[HN Gopher] Sound
       ___________________________________________________________________
        
       Sound
        
       Author : todsacerdoti
       Score  : 1456 points
       Date   : 2022-10-18 15:48 UTC (7 hours ago)
        
 (HTM) web link (ciechanow.ski)
 (TXT) w3m dump (ciechanow.ski)
        
       | bnert wrote:
       | Bartosz, you're a legend! Thank you for these amazing articles!!
        
       | [deleted]
        
       | bullen wrote:
       | Imagine if the later demos had stereo!
        
       | Waterluvian wrote:
       | I love the web audio API. I've been making a game where the theme
       | is "I don't do art" so my assets are CSS, emojis, and manually
       | made sounds using frequency and sinewaves and such.
       | 
       | The one lesson I learned the hard way is that if you run a full-
       | volume sine wave long enough you can permanently destroy your
       | laptop speakers.
        
         | Minor49er wrote:
         | Reminds me of DOS terminal games like Rogue and ZZT which used
         | ASCII characters to draw everything. I hope you post it once
         | it's ready
        
           | Waterluvian wrote:
           | Indeed it's a dungeon crawler.
           | 
           | Don't hold your breath. It'll be rudimentary. I'm making it
           | for my own joy and learning, but will probably publish it by
           | EOY.
        
         | nyanpasu64 wrote:
         | Reminds me of Marcan trying to make Asahi _not_ do that on
         | MacBooks, and so far failing
         | (https://github.com/AsahiLinux/linux/issues/53). I didn't know
         | that Windows laptops also had speakers that would burn out with
         | high-volume playback.
        
         | n4bz0r wrote:
         | > if you run a full-volume sine wave long enough you can
         | permanently destroy your laptop speakers
         | 
         | Minutes? Hours?
        
           | Waterluvian wrote:
           | Minutes.
           | 
           | I never repeated the experiment. Maybe my laptop was a dud or
           | something.
        
             | [deleted]
        
       | drcongo wrote:
       | I'm starting to think Bartosz Ciechanowski is from another
       | planet. Everything he does is the very best explainer on that
       | subject.
        
         | brnaftr361 wrote:
         | I'd really like to learn to do what he does. It's always so
         | impressive, clear, concise and comprehensive. I feel like
         | everything he does is a perfect pedagogical modality. I just
         | wish everyone could get on board, especially university
         | professors and publishers.
        
       | fuy wrote:
       | What a neat switch from metric to imperial units! I wish more web
       | pages had this.
        
       | pruthvishetty wrote:
       | This is a PhD thesis in itself!
        
       | MichaelZuo wrote:
       | Great information, well organized with intuitive flow.
        
       | lozzo wrote:
       | Interesting. Just earlier I went to Bartosz website to see if
       | there was anything and there was not... and then he publishes
       | sound and I see it here on hackernews. I am going to enjoy this.
       | thanks
        
       | ianklug wrote:
       | A fantastically written and extremely technically performant page
       | as always from Bartosz.
       | 
       | Several of the piano key demos ask you to observe what happens
       | when you play multiple keys at once. Is there a way to do this on
       | a desktop PC that I am missing? I had to switch to my phone to
       | try those sections.
        
         | dmd wrote:
         | Use the (computer) keyboard.
        
           | ianklug wrote:
           | _facepalm_
           | 
           | Thanks. Next time I'll try actually reading all the text on
           | the page.
           | 
           | Amazing that on a page with such exemplary UX my tired brain
           | still managed to gloss over the massive letters on each key.
        
         | croddin wrote:
         | For me, on desktop, there is a paragraph that says keys can be
         | played with the W E and R keys, and each key has a W E or R on
         | it, but this isn't present on mobile. Maybe the site thinks you
         | desktop browser is mobile for some reason?
        
       | imadr wrote:
       | The three keys piano at the beginning is so responsive and nice
       | that I was stuck playing with it for 5 minutes, that's how you
       | hook someone to read an article
        
       | PostOnce wrote:
       | This man needs a genius grant, and this is about the 6th time
       | I've thought this.
       | 
       | Any one of these pages would be a feat, an achievement to be
       | proud of, but as a collection, it forms one of the greatest
       | educational resources of its type that I have known.
       | 
       | These things can give you more intuition about a subject in 45
       | minutes than a textbook might be able to in 3 months, because
       | it's interesting and not dry.
       | 
       | I wish I had more time to rant about this right now, but I
       | haven't, so: Kudos. Another amazing job.
        
