Chapter 26, Problem 63A

To determine

To Find: Receiving frequency of a mobile signal having antenna length 8.3 cm.

Answer to Problem 63A

The frequency of the signal is $36.1\text{MHz}$ .

Explanation of Solution

Given:

The length of the antenna is $8.3\text{cm}$ .

Formula:

The length of an antenna in meter is given by

Length in meter = $\frac{\text{300}}{\text{Frequency}\text{in}\text{MHz}}$

Or,

  $\text{Frequency}\text{in}\text{MHz}=\frac{\text{300}}{\text{Length}\left(l\right)\text{ in meter}}$  ...... (1)

Calculation:

Substitute $8.3\text{cm}$ for length $\left(l\right)$ in meter in equation (1)

  $\begin{array}{c}\text{Frequency}\text{in}\text{MHz}=\frac{\text{300}}{\text{Length in meter}}\\ =\frac{300}{8.3}\\ =36.14\text{MHz}\end{array}$

Conclusion:

Hence, the required frequency of the signal is $36.1\text{MHz}$ .