are:

$$\begin{gathered} \stackrel{鈫�}{E}=E_{max}\cos \left(kx-蝇t\right) \\ \stackrel{鈫�}{B}=B_{max}\cos \left(kx-蝇t\right) \end{gathered}$$

$\stackrel{鈫�}{\mathrm{B}}(\mathrm{x},\mathrm{t})=-(8.25脳{10}^{-9}\mathrm{T})\hat{\mathrm{j}}\cos [(1.38脳{10}^4\mathrm{rad}/\mathrm{m})\mathrm{x}+\mathrm{蝇迟}]$Given that,

The values of wavenumber$\left(k\right)$ is$1.38脳{10}^4\mathrm{rad}/\mathrm{m}$ and the maximum magnetic field is .

${\mathrm{B}}_{\max }\mathrm{is}-8.25脳{10}^{-9}\mathrm{T}$

$\stackrel{鈫�}{\mathrm{B}}=-{\mathrm{B}}_{\max }\cos \left(\mathrm{kx}+\mathrm{蝇迟}\right)$

Since, if the phase of wave is$kx-蝇t$ then wave travels in positive x- direction. Therefore, the above equation defines the wave is travelling in negative x-direction as the phase of wave is $kx-蝇t$.

The frequency of wave is:

$$\begin{gathered} \mathrm{f}=\frac{\mathrm{c}}{\mathrm{位}} \\ =\frac{\mathrm{kc}}{2\mathrm{蟺}} \\ =\frac{\left(1.38脳{10}^4\right)\left(3.0脳{10}^8\right)}{2\mathrm{蟺}} \\ =6.59脳{10}^{11}\mathrm{Hz} \end{gathered}$$

The angular velocity of wave is:

$$\begin{gathered} \mathrm{蝇}=2\mathrm{蟺蹿} \\ =2\mathrm{蟺}\left(6.59脳{10}^{11}\right) \\ =4.14脳{10}^{12}\mathrm{rad}/\mathrm{s} \end{gathered}$$

The formula used to determine the amplitude of electric fields of the wave are:

$$\begin{gathered} {\mathrm{E}}_{\max }={\mathrm{cB}}_{\max } \\ =\left(3脳{10}^8\right)\left(-8.28脳{10}^9\right) \\ =-2.48\mathrm{V}/\mathrm{m} \end{gathered}$$

The equation of sinusoidal electromagnetic wave for magnetic field is:

$$\begin{gathered} \stackrel{鈫�}{\mathrm{E}}={\mathrm{E}}_{\max }\cos \left(\mathrm{kx}+\mathrm{蝇迟}\right) \\ =\left(-2.48\mathrm{V}/\mathrm{m}\right)\cos \left[\left(1.38脳{10}^4\mathrm{rad}/\mathrm{m}\right)\mathrm{x}+\left(4.14脳{10}^{12}\mathrm{rad}/\mathrm{s}\right)\mathrm{t}\right] \end{gathered}$$

Hence, the vector equation for is $\stackrel{鈫�}{\mathrm{E}}=\left(\mathrm{x},\mathrm{t}\right)$.

$\stackrel{鈫�}{\mathrm{E}}=\left(-2.48\mathrm{V}/\mathrm{m}\right)\cos \left[\left(1.38脳{10}^4\mathrm{rad}/\mathrm{m}\right)\mathrm{x}+\left(4.14脳{10}^{12}\mathrm{rad}/\mathrm{s}\right)\mathrm{t}\right]$