Neat unit conversion trick

Written 2022-12-11

Tags:Ham Radio 

Amateur radio requires a multiple-choice test for each new grant of operator permissions, each granting a larger amount of spectrum and capabitilies. You are allowed a calculator, but it's possible to get by with pen and paper or memorization. One question that comes up on the tests fairly often is conversion between band names and frequency band edges. If you've memorized the band-edge frequencies, you're all done. But if you haven't, you can rule out most of the possibilities from the answer set with a simple relationship.

Though I usually use a unit-aware calculator most days, that's not available on the radio tests. One simple math trick I've found I enjoy is expressing relationships in particularly useful units. The basic physics relationship we have is wavelength * frequency = speed of light. On the test, wavelength is expressed in meters, and frequency in MHz. If we represent speed of light not as 3e8 meters per second, but 300e6 meters per second, or 300 megameters per second, we can rearrange our equation without units as: wavelength = 300 / frequency or frequency = 300 / wavelength, which feels a little easier to work out.