         | princevegeta89 wrote:
         | This webpage can be converted directly into a science class.
        
         | behnamoh wrote:
         | > This man needs a genius grant, and this is about the 6th time
         | I've thought this.
         | 
         | He says this is his weekend hobby. I really wish he could work
         | on these things full-time. The world needs more people like
         | him.
        
         | ccakes wrote:
         | The little touches like being able to switch the entire article
         | to metric (or imperial) are incredibly nice and make it more
         | approachable as a result
        
         | Liron wrote:
         | Is there a way to donate?
        
           | gmd63 wrote:
           | There's a Patreon link in the top right on his blog
        
       | mathfailure wrote:
       | This man is a legend now. The awesomest quality of articles.
        
       | mabbo wrote:
       | > As a side note, I'm using metric units here, but you can
       | *switch* to the imperial system if you prefer.
       | 
       | Clicking on the word 'switch' does exactly that. That's a
       | delightful and clever touch that of course comes from Bartosz
       | Ciechanowski.
        
       | duderific wrote:
       | Incredible work as always, thanks Bartosz.
       | 
       | Interesting side note - using the "basic" frequency/amplitude
       | slider section, you can tell if you have any hearing loss in a
       | certain ear at a certain frequency, as well as high frequencies
       | in general.
       | 
       | As an ex-musician, I have some hearing loss caused by playing and
       | being around extremely loud music. Between 6KHz and 7KHz, I felt
       | the sound shift towards my right hear, indicating some hearing
       | loss at that frequency in my left ear. Between 10KHz and 11.5KHz,
       | I felt a strong shift toward my left ear, indicating hearing loss
       | at those frequencies in my right ear. Above about 12.3KHz, I lost
       | the sound entirely.
       | 
       | One very gentle bit of feedback (haha) to the author would be to
       | provide anchors to each section so they could be more easily
       | linked.
        
       | vladstudio wrote:
       | If you have not yet seen this site, please free a couple of hours
       | and browse through archives, it's the best educational material I
       | have ever seen!
       | 
       | https://ciechanow.ski/archives/
        
         | maest wrote:
         | Any idea what framework (if any) this is written in?
        
           | nwsm wrote:
           | View the source of the articles and you will find thousands
           | of lines of readable HTML, handwritten JavaScript using
           | canvas and WebGL, and handwritten audio manipulation using
           | window.AudioContext. Similar stories for the author's other
           | incredible articles.
        
           | phailhaus wrote:
           | It's hand-crafted WebGL with no frameworks, which is insane.
           | If you View Source on the page, you'll see that the JS is
           | readable because he doesn't minify at all.
        
       | aubanel wrote:
       | I love how every Ciechanowski post starts explaining from the
       | very basics, but makes things so beautifully explained that my
       | 10s attention span magically extends up to the way where I can
       | learn a lot.
        
       | [deleted]
        
       | CKMo wrote:
       | Incredible! Approachable and fun to learn.
       | 
       | All education should aim for this bar
        
       | Nition wrote:
       | I think my favourite part of this is being able to draw your own
       | waveform and then play it. Super cool. You can learn about
       | something so much faster when it's right there and instantly
       | tweakable.
        
       | marcodiego wrote:
       | WARNING: sounds you can't hear can still damages your ear. DO NOT
       | INCREASE THE VOLUME ON INFRA OR ULTRA SOUNDS BECAUSE YOU CAN'T
       | HEAR THEM
        
         | owenfi wrote:
         | Would love some additional info on this if you are aware of
         | any. My intuition says (and could very well be very wrong)
         | sound at one frequency would only damage that or very nearby
         | frequencies hearing range? If wrong I'm curious what the range
         | of damage is (I'm interested in exploring ultrasound data
         | protocols, so curious what frequency I have to go to to avoid
         | damaging anyone's - and potentially animals as well - hearing).
         | 
         | I also assume if you are starting at a reasonable (laptop,
         | small desktop speakers) at a low-to-medium level (say 50-60dB),
         | increasing a bit won't cause immediate damage even if you can't
         | hear the sound?
        
