91Ó°ÊÓ

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

$f=\frac{1}{T}or\frac{\mathrm{Ó\neg }}{2\mathrm{Ï€}}$

Where,T =Time period in seconds and $\mathrm{Ó\neg }$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:

$c=\mathrm{λ}f$

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

The wavelength is inversely proportional to the frequency.

$\mathrm{λ}=\frac{\mathrm{c}}{\mathrm{f}}\mathrm{or}\frac{\mathrm{v}}{\mathrm{f}}$

Where, v is velocity of wave in m/s .

The relation between wave number and wavelength is:

$k=\frac{2\mathrm{π}}{\mathrm{λ}}$

Where, k is wavenumber in rad/m.

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

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

Given that,

$$\begin{gathered} K=3.64 \\ {K}_m=5.18 \end{gathered}$$

The speed of the propagation is:

$$\begin{gathered} \mathrm{v}=\frac{\mathrm{c}}{\sqrt{{\mathrm{KK}}_{\mathrm{m}}}} \\ =\frac{3×{10}^8}{\sqrt{\left(3.64\right)\left(5.18\right)}} \\ =6.91×{10}^7\mathrm{m}/\mathrm{s} \end{gathered}$$

Hence, speed of propagation of the wave is $6.91×{10}^7\mathrm{m}/\mathrm{s}$.

Given that, $f=$Hz

The wavelength of wave is:

$$\begin{gathered} \mathrm{λ}=\frac{\mathrm{v}}{\mathrm{f}} \\ =\frac{6.91×{10}^7}{65} \\ =1.06×{10}^6\mathrm{m} \end{gathered}$$

Hence the wavelength of the wave is$1.06×{10}^6\mathrm{m}$ .

Given that, ${\mathrm{E}}_{\max }=7.2×{10}^{-3}\mathrm{V}/\mathrm{m}$

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

$B_{max}=\frac{{\mathrm{E}}_{\max }}{c}$

Substitute the values of variables

$$\begin{gathered} {\mathrm{B}}_{\max }=\frac{7.2×{10}^{-3}}{6.91×{10}^3} \\ =1.04×{10}^{-10}\mathrm{T} \end{gathered}$$

Hence, the amplitude of the magnetic fields of the wave$1.04×{10}^{-10}\mathrm{T}$ is respectively.