Question

Television signals pass only through the ground waves. The range $ R $ related to the transmitter height $ h $ is
 $ \left( A \right){\text{ h}} $
 $ \left( B \right){\text{ }}{{\text{h}}^{\dfrac{1}{2}}} $
 $ \left( C \right){\text{ }}{{\text{h}}^{ - \dfrac{1}{2}}} $
 $ \left( D \right){\text{ }}{{\text{h}}^{ - 1}} $

Answer 1

Hint: Since we have to find the relation between the range and the transmitter height. So for this, we know that range is given by the formula $ Range = \sqrt {2hR} $ and by solving it we will get the relation. And in this way, we can solve this question.

Formula used:
The range is given by,
 $ Range = \sqrt {2hR} $
Here, $ h $ will be the radius
And $ R $ will be the radius.

Complete step by step answer
From the question, it is given that Television signals pass only through the ground waves. Hence, we have to find the range $ R $ related to the transmitter height $ h $ . So for this, we will use the range formula. And it is given by
 $ \Rightarrow Range = \sqrt {2hR} $
And from here we can say that range will be directly proportional to the square root of height. And mathematically it can be written as
 $ \Rightarrow R \propto {h^{\dfrac{1}{2}}} $
Hence, the range $ R $ related to the transmitter height $ h $ is given by $ {h^{\dfrac{1}{2}}} $ .
Therefore, the option $ \left( B \right) $ is correct.

Additional information:
We should know that a transmitter is a device that pools the information signal to be passed with the radio frequency. And the signal which helps in generating the radio waves is called the carrier signal.

Note:
For solving this type of question we need to know the formula then we can solve it. So we have to remember those formulas so that we don’t get panicked while solving them. Combining the transmitter and the receiver in one unit is called a transceiver.