Math problem for a few local hams - they couldn't do it

[ebastler]

In the hf bands there is one frequency that has the same numerical value for both it's frequency and it's wavelength (not the same units of course).
[...]
Thoughts?

My thoughts would be that this is a meaningless question, unless you clearly specify the units you want used. Try again with the wavelength in miles or feet.

Seriously, I would not put this question to a (high school) student. It is a struggle to train them to always consider the units, and take them along in any calculations which they are doing. (Rather than just messing around with dimensionless numbers, and forgetting that they used µs here and Hz there.) Encouraging someone to take the square root of 300 to solve this is encouraging bad practice.

[Johnboy]

In my neck of the woods, a mathematical question would be considered unusual among the 2m Technician crowd. That may not be true everywhere, of course, but the majority of discussions I hear on our most-trafficked repeater seem to involve motorcycle maintenance, of all things. It's the equivalent of the "Car Talk" radio show. There is also a sizable amount of "well, my gol-durn knee's swelling up again" prognostication regarding incoming weather.

When I took the ARRL amateur exams a few years ago, the majority of the other testers in the room turned out to be drone hobby enthusiasts who were taking the Technician exam because they believed they needed an FCC license for legal drone operation. I don't know whether they actually do or not, but I'm just pointing out that you might have been asking in the wrong circles. I don't feel it's fair to generalize the majority of hams as entirely inept at simple algebra, any more than it would be fair to characterize electricians as "mathematically inferior" to engineers. I'm not flaming anyone, but I don't care for the title of the topic. If you'd asked a group of community college professors to show you that they didn't have to rely on oversimplified formulas to arrive at wavelength in meters, you might have gotten a similar result.  I'll vouch for the likelihood that there are many hams whom almost certainly would have had no problem understanding what you were asking them to do.

(Although you might need a considerably larger antenna to inquire about it, because those ops tend not to hang around on two meter, or even 40m for that matter. You might even need to send your query with a straight key or bug to establish your own "credentials" in order to get a response from such hams at all. Even a friendly intellectual exercise like this might seem like a set-up, a "trick question" that only people dumbfounded by it would feel obligated to respond to.)

I was a little shocked by the concept of metric/imperial/metric conversion in order to make an antenna. It's certainly true that the ARRL handbook (among other similar sources of information) has become almost a parody of itself; to me at least, it does seem to be more geared toward "appliance operators" rather than experimenters/makers in its current incarnation than, say, the one on my shelf (from 1986, even). I would be thrilled to hear more discussions of the technical aspects of RF on the bands on a regular basis, but it is much rarer than it used to be, for sure.

[xrunner]

I don't feel it's fair to generalize the majority of hams as entirely inept at simple algebra, any more than it would be fair to characterize electricians as "mathematically inferior" to engineers. I'm not flaming anyone, but I don't care for the title of the topic.

I understand and I changed the original title to a better one, which is as true as I can get. I have not asked anyone other than hams and it was just a few.

Thank you.

[Johnboy]

I don't feel it's fair to generalize the majority of hams as entirely inept at simple algebra, any more than it would be fair to characterize electricians as "mathematically inferior" to engineers. I'm not flaming anyone, but I don't care for the title of the topic.

I understand and I changed the original title to a better one, which is as true as I can get. I have not asked anyone other than hams and it was just a few.

Thank you.

I wasn't being snarky, xrunner; thank you for not taking offense. I myself had never considered your question before, and I thought it's just the type of riddle that ought to be included on the amateur exams. I think the US exams seem to be more focused on making sure the hams "know their place" and don't interfere with signals outside of their bandwidths, rather than on showing that they understand the science behind the hobby.

[vk6zgo]

I've just gotta throw this in here...

300 is just a rough number - like using ²²/₇ for Pi.  I'd be happier with something like 299.792458

Life is a "rough number"-----I'm quite happy with 0.0692% accuracy, as I'm quite sure I couldn't measure wavelength to that degree of accuracy, anyway!

