An electromagnetic wave of frequency 3 , GHz | vedclass

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Question

(A) The frequency of the wave is $f = 3 \, GHz = 3 	imes 10^9 \, Hz$.In vacuum,the wavelength is $\lambda_0 = \frac{c}{f} = \frac{3 	imes 10^8 \, m/

Vedclass · Accepted Answer

$667$

Vedclass · Answer

(A) The frequency of the wave is $f = 3 \, GHz = 3 	imes 10^9 \, Hz$.In vacuum,the wavelength is $\lambda_0 = \frac{c}{f} = \frac{3 	imes 10^8 \, m/s}{3 	imes 10^9 \, Hz} = 0.1 \, m = 10 \, cm$.The refractive index of the medium is given by $n = \sqrt{\epsilon_r \mu_r}$. Assuming the medium is non-magnetic,$\mu_r = 1$.Thus,$n = \sqrt{2.25} = 1.5$.The wavelength in the medium is $\lambda_m = \frac{\lambda_0}{n} = \frac{10 \, cm}{1.5} = \frac{100}{15} \, cm = 6.666... \, cm \approx 6.67 \, cm$.Expressing this in the form $x 	imes 10^{-2} \, cm$,we get $6.67 \, cm = 667 	imes 10^{-2} \, cm$.

An electromagnetic wave of frequency $3 \, GHz$ enters a dielectric medium of relative electric permittivity $2.25$ from vacuum. The wavelength of this wave in that medium will be $....... \times 10^{-2} \, cm$.

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