I’ve said it before, and I’ll say it again, there’s always something new to be learned if you are of a curious nature and you keep your eyes open, as it were.
Just the other day, for example, my chum Michael Dunn who hails from the frozen north in Canada sent me an email containing a graphic he’d seen bouncing around the internet entitled “Amateur Radio Guide to Social Distancing (keep one wavelength apart at 144 MHz).”
Unfortunately, I can’t reproduce the original image here because I don’t know who owns it, so I created my own interpretation (feel free to reproduce this as you will — it would be awesome if you were to include a link back to this column, but that’s not required).
I flatter myself that my version is an improvement. First, the image Michael sent shows what we might assume to be two male engineers (“How mid-20th century, my dear!”). By comparison, my adaptation is much more politically correct since it shows one person in a dress and another wearing trousers (I’ll leave it to the viewer to select whatever gender classifications and sexual orientations they think these characters represent).
Second, as noted earlier, the image from Michael said to keep one wavelength apart at 144 MHz, but how do we know this is correct? As you will observe from my diagram, I opted for 150 MHz. Can I defend this change? Why yes, I can!
As a starting point, we all have to agree on what actually is the required social distancing distance. According to the Wikipedia’s Social Distancing page: “It involves keeping a distance of six feet (2 meters) from others and avoiding gathering together in large groups.”
Hmmm, it seems we’re already off to a rocky start, because six feet is only 1.8288 meters (at least, it is where I come from).
Let’s assume we are really talking about a two-meter separation distance (better safe than sorry). The next question is to ask what wave velocity we’re talking about, because frequency, wavelength, and wave velocity are all intertwined. For example, the velocity of electromagnetic radiation in a vacuum is the speed of light, which is 299,792,458 m/s. While it’s true that I’ve never actually met them, I feel reasonably confident in speculating that Michael’s amateur radio enthusiasts spend relatively little of their time operating their systems in a vacuum, so I opted for the velocity of electromagnetic radiation in air, which is 299,702,547 m/s. Although the difference of 89,911 m/s betwixt these values may seem to be comparatively insignificant in the scheme of things, it’s nice to use real numbers (we’re not politicians, for goodness sake!).
Next, I bounced over to the Omnicalculator.com website, where they currently have 1,055 free calculators and counting (no pun intended). Using their Wavelength Calculator, we discover that a wavelength of 2 m demands a frequency of 149.8513 MHz for an electromagnetic wave propagating through air (I made so bold as to round this value up to 150 MHz in my diagram, because I didn’t want to appear pedantic).
The only remaining issue as far as I’m concerned is the origin of the 144 MHz value in Michael’s diagram. I’ve tried the various combinations between air and vacuum and 2 m and 6 feet (1.8288 m), but to no avail. I fear this is a conundrum that will keep me awake at night unless someone can explain it to me.
But none of this is what I wanted to talk to you about.
When I received Michael’s email, it reminded me of something similar that had graced my Inbox a few days earlier sent by my chum Martin Rowe. In Martin’s case, the caption read “Social Distancing for Audio Engineers (keep one wavelength apart at 140 to 165 Hz).”
I must admit that when I’d first seen this, the “140 to 165 Hz” part had struck me as being a trifle vague, but I had other fish to fry at that time. Now, following my cogitations and ruminations on the Radio Engineer’s version, I decided to probe a little deeper.
Let’s assume we are still talking about a 2 m separation distance. Let’s also assume we are talking about sound propagating through air (as opposed to water, for example). Finally, let’s assume that we are talking about an ambient temperature of 20°C (68 F), which — by some strange quirk of fate, and as confirmed by my Amazon Echo — happens to be the temperature outside my house as I pen these words (see also What the FAQ are Celsius and Fahrenheit? and What the FAQ are Kelvin, Rankine et al?).
Are you wondering why we aren’t also qualifying things by saying something like, “…at sea level”? Well, as we will come to see, there’s a reason for this, over and above the fact that I just discovered the concept of sea level is itself more convoluted than I had previously supposed.
Anyway, still using Omnicalculator’s Wavelength Calculator, I selected “Sound in air at 20°C,” which gave me a wave velocity of 343 m/s. Next, I specified a wavelength of 2 m, which returned corresponding frequency of 171.5 Hz (I rounded this up to 172 Hz in my diagram using the “round-half-up” approach as described in my Rounding Algorithms paper).
So, where did the “140 to 165 Hz” range on the original cartoon image come from? I have no idea. I’ve tried changing the distance to 6 feet (1.8288 m) and playing with the temperature, but nothing comes close (if you have any thoughts on this, I’d love to hear them). I also went to Omnicalculator’s Speed of Sound calculator, which is where I discovered that (a) air is almost an ideal gas and (b) the formula for the speed of sound in an ideal gas is a function of the molar gas constant, the molar mass of the gas, the adiabatic index for the gas, and the temperature of the gas.
The point here is that the speed of sound is not a function of air pressure (or density), which is why we weren’t obliged to quality things earlier by saying something like, “…at sea level.”
I remember once seeing an advert in a print magazine for something that mentioned a huge number of days spanning a vast amount of time (like a hundred thousand years, or something of that ilk), and my knee-jerk reaction was to say to myself “I wonder if they included leap days?” So, I checked, and they had, and I was happy because I knew the advert had been verified by someone who cares about this sort of thing.
Now I’m wondering if it’s only me who does this sort of checking, or is it the natural response of every true engineer? I’m also wondering if we could come up with similar “Social Distancing” concepts and create analogous diagrams to those above for other types of engineers, like analog engineers, digital engineers, mechanical engineers, marine engineers, civil engineers, and so forth. If you have any ideas along these lines, please share them with the rest of us in the comments below.