Question:

At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the tower should be increased to

Updated On: Dec 31, 2025
  • 200 m
  • 300 m
  • 600 m
  • 900 m
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The Correct Option is D

Approach Solution - 1

To solve this question, we need to understand the relationship between the height of a TV transmission tower and its coverage range. The range of coverage of a transmission tower is directly proportional to the square root of its height. Mathematically, this can be expressed as:

\(R \propto \sqrt{h}\) 

Where \(R\) is the range and \(h\) is the height of the tower.

Given that initially, the tower has a height of 100 m, and we want to triple its coverage range, the calculation can be done as follows:

  1. \(R_1 = k\sqrt{100} = 10k\) (for initial height where \(k\) is a proportionality constant)
  2. We want the new range \(R_2\) to be triple the initial range, so \(R_2 = 3R_1 = 3 \times 10k = 30k\)
  3. For the new range, the formula becomes \(R_2 = k\sqrt{h_2}\)
  4. Equating, \(k\sqrt{h_2} = 30k\)
  5. Divide both sides by \(k\) (assuming \(k\neq0\)), \(\sqrt{h_2} = 30\)
  6. Square both sides to solve for \(h_2\), we get \(h_2 = 30^2 = 900\)

Thus, to triple the coverage range, the height of the tower should be increased to 900 m.

Correct Answer: 900 m

The options provided were 200 m, 300 m, 600 m, and 900 m, and based on our calculations, the correct option is indeed 900 m.


 

Tip: Remember that the relationship between tower height and coverage range follows the formula \(R \propto \sqrt{h}\). This can help quickly solve similar problems.

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Approach Solution -2

The correct answer is (D) : 900 m
\(∴r_m=\sqrt{2Rh}\)
\(⇒\frac{r_1}{r_2}=\sqrt{\frac{h_1}{h_2}}\)
\(⇒\frac{1}{3}=\sqrt{\frac{100}{h_2}}\)
\(⇒h_2=900\ m\)
\(\therefore\) height of the tower should be increased to 900 m

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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:

  1. Internet
  2. Public Switched Telephone network
  3. Intranet and Extranet
  4. Television

Types Of Communication Systems:

Turning on Signal specification or technology, the communication system is categorized as follows:

  1. Analog technology communicates data as electronic signals of differing frequencies or amplitude. For instance Broadcast and telephone transmission.
  2. 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:

Elements of a Communication System