Zyra's site //// Concepts //// Science //// Radio //// Maths //// Frequency Spectrum //// Speed of Light //// Site Index

The relationship between

Frequency & Wavelength

How to convert wavelength to frequency and to convert frequency to wavelength:

On a radio dial, stations are at positions measured in wavelengths by "metres" and in frequencies by "kilohertz" (KHz). Each particular spot on the dial has a wavelength and a corresponding frequency. There is a way to convert between frequency (f) and wavelength (l) which is as easy as the conversion between Fahrenheit and Celsius or between pounds and kilogrammes.

To convert any frequency to a wavelength, divide the speed of light by it.

So, it's: wavelength = 299792458 divided by frequency.

The formula works the other way round, like this:

frequency = 299792458 divided by wavelength.

To make it easier, it's possible to approximate the speed of light to 300 million. Also, wavelengths are always measured in metres in this formula, and frequencies are in Hertz. 1KHz (kilohertz) is a thousand hertz; 1MHz (megahertz) is a million hertz.

Example: What's the wavelength of Radio1 FM 97-99 megahertz?

99 megahertz is 99 million hertz, so to get the wavelength, it's...

wavelength = 300 million divided by 99 million

= slightly more than 3 metres.

Another example: What's the frequency of BBC Radio4 long wave 1500 metres?

Ok, it's frequency = 300 million divided by 1500 = about 200,000 = 200 kilohertz

(The station is now on 198 kilohertz)

Why? How come this works? You can see this by walking past a wall (at say 3 metres/second to make it conveniently one hundred millionth of the speed of light) and drawing a wave on the wall with chalk by moving the chalk up and down. If you move the chalk up and down at a frequency of three times a second that's 3 Hertz, and the wave you've drawn on the wall has a wave length (from peak to peak) of One metre. Radio waves travelling at the speed of light and moving up and down at so-many millions of times a second have a corresponding wavelength drawn in space. At 300 million metres per second, a radio frequency of 300 million cycles per second (300 megahertz) draws a line in space with peaks one metre apart.

Ok, so you can convert any* frequency to a wavelength. And any wavelength to a frequency.

* We're talking electromagnetic waves here, radio, microwave, light, etc. These all travel at the speed of light. For Sound, and other mechanical waves, the calculations are a bit different, because they travel at the speed of sound. So, if you are calculating frequency versus wavelength for sound, you need to use the speed of sound in the equations rather than the speed of light. It's possible to have radio waves with frequencies as low as 10KHz, but their wavelengths are very much longer than those for sound waves of the same frequency.

If you find this kind of thing helpful at this site, see [response]

Other items in this style include: The conjuring trick of Logarithms explained and How a Microwave Oven works. Also see What's wrong with Google?! Well Done to Blekko for getting this right when Google was getting it wrong!

Other frequency/wavelength links include:

http://www.gordon.army.mil/stt/31c/b03SAP2.html - that was a really good link

www.qrg.northwestern.edu/projects/vss/docs/communications/2-how-are-frequency-and-wavelength-related.html