日本語

Mechanical engineers and electrical engineers have different mental models of oscillation

(Diary of an Old AI Researcher who is still Programming)

30 October 2019

When I was a young associate professor, a professor of flight dynamics - great Professor K - suddenly came to my office and said, ‘Professor Hori, since your major was electronics, let me ask you a question. A radio wave of higher frequency has larger energy than a radio wave of lower frequency. Is this correct?’.
I answered, ‘No, I do not think so, sir, Professor K. If a radio wave of higher frequency has larger energy than a radio wave of lower frequency, UHF TV stations should spend more electricity charge than the VHF TV stations. I have never heard that.’
Professor K continued, ‘But imagine you are in a bath tub. When you make a water wave of higher frequency by tapping the surface of the hot water in the bath tub, you get more tired than when you make a wave of lower frequency. Professor M of fluid dynamics says I am right.’
I was surprised, ‘What? Professor M also says so? OK, let me go to the library and confirm.’
At that time, we did not have the world wide web, yet, and I went to the library of the department of electronics.
Of course, there is no relation between the frequency and the energy in radio waves(*1). I heard afterward that the great professor K was investigating the problem of intrusion into auto-pilot systems of airplanes.

When I tell this episode while drinking with my colleague professors of the school of engineering, the reactions are always far stronger than I expect, and a long argument emerges with laughter.
At first, most of the engineering professors who majored in mechanical engineering respond ‘I think the great professor K is right!’.
They say, ‘Imagine a mass and a spring. When the mass moves faster, the mass has more energy. So, the oscillation of higher frequency has larger energy.’
I say, ‘No, imagine a simple pendulum. If we give the same initial potential energy, the oscillations have the same energy independent of the frequencies.’

Isn't this interesting?
The basic mental model of oscillation is the mass-spring system in the mechanical engineers' minds, and the basic mental model of oscillation is a simple pendulum in the electrical engineers' minds.
I have not examined this hypothesis on the engineers' mental models scientifically, but, I believe that you will get the same responses from the engineers if you tell this episode.

By the way, even in the mass-spring model, the oscillation has the same energy independent of the frequency if we give the same initial potential energy, of course. But, in the mechanical engigneers' minds, the figures of the oscillations of the same amplitude seem to be drawn unconsciously.
If the mass and the amplitude are fixed and the spring constant is changed, the energy and the frequency will change.
If you like, please confirm the formulae below. :-)
$E=\frac{1}{2}k{A}^{2}$,
$f=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$ ,
where $E$ is energy, $f$ is frequency, $k$ is spring constant, $A$ is amplitude, and $m$ is mass.
Sorry, depending on your browsers, the above formulae may not be shown correctly(*2).
In a plain text, the above formulae are,
E = (1/2)*k*(A squared),
f = (1/2π)*squareroot(k/m).

Moreover, in many cases, resonance is a dangerous phenomenon for mechanical engineers, while it is a phenomenon positively used for electrical engineers.

(*1) In electromagnetism, the energy density of a radio wave is the sum of the energy density from the electric field and the energy density from the magnetic field, which are independent of the frequency.
On the other hand, in quantum mechanics, when we consider the particle nature of electromagnetic radiations, a photon has the energy of hν, where h is the Planck constant and ν is frequency.
We can say Professor K was right in a sense, focusing on one photon.

(*2) MathML is used. Following is the source html code.

$<mi>E</mi> <mo>=</mo> <mfrac><mn>1</mn><mn>2</mn></mfrac><mi>k</mi><msup><mi>A</mi><mn> 2</mn></msup>$, <br>
$<mi>f</mi> <mo>=</mo> <mfrac><mn>1</mn><mrow><mn>2</mn><mi>&pi;</mi></mrow> </mfrac><msqrt><mfrac><mi>k</mi><mi>m</mi></mfrac></msqrt>$
,<br>