Radio waves propagate in air (or space) at the speed of light (300 million metres per second). The velocity of propagation, v, wavelength, λ, and frequency, f, of a radio wave are related by the equation:

This equation can be arranged to make f or λ the subject, as follows:

and

As an example, a signal at a frequency of 1 MHz will have a wavelength of 300 m whereas a signal at a frequency of 10 MHz will have a wavelength of 30 m. When a radio wave travels in a cable (rather than in air or ‘free space’) it usually travels at a speed that is between 60% and 80% of that of the speed of light. Example 1.3.1

Determine the frequency of a radio signal that has a wavelength of 15 m. Here we will use the formula Putting λ = 15 m gives:

Example 1.3.2

Determine the wavelength of a radio signal that has a frequency of 150 MHz. In this case we will use Putting f = 150 MHz gives:

Example 1.3.3

If the wavelength of a 30 MHz signal in a cable is 8 m, determine the velocity of propagation of the wave in the cable. Solution

Using the formula where v is the velocity of propagation in the cable, gives:

8 3 10 m/sλ= = ×v f

8 3 10

Hz λ

× =f

8 3 10

Hz λ

× =f

8 3 10

mλ ×

= f

3 10 3 10 300 10 = = 2 m 150 10 150 10

λ × × ×

= = × ×f

6 6 8 30 10 8 m = 240 10 2.4 10 m/sλ= = × × × = ×v f

The earth’s atmosphere (see Figure 1.4) can be divided into five concentric regions having boundaries that are not clearly defined. These layers, starting with the layer nearest the earth’s surface, are known as the troposphere, stratosphere, mesosphere, thermosphere and exosphere. The boundary between the troposphere and the stratosphere is known as the tropopause and this region varies in height above the earth’s surface from about 7.5 km at the poles to 18 km at the equator. An average value for the height of the tropopause is around 11 km or 36,000 feet (about the same as the cruising height for most international passenger aircraft). The thermosphere and the upper parts of the mesosphere are often referred to as the ionosphere and it is this region that has a major role to play in the long distance propagation of radio waves, as we shall see later.