Notes on Resonance

Bret describes a "local signal" and a "signal received from a distant source." I think most people (non electrical engineers, anyway) would imagine the local source as someone speaking into a microphone, and the distant source as someone shouting from across the room. In this scenario, we should add the signals, and everything that follows is incorrect.

But to an electrical engineer, the "local signal" could be a local oscillator, and the "distant signal" could be the received signal at the antenna. In this case, we feed both signals into an electronic mixer, and multiplying is the correct way to think about it.

I know Bret is really big on abstractions, but the context actually matters here. You might be able to abstract away some of the physical parts (microphone, antenna, demodulator, etc.), but you can't just skip over additive vs multiplicative contexts.

He introduces you to a vast network of ideas, most of which, if you're like me, you only start to appreciate after you've seen a bit of Bret's work. He makes those ideas accessible, beside furthering them on his own.

From Engelbart's idea of "aligning human systems and tool systems, with workers spending time improving their tools for improving their tools, leading to accelerating rate of progress," to Papert's brilliant work on the nature of learning and play, ideas that focus my direction and give me joy, I can't help but always remind myself that I may have never learned of these ideas had it not been because of Bret's work. Thank you Bret.

Any explanation of resonance should deal first and foremost with a physical system, not a signal. Having two signals 'resonate with each other' does not make a lot of sense.

Not sure what is meant with multiplying because the author then goes to mention integration which in essence, is adding, not multiplying.

A physical system is able to store energy at specific frequency -- a pendulum will swing for a long time, energy slowly decaying. But if the system is excited (imagine a kid on a swing), with each push, we will add some more energy, which will accumulate each time adding to a large response (resonance). The key part is, we need to add energy at the right frequency, push at the right interval, sing with the proper pitch.

This is incorrect, even according to the wikipedia article it links to.

Resonance occurs when the excitation frequency matches a natural frequency of the system being excited, causing it to vibrate at larger amplitudes, even perhaps uncontrollably.

It seems that the author misunderstands mixing also - the graph that he presents for the mixed signal seems to be incorrect according to the other wikipedia article he links to.

Imagine an system composed of a mass hanging from a spring, like this [1]. If you pull down the mass and release, the mass will move up and down (oscillate) at a set rate (the system's natural frequency). No matter how far you pull down the mass before release (the amplitude), the system will always oscillate at the same frequency.

Now, imagine you start pushing on the mass (applying forces) while it is in motion. If you were to push up on the mass while it is traveling down, you would decrease the distance the mass would move on subsequent oscillations (damping the amplitude). But if you were to push up on the mass as it travels up, you would be increasing the amplitude of oscillation.

That is what we call resonance.

[1]: https://i.ytimg.com/vi/lZPtFDXYQRU/maxresdefault.jpg

If it were just a technical article, the last step — where you bring the two signals back into phase with each other — would be pointless and redundant. But if the true meaning is outside the mechanistic / technical, then that last step has tremendous purpose.

Bret's background is in electrical engineering. He knows the proper technical meanings of all the terms and concepts in the article. So rather than simply pointing out that he's "misusing" them, perhaps look for reasons that he might have intentionally chosen to do so.

A bit more justification for the math being done would be good.

[1]: https://en.wikipedia.org/wiki/Frequency_mixer

But no.

Inventing on Principle https://vimeo.com/36579366

If this were remotely true, then when I synced the oscillators on my synthesizer, the volume level would grow uncontrollably. But of course what actually happens is that the amplitude (approximately) doubles.

The problem is that the diagrams do not show what resonance actually is, but only what happens then the frequency of an excitation source matches the resonant frequency of a receiving medium, and in addition when the energy input exceeds the damping effect of the medium.

Nevertheless, it's still a great visual, provided the explanation is corrected.

It must be a real high as an author when you see your site is getting a flood of traffic from hacker news - then a hell of a crash when you check it out and all the comments are torching your work.

> The coupling between the two sources is represented by the product of these signals. (Bringing signals into a context for multiplying is called “mixing”.)

The parenthetical is technically correct, but when two systems are coupled they only "mix" if there are strong nonlinearities. Normally when considering resonance you’re thinking of systems that are approximately linear, or even linear time-invariant systems. Under these approximation, the multiplication happens in the frequency domain which is fundamentally different.

Consider a wine glass and a speaker emitting a sound wave. If the speaker is tuned to the resonant frequency of the sound wave, you can shatter the glass—this is not because the signals are multiplied, but this is just because frequencies near the resonant frequency decay more slowly, so the speaker can keep adding more and more energy to the glass until it breaks.