Height of the receiving and transmitting antenna in communication of a signal are 245 m and 180 m respectively. Find the maximum distance between the two antennas for proper communication.
- 104 km
- 208 km
- 52 km
- 96 km
The Correct Option is A
Solution and Explanation
Understanding the Problem
We need to find the maximum distance in the line of sight between two antennas using the formula:
\( d = \sqrt{2Rh_t + 2Rh_r} \)
where:
- \( R = 6400 \, \text{km} \) (radius of the Earth)
- \( h_t = 180 \, \text{m} \) (height of the transmitting antenna)
- \( h_r = 245 \, \text{m} \) (height of the receiving antenna)
Corrected Solution
1. Convert Units:
Since \(R\) is in kilometers, we need to convert \(h_t\) and \(h_r\) to kilometers.
\( h_t = 180 \, \text{m} = 0.18 \, \text{km} \)
\( h_r = 245 \, \text{m} = 0.245 \, \text{km} \)
2. Substitute Values into the Formula:
\( d = \sqrt{2(6400)(0.18) + 2(6400)(0.245)} \)
\( d = \sqrt{2(6400)(0.18 + 0.245)} \)
\( d = \sqrt{12800(0.425)} \)
\( d = \sqrt{5440} \)
3. Calculate the Distance:
\( d \approx 73.76 \, \text{km} \)
Error in Your Calculation
You directly added the heights in meters and multiplied them by the radius in kilometers without converting the heights to kilometers. This led to a significantly larger and incorrect result.
Final Answer
The maximum distance in the line of sight between the two antennas is approximately \( 73.76 \, \text{km} \).
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Concepts Used:
Communication Systems
A system that describes the information exchange between two points is called the communication system. The transmission and reception process of information is called communication. The major elements of communication are such as:
- The Transmitter of information
- Channel or medium of communication
- The Receiver of information
Examples Of Communication Systems:
The following are the examples of communication systems:
- Internet
- Public Switched Telephone network
- Intranet and Extranet
- Television
Types Of Communication Systems:
Turning on Signal specification or technology, the communication system is categorized as follows:
- Analog technology communicates data as electronic signals of differing frequencies or amplitude. For instance Broadcast and telephone transmission.
- In Digital technology, the data are created and processed in two states: High (represented as 1) and Low (represented as 0). Also this technology stores and transmits data in the form of 1's and 0's.
Elements of a Communication System:
