The image below is of a pure sine wave <math> y = six </math>

- The amplitude of the wave is the distance from the median line of the wave to either a peak or a trough.

- The wavelength <math> \lambda </math> is the distance between two corresponding points on successive waves and is measured in meters.

- The period of a wave is the time it takes for it to pass a fixed reference point, and is measured in seconds.

- Frequency is the number of waves that pass a fixed reference point per second, with units Hertz (Hz) where 1 Hz = 1 complete cycle per second.

The velocity of electromagnetic waves is close to the speed of light in the atmosphere, approximately 300 000 000 m/s.

## Basic formulas

- Period = 1/frequency <math> p = \frac {1}{f} </math>
- Velocity = Frequency x Wavelength <math> v = f \times \lambda </math>

Since velocity is the speed of light and is constant, we denote it with the letter **c**:

<math>c = f \times \lambda</math>

This allows us to deduce the wavelength from the frequency and vice-versa.

## Calculating the wavelength from frequency and vice versa

From the above, we can infer that the frequency can be calculated from the wavelength using:

<math>f = \frac{300 000 000m/s}{\lambda}</math>

and the reverse, calculating the wavelength from the frequency, is a similar operation:

<math>\lambda = \frac{300 000 000m/s}{f}</math>

This should be familiar to people that studied algebra.

Note that most of the time, since those numbers are so high, most operators prefer to operate with the **mega** prefix, so the formulas become simpler:

<math>\lambda = \frac{300Mm/s}{f’}</math>

<math>f’ = \frac{300Mm/s}{\lambda}</math>

Here, **f’** is in Mhz and a **Mm/s** is a mega-meter per second.

## Basic tricks

**Just dive 300 by the number you have to get the number you want.****Don’t forget to convert to megahertz first.****Wavelength is always in meters.**

## Example calculations

### Calculating the frequency

The frequency of a 20m radio wave is:

<math> c = f \times \lambda</math>

<math>300 000 000m/s = f \times 20m</math>

<math>f = \frac{300 000 000m/s}{20m}</math>

Therefore, the frequency is 15Mhz (15 000 000/s or 15 000 000Hz).

An easier way to calculate this is treat **c** as “300Mm/s” (300 megameters per second) and just divide by the wavelength (in meters) to get the frequency (**in Megahertz**).

<math>f = \frac{300Mm/s}{20m} = 150Mhz</math>

### Calculating the wavelength

The reverse operation is of course possible and very similar.

<math>\lambda = \frac{c}{f}</math>

Here you would get the wavelength in meters, provided that **f** is in Hz. An easier way is to do the same as above and just use *mega* prefixes everywhere:

<math>\lambda = \frac{300}{f’}</math>

Here, **f’** is in Mhz. Finding the wavelength of a 447Mhz signal would be:

<math>\lambda = \frac{300}{447} = 0.6711m = 67.1cm</math>

This is in the 70cm band.

Those calculations are very useful to find the length of a good antenna, as antennas operate better when they have a size that is close to the wavelength or an integer multiple of the half-wavelength.