Question

In an optical communication system operating at $1200mm$, only $2\%$ the source frequency is available for TV transmission having a bandwidth of $5MHz$. The number of TV channels that can be transmitted is

• A. $2million$
• B. $10million$
• C. $0.1million$
• D. $1million$
• E. $0.5million$

Answer 1

The correct option is D

$1million$

Solution:

Step 1: Given information

Optical communication system operating at $1200mm$

Frequency available $=$$2\%$

Bandwidth $=5MHz$

Step 2: Calculate the number of TV channels that can be transmitted

The optical communication frequency, $f=\frac{c}{\lambda }$

Where, $f=$Frequency, $c=$Speed of light, and $\lambda =$Wavelength

Therefore,

$f=\frac{(3\times {10}^8)}{(1200\times {10}^{-9})}$

$f=25\times 1013Hz$

Only $2\%$ of the source frequency is available for TV transmission,

$f=25\times 1013\times \left(\frac{2}{100}\right)$

$f=5\times 1012Hz$

Number of channels = $\frac{frequency}{bandwidth}$ or

Number of channels$=\frac{(5\times {10}^{12})}{5MHz}$

Number of channels $=\frac{(5\times {10}^{12})}{(5\times {10}^6)}$

$$\begin{gathered} ={10}^6 \\ =1million \end{gathered}$$

Hence, the correct option is (D).