Properties of Radio Waves — Page 10, Lesson 11

Let’s start with the very idea of a radio wave as a repeating cycle. The time it takes to generate one complete cycle is called the period, and we write it with the Greek letter tau (τ), measured in microseconds (µs). One microsecond is one millionth of a second — that’s 10⁻⁶ seconds. Now, if one cycle takes 0.125 µs, how many cycles fit into one second? You take the reciprocal — one divided by the period. So 1 ÷ (0.125 × 10⁻⁶) gives 8,000,000 cycles per second. That number of cycles per second is the frequency (f) of the wave. So the formula is: f = 1 / τ Frequency is expressed in hertz (Hz). Because radio frequencies are huge numbers, we use convenient prefixes: 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 — 8,000,000 cycles per second — is simply 8 MHz. Now let’s talk about wavelength. 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 µs, then the length of each wave — the wavelength (λ) — is the speed times the period: λ = c × τ So 300 × 10⁶ × 0.125 × 10⁻⁶ = 37.5 metres. But since frequency is the reciprocal of period, we can also write wavelength as speed divided by frequency: λ = c / f And rearranging that gives us frequency from wavelength: f = c / λ So if you know frequency, you get wavelength; if you know wavelength, you get frequency. Let me walk you through the worked examples. First, if the frequency is 121.5 MHz, the wavelength is 300 × 10⁶ divided by 121.5 × 10⁶, which is 2.47 metres. Second, if the wavelength is 1515 metres, the frequency is 300 × 10⁶ divided by 1515, which is 198,000 Hz — that’s 198 kHz. Now, to make calculations easier, we can simplify the formulae. For wavelength in metres with frequency in MHz, use: λ (m) = 300 / f (MHz) And for frequency in MHz with wavelength in metres: f (MHz) = 300 / λ (m) But you must be careful with units — to get frequency, the wavelength must be in metres; to get wavelength, the frequency must be in MHz. Let’s apply that. Example 3: a wavelength of 3.2 cm. Convert to metres — that’s 0.032 m. Then frequency = 300 ÷ 0.032 = 9375 MHz, which is 9.375 GHz. Example 4: a frequency of 357 kHz. Convert to MHz — that’s 0.357 MHz. Then wavelength = 300 ÷ 0.357 = 800 metres. So the key relationships are: period τ in microseconds, frequency f = 1/τ in hertz, wavelength λ = c × τ = c/f, and the simplified forms using 300 with MHz and metres. Keep those unit conversions straight — metres for wavelength, MHz for frequency — and the numbers fall out cleanly.