“When am I ever going to use this?” has been asked about various parts of math by students through history.

Come on. Admit it. You asked it before, didn’t you? 🙂

Ever used decibels? Then, my friend, you have used logarithms! From ”Understanding Decibels” on The SWLing Post:

dB = 10 log

_{10}(P2/P1)

Okay, you should read the article for more than just that. 🙂

However, just like how we measure earthquakes, hurricanes, and other items that vary by a large range, leveraging powers of 10 to measure signal or sound strength makes a lot of sense. Using earthquakes as an example, would you really want a Richter scale \(10^5\), that is, a Richter scale 100,000 earthquake? Richter scale 5 is so much easier for the brain, isn’t it?^{1}

Although, in the spirit of Spinal Tap’s guitar amp with a maximum volume of 11 versus 10, I suppose I’d love it if when I cranked Shinedown I could tell people I turned it up to 1,000,000. 🙂

Getting back to the mathematics…

Logs are just inverse powers (e.g. \(log_{10} 10^n=n\)). If you do not see a base with your log (e.g. \(log10^n\), then it is the “common log,” which is base 10.

Of course, a dB is a bit more complicated because (a) it is 10 times the common log; (b) it is the log of a ratio and (c) we don’t know what \(P1\) above is. 🙂

Well, “c” is what immediately came to mind for me. 🙂

And since I am most familiar with decibels for sound levels (in nature and in audio files), I wanted to find out what the reference value is for sound. “dB: What is a decibel?” from Physclips (University of South Whales) not only was a great discussion of decibels overall, but it provided the reference value for sound (and more):

What does 0 dB mean? This level occurs when the measured intensity is equal to the reference level. i.e., it is the sound level corresponding to 0.02 mPa. In this case we have

sound level = 20 log (p

_{measured}/p_{ref}) = 20 log 1 = 0 dBRemember that decibels measure a ratio. 0 dB occurs when you take the log of a ratio of 1 (log 1 = 0). So

0 dB does not mean no sound, it means a sound level where the sound pressure is equal to that of the reference level. This is a small pressure, but not zero. It is also possible to have negative sound levels: – 20 dB would mean a sound with pressure 10 times smaller than the reference pressure, i.e. 2 μPa.

Now, since I titled this “Shortwave Decibels,” I suppose it would be a bait and switch to leave it there. 🙂

However, I am not (yet) a Ham radio operator…so my knowledge is limited…and this neat article, “Decibel & S-Readings,” by Serge Stroobandt, ON4AA, convinced me it’s best to let you read it and decide which cases where decibels intersect with shortwave you care most about.

Either way, you now know, with logarithms, at least some cases you’ll use the math…even if you don’t realize you are. 🙂

P.S. Are there anything neater than good, old-fashioned analog stereo meters?

^{1}Yes, I am oversimplifying how the Richter scale works. However, when we hear a newsperson say “Richter scale,” they aren’t really using it anyway. 🙂

Oh, and don’t forget that what you are measuring is important. For instance, a category 5 hurricane doesn’t have 10 times faster winds then a category 4, it has 10 times the “damage potential multiplier.”

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