Wavelength and Frequency

It is important to know that no matter what region of the EM spectrum that you are in, we will still refer to all the regions as "light". So electromagnetic radiation (EM) is light. Yes, we say "light" even when the EM radiation itself is not in the visible realm. We also say light-wave or wave of light. Not always, but often. Why? Because light has wave-like properties - that is, it behaves like a wave. It has velocity, a periodicity which is called frequency, and it has a wavelength. These are all illustrated in the diagram below.

speed of light → c frequency ν wavelength λ

The whole point of the movement is for you to know that these waves are moving. As a matter of fact, they are moving at the speed of light, \(c\), which is really fast. Putting all of these things together leads to this very useful mathematical relationship (aka formula):

\[c = \lambda \cdot \nu\]

The speed of light is 3.00 × 108 m/s.

Note how the wavelength (\(\lambda\), greek lambda) is inversely proportional to the frequency (\(\nu\), greek nu). This means that they work the same way pressure and volume worked for Boyle's Law. So if you double one, you half the other. Double the frequency of light and you half the wavelength. Let's have an example.

Wavelength from Frequency

Question: 93.7 KLBJ is an FM radio station broadcasting from here in Austin, TX. What is the wavelength of their carrier signal?

Solution: FM radio covers 88.1 to 108.1 MHz on your radio dial (electromagnetic spectrum - radio). So that number is in megahertz or 106 s–1. So this is just a conversion of 93.7 × 106 s–1 to wavelength. We will use the equation:

\[{c\over \nu} = \lambda\]

\[\require{cancel} \newcommand\ccancel[2][black]{\color{#1}{\bcancel{\color{black}{#2}}}} {3.00\times 10^8 \,{\rm m\cdot}\ccancel[red]{\rm s^{-1}}\over 93.7\times 10^{6}\,\ccancel[red]{\rm s^{-1}}}= 3.20\,{\rm m}\]

If you do this for the two ends of the FM range, you'll find out that the FM range in wavelength is 2.78 to 3.41 meters.

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