Additional problems - Chapter 10 - Communication Systems - 12th Physics Guide Samacheer Kalvi Solutions

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Additional problems
Question 1.
A radio can tune to any station in $7.5 \mathrm{MHz}$ to $12 \mathrm{MHz}$ band. What is the corresponding wavelength band?
Solution:
Frequency of $7.5 \mathrm{MHz}$ belongs to SW band. The corresponding wavelength is
$
\lambda=\frac{c}{v}=\frac{3 \times 10^8}{7.5 \times 10^6}=40 \mathrm{~m}
$
Frequency of $12 \mathrm{MHz}$ belongs to $\mathrm{HF}$ band, the corresponding wavelength is
$
\lambda=\frac{c}{v}=\frac{3 \times 10^8}{12 \times 10^6}=25 \mathrm{~m}
$
Corresponding to the given frequency band, the wavelength band is $25 \mathrm{~m}-40 \mathrm{~m}$ band.
Question 2.
A TV transmitting antenna is $125 \mathrm{~m}$ tall. How much service area can this transmitting antenna cover, if the receiving antenna is at the ground level? Radius of earth $=6400 \mathrm{~km}$.
Solution:
$\mathrm{h}_{\mathrm{T}}=125 \mathrm{~m}$ and $\mathrm{R}=6400 \times 10^3 \mathrm{~m}$
$\mathrm{d}=\sqrt{2 h_T R}=\sqrt{2 h_T R}=40 \times 10^3 \mathrm{~m}=40 \mathrm{~km}$
Area covered $\mathrm{A}=\pi \mathrm{d}^2=3.14 \mathrm{x}(40)^2=5024 \mathrm{~km}^2$

Question 3.
A transmitting antenna at the top of a tower has a height $32 \mathrm{~m}$ and that of the receiving antenna is $100 \mathrm{~m}$. What is the maximum distance between them for satisfactory communication in LOS mode? Given radius of earth $6.4 \times 10^6 \mathrm{~m}$
Solution:
$
\begin{aligned}
& \mathrm{h}_{\mathrm{T}}=32 \mathrm{~m}, \mathrm{~h}_{\mathrm{R}}=100 \mathrm{~m} \\
& \mathrm{R}=6.4 \times 10^6 \mathrm{~m} \\
& \mathrm{~d}_{\mathrm{m}}=\sqrt{2 R h_T}=\sqrt{2 R h_R} \\
& =\sqrt{2 \times 604 \times 10^6 \times 32}+\sqrt{2 \times 604 \times 10^6 \times 100} \\
& \left.=\left(64 \times 10^2 \sqrt{10}\right)+98 \times 10^3 \sqrt{10}\right)=144 \times 10^2 \sqrt{10} \text { machines } \\
& \mathrm{d}_{\mathrm{m}}=45.5 \mathrm{~km}
\end{aligned}
$