Notes on Resonance
worrydream.com
Notes on Resonance
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Re: Notes on Resonance
#2I have watched this talk from Bret Victor at least once a year to help me think about what to work on:
Inventing on Principle https://vimeo.com/36579366
Re: Notes on Resonance
#3In what physical context do we multiply signals together instead of adding them?
Re: Notes on Resonance
#4"Resonance occurs when two sources of excitation fall completely in sync, and reinforce one another endlessly."
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.
Re: Notes on Resonance
#5In what physical context do we multiply signals together instead of adding them?
In a radio, this is done by a mixer circuit, for instance https://en.wikipedia.org/wiki/Gilbert_cell
Re: Notes on Resonance
#6(Small grey sans-serif text means you hate your readers' eyes.)
Re: Notes on Resonance
#7This is, at best, a misleading presentation on resonance, and my first reaction is that it’s completely and horribly wrong.
> 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.
Re: Notes on Resonance
#8Why are the signals being multiplied together instead of added together? Multiplying them is very unusual. Even the wikipedia article linked by the site, with the text "Bringing the signals into a context for multiplying is called 'mixing' [1]", is talking about adding signals; not about multiplying them.
A bit more justification for the math being done would be good.
Re: Notes on Resonance
#9I guess he just means sympathetic frequencies or something like that, rather than resonance. As an admirer of Bret's other work, I'm guessing he intended this as a showcase of interactive illustrations of how frequency works in composite. Too bad the terminology is off.
Re: Notes on Resonance
#10I don’t know what kind of resonance this post is talking about, but I’ve never heard of time domain signals being multiplied in a physical system...