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Sagot :
Answer:
The wavelength of the wave is [tex]1.06\times10^6 m[/tex]
Explanation:
Lets calculate
We know an electromagnetic wave is propagating through an insulating magnetic material of dielectric constant K and relative permeability [tex]K_m[/tex] ,then the speed of the wave in this dielectric medium is [tex]\nu[/tex] is less than the speed of the light c and is given by a relation
[tex]\nu=\frac{c}{\sqrt{KK_m} }[/tex] --------- 1
In case the electromagnetic wave propagating through the insulating magnetic material , the amplitudes of electric and magnetic fields are related as -
[tex]E_m_a_x= \nu B_m_a_x[/tex]
The magnitude of the 'time averaged value' of the pointing vector is called the intensity of the wave and is given by a relation
[tex]I = S_a_v[/tex]
[tex]\frac{E_m_a_xB_m_a_x}{2K_m\mu0}[/tex]----------- 3
now , we will find the speed of the propagation of an electromagnetic wave by using equation 1
[tex]\nu=\frac{c}{\sqrt{KK_m} }[/tex]
Putting the values ,
=[tex]\nu= \frac{3.00\times10^8}{\sqrt{(3.64)(5.18)} }[/tex]
=[tex]0.6908\times10^8m/s[/tex]
= [tex]6.91\times10^7m/s[/tex]
Now , using this above solution , we will find the wavelength of the wave -
[tex]\lambda=\frac{\nu}{f}[/tex]
Putting the values from above equations -
[tex]\frac{6.91\times10^7m/s}{65.0Hz}[/tex]
[tex]\lambda= 1.06\times10^6 m[/tex]
Hence , the answer is [tex]\lambda= 1.06\times10^6 m[/tex]
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