Properties of Radio Waves — Page 10, Lesson 11

Let’s start with the very foundation: what a radio wave actually is, in terms of time. The length of time it takes to generate one complete cycle of a radio wave is called the period, and it’s given the Greek letter tau (τ). We measure it in microseconds (µs), and one microsecond is one millionth of a second — that’s 10⁻⁶ seconds. So the period is the time for one full wave to be produced. Now, if a single cycle takes 0.125 microseconds, then the number of cycles produced in one second is simply the reciprocal of that period — one divided by 0.125 × 10⁻⁶. That works out to 8,000,000 cycles per second. That number of cycles per second is what we call the frequency, given the symbol f. So the defining relationship is: f = 1 / τ Frequency is expressed in hertz (Hz), which is just cycles per second. Because radio frequencies are so large, we use convenient multiples: kilohertz (kHz) is 10³ Hz, or 1,000 Hz; megahertz (MHz) is 10⁶ Hz, or 1,000,000 Hz; and gigahertz (GHz) is 10⁹ Hz, or 1,000,000,000 Hz. So our example of 8,000,000 cycles per second is expressed as 8 MHz. Now let’s move to the spatial side of the wave — the wavelength, given the symbol lambda (λ). Radio waves travel at the speed of light, which is approximately 300,000,000 metres per second — that’s 300 × 10⁶ m/s, or equivalently 162,000 nautical miles per second. If a wave travels at that speed and its period is 0.125 microseconds, then the length of each wave — the wavelength — is the speed multiplied by the period: λ = c × τ That gives 300 × 10⁶ × 0.125 × 10⁻⁶ = 37.5 metres. But here’s the elegant part: since frequency is the reciprocal of period, we can also express wavelength directly in terms of frequency. Substituting, we get: λ = c / f And rearranging that gives us the frequency from the wavelength: f = c / λ So if you know the frequency, you can find the wavelength, and if you know the wavelength, you can find the frequency — they’re two sides of the same coin. Let me walk you through the worked examples. First, if the frequency is 121.5 MHz, the wavelength is c divided by f: 300 × 10⁶ divided by 121.5 × 10⁶, which gives 2.47 metres. Second, if the wavelength is 1515 metres, the frequency is c divided by λ: 300 × 10⁶ divided by 1515, which gives 198,000 Hz — that’s 198 kHz. Now, for ease of calculation, we can simplify the formulae. To find wavelength in metres, we use λ = 300 / f (in MHz). To find frequency in MHz, we use f = 300 / λ (in metres). But we must be careful with our input units: to calculate frequency, the wavelength must be in metres; to calculate wavelength, the frequency must be in MHz. Let’s apply that. Third example: determine the frequency for a wavelength of 3.2 cm. First, convert to metres — 3.2 cm is 0.032 m. Then f = 300 / 0.032, which is 9,375 MHz — that’s 9.375 GHz. Fourth example: determine the wavelength for a frequency of 357 kHz. Convert that to MHz — 357 kHz is 0.357 MHz. Then λ = 300 / 0.357, which gives 800 metres. So the whole picture is this: period is time per cycle, frequency is cycles per second, and wavelength is the physical length of one cycle in space. They’re all linked by the speed of light, and once you master the unit conversions, you can move freely between them.