Search any question & find its solution
Question:
Answered & Verified by Expert
Is it necessary for a transmitting antenna to be at the same height as that of the reveiving antenna for line-ofsight communication? A TV transmitting antenna is $81 \mathrm{~m}$ tall. How much service area can it cover if the receiving antenna is at the ground level?
Solution:
2644 Upvotes
Verified Answer
No.
Height of antenna $=81 \mathrm{~m}$
Covered service area $=\pi \mathrm{d}_{\mathrm{T}}^2$ where
$$
\begin{aligned}
\mathrm{d}_{\mathrm{T}} &=\sqrt{2 \mathrm{Rh}}=\sqrt{2 \times 6.4 \times 10^6 \times 81} \\
\pi \mathrm{d}_{\mathrm{T}}^2 &=3.14 \times 2 \times 6.4 \times 10^6 \times 81 \mathrm{~m}^2 \\
&=3258 \times 10^6 \mathrm{~m}^2=3258 \mathrm{~km}^2
\end{aligned}
$$
Height of antenna $=81 \mathrm{~m}$
Covered service area $=\pi \mathrm{d}_{\mathrm{T}}^2$ where
$$
\begin{aligned}
\mathrm{d}_{\mathrm{T}} &=\sqrt{2 \mathrm{Rh}}=\sqrt{2 \times 6.4 \times 10^6 \times 81} \\
\pi \mathrm{d}_{\mathrm{T}}^2 &=3.14 \times 2 \times 6.4 \times 10^6 \times 81 \mathrm{~m}^2 \\
&=3258 \times 10^6 \mathrm{~m}^2=3258 \mathrm{~km}^2
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.