## Frequency

This page discusses the concept of frequency and wavelength. Determining wavelength was critical to designing efficient aerials at NZ Post Office communications radio stations.

What is a frequency?

Frequency is a measurement of how often a repeating event occurs. For instance, a heartbeat is a physical event that might occur say, 80 times a minute. A piano is tuned to have its 'Middle C' audio note at 440 vibrations per second. These examples show us that frequency is measured over a period of time.

A heartbeat is a physical activity we feel. A piano note we can sometimes feel, but mainly we hear. When discussing radio frequencies we need to think instead about repeating changes in electric and magnetic fields.

Measuring frequency

Because a repeating event is also known as being 'cyclical' or occurring in a repeating cycle, the measurement of frequency was originally defined as occurring in a number of 'cycles per second' (c/s). In 1960 the International System of Units (SI) standard defined 'hertz' (Hz) as the new term for frequency. This name acknowledges Heinrich Rudolph Hertz, the first person to provide conclusive proof of electromagnetic waves. 1 c/s = 1 Hz.

Because radio signals occur at very fast frequencies, a system of SI 'multipliers' is used. The common multipliers give us kilohertz (KHz) - 1000 times, megahertz (MHz) - 1000,000 times and gigahertz (GHz) - 1000,000,000 times greater than 1 Hz. Examples are 500 KHz or 500,000 Hz and 2.182 MHz or 2182 KHz or 2,182,000 Hz.

When we refer to frequency in a mathematical formula we use the character 'f'.

How fast does a radio wave travel?

Radio waves travel through space (a vacuum) at the speed of light (c) and slightly slower when travelling through the earth's atmosphere. The standard value used with radio signal calculations is 300,000,000 meters/second (m/s).

When we refer to the speed of a radio wave we use the character 'v', for velocity.

What is a period?

A period is a measurement of how long it takes for one cycle (or Hz) of an event to occur.

When we refer to the period in a mathematical formula we use the character 'T' because it is a measure of Time.

A 80 Hz heartbeat takes 1/80th of a second per cycle. A 440 Hz piano note takes 1/440th of a second for a cycle to complete.

These figures show us that the period equals one over the frequency (1/f) or the reciprocal of the frequency.

Equally, the frequency equals one over the period (1/T) or the reciprocal of the period.

What is a wavelength?

This is the key point we need to know, because aerials work at maximum efficiency if constructed to suit the wavelength of a particular radio signal.

A wavelength is the period, but we measure it in metres rather than by time. We use the Greek symbol Lambda (λ) to show wavelength.

Consider that when we drop a stone into a pond and watch the ripples spread out across the water, we can see that the ripple peaks are a certain distance apart (the wavelength in meters) and will pass a stick in the water at a certain rate (the period in seconds). The period and wavelength tell us the wave velocity in meters per second. So if the ripples take 1 second to pass the stick (s) and the wave peaks are 1 metre apart (m) then the wave velocity (v) is 1 metre every second (1m/s).

Our mathematical formula is therefore v = f x λ m/s.

This formula converts simply to allow us to determine either frequency or wavelength if the other two factors are known. We know that velocity (v) is 300,000,000 m/s. If we choose a frequency (f) of 1,000,000 (1 MHz) then we would divide both sides of the formula by f so our equation becomes λ = v/f in meters. Lets put the numbers in.

λ = 300,000,000/1,000,000

λ = 300 m

We now have a wavelength of 300 metres as the wavelength of a 1 MHz radio wave. If the frequency was 10 MHz, what would the wavelength be?

λ = 300,000,000/10,000,000

λ = 30 m

A 10 MHz radio wave has a wavelength of 30 m.

## Summary

Because the speed of radio waves is fixed and the formula for frequency, wavelength and velocity of a wave is fixed, we can adjust the formula to determine either frequency or wavelength as needed.

Determining the wavelength of a radio frequency allows us to design an aerial to make most efficient use of that frequency.