The height of a transmitting antenna is h m | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The maximum line-of-sight distance $d$ between a transmitting antenna of height $h_T$ and a receiving antenna of height $h_R$ is given by the form

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(B) The maximum line-of-sight distance $d$ between a transmitting antenna of height $h_T$ and a receiving antenna of height $h_R$ is given by the formula: $d = \sqrt{2Rh_T} + \sqrt{2Rh_R}$.Given: $d = 40 \ km = 40 	imes 10^3 \ m$,$h_R = 45 \ m$,$R = 6400 \ km = 6.4 	imes 10^6 \ m$.Substituting the values:$40 	imes 10^3 = \sqrt{2 	imes 6.4 	imes 10^6 	imes h_T} + \sqrt{2 	imes 6.4 	imes 10^6 	imes 45}$$40 	imes 10^3 = \sqrt{12.8 	imes 10^6 	imes h_T} + \sqrt{576 	imes 10^6}$$40 	imes 10^3 = \sqrt{12.8 	imes 10^6 	imes h_T} + 24 	imes 10^3$$40 	imes 10^3 - 24 	imes 10^3 = \sqrt{12.8 	imes 10^6 	imes h_T}$$16 	imes 10^3 = \sqrt{12.8 	imes 10^6 	imes h_T}$Squaring both sides:$(16 	imes 10^3)^2 = 12.8 	imes 10^6 	imes h_T$$256 	imes 10^6 = 12.8 	imes 10^6 	imes h_T$$h_T = \frac{256}{12.8} = 20 \ m$.

Similar Questions

The heights of transmitting and receiving antennas are respectively $\frac{1}{20000}$ and $\frac{1}{80000}$ times the radius of the earth. The maximum distance between these two antennas for satisfactory communication in line of sight mode is (Radius of the earth $= 6.4 \times 10^6 \ m$) (in $km$)

In an amplitude modulated signal,the maximum amplitude is $15 V$ and the minimum amplitude is $5 V$. The amplitude of the modulating wave will be (in $V$)

The height of a transmission antenna is $49 \,m$ and that of the receiving antenna is $64 \,m$. What should be the maximum distance between them for line of sight transmission (in $\,km$)?

$A$ $100\,m$ long antenna is mounted on a $500\,m$ tall building. The complex can become a transmission tower for waves with $\lambda$ (approx) ........ $m$.

The height of a $TV$ transmitter antenna is $100 \ m$. What is the area covered by the transmitter for broadcasting? $(R = 6.4 \times 10^{6} \ m)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module