Question

The maximum distance between the transmitting and receiving antennas is D. If the heights of both transmitting and receiving antennas are doubled. The maximum distance between the two antennas is: 
Choose the correct answer from the options given below:

• (1) 2D
• (2) D√2
• (3) 4D
• (4) D/√2

Hint:

Remember that the maximum transmission distance in this case depends on the height of the antennas, and the square root relationship reflects how the distance increases with height.

Answer 1

The Correct Option is B

The distance between transmitting and receiving antennas is related to the height of the antennas based on the properties of wave propagation. In general, for electromagnetic waves, the relationship between the height of the antenna and the distance it can effectively transmit is governed by the formula: \[ \text{Distance} \propto \sqrt{\text{Height of antenna}} \] Let the original height of both antennas be \( h \), and the original maximum distance between the antennas be \( D \). Now, if the height of both transmitting and receiving antennas is doubled, the new height becomes \( 2h \). Using the proportionality: \[ \text{New Distance} \propto \sqrt{2h} = \sqrt{2} \times \sqrt{h} \] Since the original distance is proportional to \( \sqrt{h} \), the new distance will be: \[ \text{New Distance} = D \times \sqrt{2} \] Thus, the new distance between the antennas is \( D \sqrt{2} \).