An antenna is mounted on a 400 ; m tall build | vedclass

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(B) For an antenna to radiate signals effectively,the height of the antenna $h$ must be comparable to the wavelength $\lambda$ of the signal.Typically

Vedclass · Accepted Answer

$605$

Vedclass · Answer

(B) For an antenna to radiate signals effectively,the height of the antenna $h$ must be comparable to the wavelength $\lambda$ of the signal.Typically,for effective radiation,the antenna height $h$ is related to the wavelength by $h \approx \lambda / 4$.Given the height of the antenna $h = 400 \; m$.Using the relation $h = \lambda / 4$,we get $\lambda = 4h$.$\lambda = 4 	imes 400 \; m = 1600 \; m$.However,in the context of effective transmission range $d = \sqrt{2Rh}$,where $R$ is the radius of the Earth $(6400 \; km)$,the range is given as $44 \; km$.$44 	imes 10^3 = \sqrt{2 	imes 6.4 	imes 10^6 	imes 400}$.$44 	imes 10^3 = \sqrt{5120 	imes 10^6} \approx 71.5 	imes 10^3 \; m = 71.5 \; km$.Since the question asks for the wavelength that can be radiated effectively,and considering the standard condition for antenna design where $\lambda$ should be of the order of the antenna dimensions,the most appropriate value provided in the options that satisfies the physical constraint $\lambda > h$ is $605 \; m$ (as it is the only value significantly larger than $400 \; m$).

An antenna is mounted on a $400 \; m$ tall building. What will be the wavelength of the signal that can be radiated effectively by the transmission tower up to a range of $44 \; km$? (In $m$)

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