[vk6zgo]

In the hf bands there is one frequency that has the same numerical value for both it's frequency and it's wavelength (not the same units of course).
[...]
Thoughts?

My thoughts would be that this is a meaningless question, unless you clearly specify the units you want used. Try again with the wavelength in miles or feet.

Seriously, I would not put this question to a (high school) student. It is a struggle to train them to always consider the units, and take them along in any calculations which they are doing. (Rather than just messing around with dimensionless numbers, and forgetting that they used µs here and Hz there.) Encouraging someone to take the square root of 300 to solve this is encouraging bad practice.

I think this is the root of the problem, we have all had it hammered into us that "numerical values without units are meaningless!"
This makes it difficult to re-organise our brains to work with just the unitless values.

We cannot, in conscience, say, "frequency =wavelength", as it is like saying "Cat=building", so we must have the verbose explanation.

In the end, it is a mathematical curiosity, of no more importance than the fact that, in Ohms Law, the numerical value of  R, I, &  V  are equal when they all=1.

Pretty much----"So what?"

[fourfathom]

In the end, it is a mathematical curiosity, of no more importance than the fact that, in Ohms Law, the numerical value of  R, I, &  V  are equal when they all=1.

Pretty much----"So what?"

So what?  So what??? "1 V / 1 Ohm = 1 A" is a beautiful thing.  So is "1 V * 1 A = 1 W"  I refuse to let you dismiss these identities as a mere curiosity.

[hamster_nz]

In the end, it is a mathematical curiosity, of no more importance than the fact that, in Ohms Law, the numerical value of  R, I, &  V  are equal when they all=1.

Pretty much----"So what?"

So what?  So what??? "1 V / 1 Ohm = 1 A" is a beautiful thing.  So is "1 V * 1 A = 1 W"  I refuse to let you dismiss these identities as a mere curiosity.

1 is pretty straight up and down, and I have nothing against 0, but what about pi, e and i?

Those numbers have a real (and even imaginary) significance - maybe even a little bit of special magic about them.

[ebastler]

"1 V / 1 Ohm = 1 A" is a beautiful thing.  So is "1 V * 1 A = 1 W"  I refuse to let you dismiss these identities as a mere curiosity.

And if you divide one by 5, the result is 1/5.
Hey, look -- the same number in the denominator which we just divided by! Amazing!!

This stuff doesn't even qualify as a "curiosity" in my book. 

[Sal Ammoniac]

Remember, these are technical people.

Technical people? I think most of these guys take a one-day cram session to memorize just enough to pass the test, and then they promptly forget it.

[fourfathom]

"1 V / 1 Ohm = 1 A" is a beautiful thing.  So is "1 V * 1 A = 1 W"  I refuse to let you dismiss these identities as a mere curiosity.

And if you divide one by 5, the result is 1/5.
Hey, look -- the same number in the denominator which we just divided by! Amazing!!

This stuff doesn't even qualify as a "curiosity" in my book. 

It's not the numbers, it's the relationship -- one of the most fundamental relationships in electronics.  I will admit that plugging "1" into the equations is not strictly necessary to appreciate the beauty of Ohm's Law, but it does seem to make the example more concrete. 

It's an engineering aesthetics thing, perhaps you and I will never agree.

[james_s]

I've never been a math guy, I know that's odd for someone in engineering but I've just always struggled with the math part. I can learn how to solve the equations I need and the basic stuff like Ohms law I know like the back of my hand, but I've never really grasped or been interested in the abstract mathematics behind it all, it's just not how my brain works. I'm a very visual thinker, I can easily visualize complex mechanical systems in my head and see how everything fits together. I'm good at applied math, when I can see the math "doing something" and relate it to the physical world I can usually pick it up no problem. When it's just manipulating numbers for the sake of manipulating numbers though my eyes glaze over.

[Bicurico]

I have not understood what the original poster wants to be calculated.
While I do believe that there may be HAMs unable to solve mathematical questions, in this case it seems that the question is not clear.

