Chapter 26.2, Problem 28SSC

To determine

To explain: The FM antenna design which would be more sensitive to stations near 88 $\text{MHz}$ , shorter or longer than one designed to receive stations near 108 $\text{MHz}$ .

Explanation of Solution

Introduction:

There is a sinusoidal graph displaying the electromagnetic waves. It consists of time-varying electrical and magnetic fields perpendicular to each other, and also perpendicular to wave propagation direction. Electromagnetic wavesare transverse wave and the speed of EM wave in vacuum is $3\times {10}^8\text{m/s}$ .

An Electromagnetic wave travels at the speed of light, i.e. $c=3\times {10}^8\text{m/s}$ and the relation between frequency and wavelength can be represented as,

  $c=f\lambda$  ...... (1)

Here, $c$ is the speed of propagation of the wave, f is the frequency, and $\lambda$ is the wavelength.

From equation (1), it can be observed that the frequency is inversely proportional to the wavelength. For all types of electromagnetic waves, the greater the frequency, the smaller will be the wavelength.

Thus, in order to be sensitive to stations near 88 MHz would require a longer wavelength antenna and for stations near 108 MHz, would require shorter wavelength antenna.

Conclusion:

Hence, it can be concluded that for 88 MHz station longer antenna design would be sensitive and for 108 MHz, shorter antenna design would be sensitive.