# Calculating Wavelengths - Just Incase You Wondered!

There are 3 components to this calculation:

- Speed of light (Nice and easy as this is a constant)
- Frequency (Number of Wave cycles per second)
- Wavelength (What we are trying to work out)

#### CALCULATING WAVELENGTH

Speed of Light(m/s) / Frequency(cycles/s) = Wavelength(m/s)

Wireless signals travel at the speed of light which is 299,792,458 meters per second. That's pretty fast. it's also a long number to remember! To keep things simple lets round up to 300,000,000 meters per second. This will make the end result slightly off, but not enough to be concerned about for this exercise.

Next lets pick a frequency.. how about 2.4GHz as its one of the most commonly used. 1GHz is 1,000,000,000 (1 Billion) cycles per second so 2.4GHz is 2,400,000,000 (2.4 Billion) cycles per second. Now by doing some simple maths and dividing the speed of light by the number of cycles per seconds we get:

300,000,000 / 2,400,000,000 = 0.125

As the unit we began with was meters we now know that the wavelength of a 2.4GHz signal is 0.125 meters or 12.5cm.

#### CALCULATING FREQUENCY

Speed of Light(m/s) / Wavelength(m/s) = Frequency(cycles/s)

Now we could just as easily turn the above calculation on its head and use the wavelength to work out the frequency by doing the following calculation:

Lets assume we want to work out what frequency uses a 5.2cm wavelength, we would simply do the calculation:

300,000,000 / 0.051 = 5,882,352,941

As the first 2 figures where in meters we know that the result is the number of cycles per second (the number of hertz). In this case 5.88GHz

#### WHY KNOWING WAVELENGTHS IS IMPORTANT

When designing Antennas it is important that they are built to sizes which are a fraction of the wavelength. For example, 1/4 or 1/2 of the wavelength. The same also applies when spacing apart antennas on Access Points that use antenna diversity and similar technologies (they should typically be 1 wavelength apart if possible)

Lower frequencies have longer wavelengths and longer wavelengths penetrate obstacles better. For example if you are operating at the top end of 5GHz Band B and are trying to penetrate obstacles then dropping to the lower end channels can increase your wavelength by around 2-3mm which (although it seems a small amount) can only help increase your chance of reliably getting your signal to pass through.

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