Regards,
Vitor

[ebastler]

It's not the numbers, it's the relationship -- one of the most fundamental relationships in electronics.  I will admit that plugging "1" into the equations is not strictly necessary to appreciate the beauty of Ohm's Law, but it does seem to make the example more concrete. 

Sorry, but now you are muddying the waters. It was exactly the fixation on numbers, ridding them of units and physical meaning, which I was questioning in the first place.

It's an engineering aesthetics thing, perhaps you and I will never agree.

To the extent that "1/1 = 1" means engineering aesthetics to you, indeed, I'm afraid we won't agree. 

[Sal Ammoniac]

I've never been a math guy, I know that's odd for someone in engineering but I've just always struggled with the math part. I can learn how to solve the equations I need and the basic stuff like Ohms law I know like the back of my hand, but I've never really grasped or been interested in the abstract mathematics behind it all, it's just not how my brain works. I'm a very visual thinker, I can easily visualize complex mechanical systems in my head and see how everything fits together. I'm good at applied math, when I can see the math "doing something" and relate it to the physical world I can usually pick it up no problem. When it's just manipulating numbers for the sake of manipulating numbers though my eyes glaze over.

One of the things that's wrong with physics these days (IMO) is that too many physicists equate "beautiful" math with reality--theories that have no experimental proof (and no prospects of any in the future), but "it must be right" because the math is pretty. 

[SiliconWizard]

Like String theory? 

[worsthorse]

I think the cause of this is human apathy and acceptance of incompetence.

  *
  *
  *

It's a race to the bottom. We avoid hard things. We accept incompetence. Or we buy our way around it. In some circles there is even social solidarity about mathematical inability.

/begin 

In the US, these points are in the preamble of Part 97, the regs that set up the amateur radio service. They lay out why we get to use the RF spectrum:

• Continuation and extension of the amateur's proven ability to contribute to the advancement of the radio art.
• Improvement of the amateur service through rules which provide for advancing skills in both the communication and technical phases of the art.
• Expansion of the existing reservoir within the amateur radio service of trained operators, technicians, and electronics experts.

That is, we are allowed to use the RF spectrum because doing so makes us more technically competent. For a long time, this was actually true of most hams.

But it has been decades since organizations like the ARRL promoted technical skill over, say, contesting or collecting badges. You don't have to look any further than the current book list or QST magazine to see that.  I think this is, in part, because the ARRL has become a marketing channel for companies selling high end gear but whatever the reason, the result is a community of radio amateurs who mostly don't advance the art in any sense of the phrase.

That is not to say that every ham before 1999 was an RF or analog engineer. The vast majority weren't.  But most of them learned the hobby through building and fixing gear and by studying technically oriented books like A Course in Radio Fundamentals.  Today, the vast majority of hams in my part of the world attend a one day cram course to memorize answers to the test, get a technician license, and never think about the technical aspects of radio again.

While it is certainly human nature to find the easiest, lowest energy way to attain some goal (I am a prepper. I need a powerful radio. I can get a ham radio license in one day for less than fifty bucks. Done.) it is also human nature to be curious about how things work. (How does this work? What happens if I change that? How can I make it better?) Unfortunately, our culture rewards efficient goal attainment (get your DXCC in five months with FT8 vs. twenty years with CW) over understanding how shit works.  And while this is the way things are, understanding RF or maths or geology or astronomy will not be of much interest to most folks.

/end

[janoc]

Guys, don't diss HAMs here.

I used to teach at a fairly decent tech university and I had students totally dumbfounded  with elementary school math on more than one occasion. E.g. once I wrote fractions on the blackboard as a result of some calculation (didn't have a calculator on hand and the numerical result didn't really matter anyway), I drew blank stares from the class and a complaint that "The result is wrong because it is not what his calculator is showing!"

Colleague that taught also at a local gymnasium (type of high school, not a gym!) explained me later that they have never seen fractions because apparently some smart cookie at the education ministry has decided some time ago that today everyone has a calculator and fractions were dropped from the curriculum!

Another time I had to explain how to do calculations with negative numbers (not kidding!). Or complex numbers. Or basic algebra, like equation solving. Or ...

Even had an engineering master student (4th year!) be totally stumped with having to multiply two matrices during an exam - he has never learned how to do this because "I have never needed it." (?!) (he failed that exam)

And those were all engineering students, with at least the mandatory first year of algebra and calculus under their belts when I got them, studying stuff like computer science and electrical engineering!

So don't poke fun at mostly elderly guys that had to do some algebra sometime in the high school the last time, some 30-40 years ago. Lack of basic math skills is a general population problem, HAMs are not special here by any measure.

[fourfathom]

To the extent that "1/1 = 1" means engineering aesthetics to you, indeed, I'm afraid we won't agree. 

I agree with you that "1/1 = 1" is neither interesting nor beautiful.  I'm sure that we can find something more interesting to argue about somewhere down the road.

[joeqsmith]

Remember that video a few years ago where some fresh MIT grads were being asking a simple question about a light bulb and battery?   

[Nominal Animal]

You are calling people out for not making an intuitive leap you yourself did not even describe.
    λ = c/f ⇔ λ·f=c
is the easy part, and a lot of people will get that far.  The trick is understanding that the next step is
    λ = x·1 [m]
and
    f = x·1,000,000 [Hz]
and substituting them to the original equation:
    x·1 [m] · x·1,000,000 [Hz] = 299,792,458 [m/s]
which simplifies to
    x² = 299,792,458 [m/s] / (1 [m] · 1000000 [Hz])
and to
    x² = 299.792458
yielding the solution,
    ±x = √299.792458 ≅ 17.314516
Substituting back to the original variables, only positive values make physical sense, so
    λ ≅ 17.315 [m]
    f ≅ 17.315 [MHz]

Unless you show the entire sequence of operations needed to get to the result, you're skipping things, and not presenting the problem and solution realistically; you are skipping major steps that you might have found intuitive.  Mathematicians do this extremely often; even in peer-reviewed articles, the interesting bit, how to find a numerical answer, is very often completely ignored and skipped.  That may work for mathematicians, but it does not work for us who just use math as a tool.

Do not be a mathematician.

So, in a way, it is a similar trick question as asking how much is e^π-π.  When you calculate that, you'll recalculate it again, because you'll think you calculated it wrong.  You didn't, it is just a numerical coincidence.

[fourfathom]

 λ·f=c (meters, megahertz, 300)
Given that  λ=f, F*F=c, f²=c, f=√c
since c=300, f=λ ≅ 17.32MHz

[Nominal Animal]

Given that  λ=f

That makes absolutely no sense whatsoever.

It only makes sense if you think physical quantities can be represented by dimensionless numbers.  People should not think that way, because it leads to errors (both numerical and logical).  Dimensional analysis is your friend, and a very important tool in understanding things.

[fourfathom]

Given that  λ=f

That makes absolutely no sense whatsoever.

It only makes sense if you think physical quantities can be represented by dimensionless numbers.  People should not think that way, because it leads to errors (both numerical and logical).  Dimensional analysis is your friend, and a very important tool in understanding things.

OK, how about this:

 λ·f=c (meters, megahertz, 300)
Let λ = k
Let f = k
k * k = 300
k = √300
k =  ≅ 17.32
f =  ≅ 17.32MHz, λ ≅ 17.32meters

[RoGeorge]

About measuring units, it's crucial to keep them attached to the numbers.
1*1=1 is very, very different from 1A*1 =1V or from 1A*1V=1W, because each equality describes something else.

Also, 1 centimeter is not the same as 1 meter or 1 inch
https://www.simscale.com/blog/2017/12/nasa-mars-climate-orbiter-metric/   

No way to neglect the physical units in engineering, not even by mistake.   

In the hf bands there is one frequency that has the same numerical value for both it's frequency and it's wavelength (not the same units of course). It's 17.321 MHz, which has a wavelength of 17.321 meters.

First, why would this value be interesting?  I don't get it.

Second, the sentence is misleading, because usually "same numerical value for both it's frequency and it's wavelength" does not imply MHz and meters, but Hz and m.