       | system2 wrote:
       | Phenomenal post. Hard to find these type of posts unless I look
       | at HN.
        
       | extantproject wrote:
       | https://archive.ph/woqkb
        
       | qazpot wrote:
       | This is awesome, reminds me of some of Bret Victor's work.
        
       | tambourine_man wrote:
       | Audio is not working for the three keys on iOS.
       | 
       | Amazing content as always otherwise.
        
         | 0x5345414e wrote:
         | Works fine for me on iOS 16
        
         | incanus77 wrote:
         | Make sure your alerts aren't muted. I'm on an iPad and I had to
         | check the widget in Control Center to get sound, but then it
         | worked fine.
        
           | tambourine_man wrote:
           | Right you are, thanks
           | 
           | :facepalm
        
             | incanus77 wrote:
             | I still don't understand why this mutes functionality like
             | this page's, but not web video or audio players or the like
             | in web pages.
        
               | tambourine_man wrote:
               | Yeah, iOS sound is an enigma. If you lower the sound,
               | does it change the ringtone? How about the alarm?
               | 
               | No one knows for sure, one of the true mysteries of the
               | universe.
        
       | Erwin wrote:
       | I was surprised by how much I was surprised by the very first
       | fact -- that air molecules move around at extremely high speed of
       | 450m/s, but just bump into each other cancelling this speed out,
       | and this speed is based on pressure & temperature.
       | 
       | And it's due to this speed, despite air's low density, the force
       | air exerts is enormous -- equivalent to 10 tons per square meter.
       | Somehow, the human sandwich does not explode nor implode due to
       | equivalent pressure coming from the other side and inside.
        
         | zeroonetwothree wrote:
         | Note that diving to a depth of only 10m will double the
         | external pressure on your body yet humans can easily survive
         | this.
         | 
         | Indeed the all time record is >300m which is something like 32x
         | pressure.
         | 
         | So it's not merely that there is equivalent pressure from
         | inside.
        
       | gtirloni wrote:
       | How can one learn to create these visualizations?
        
         | exikyut wrote:
         | Depends what point on the spectrum you refer to by "how".
         | Implementation, creativity, or the focus and discipline
         | required to combine the two? :P
         | 
         | I had a quick look; as always with the presentations on this
         | website, all the un-minified JavaScript is right there for you
         | to pour over: https://ciechanow.ski/js/sound.js
         | 
         | So that covers the implementation: a giant pile of WebGL to
         | power the rotatable boxes and animate effectively using the
         | GPU, alongside in this case a bunch of Web Audio code.
         | 
         | Unfortunately that _doesn 't_ cover the focus/discipline part,
         | which I would definitely appreciate some pointers on... one of
         | these days I'll find some that fit within my ADHD address space
         | xD
        
         | phailhaus wrote:
         | I don't want to dissuade you, but you probably should not try
         | to do it the same way he does: completely from scratch using
         | pure JS + WebGL and without any frameworks. He's able to pull
         | it off because he clearly has an incredible depth of knowledge
         | of how it works, but mere mortals like you and me will likely
         | get stuck in the bog of minutiae.
         | 
         | I recommend starting off by playing around with Three.js, which
         | will get you up and running really quickly while still staying
         | pretty grounded in WebGL. [1] You can make blog posts very
         | similar to Ciechanowski using ObservableHQ. [2]
         | 
         | [1]
         | https://threejs.org/docs/index.html#manual/en/introduction/C...
         | 
         | [2] https://observablehq.com/@mbostock/hello-three-js
        
           | gtirloni wrote:
           | Thank you, very useful pointers.
        
         | skilled wrote:
         | By inspecting page source.
         | 
         | If you mean technical, you have no choice but to actually study
         | the topic and understand it so that you can create examples
         | like the author did.
        
       | iammjm wrote:
       | Superb
        
       | mirkodrummer wrote:
       | This. This is the internet. I'm glad we can still enjoy quality
       | driven content. To author if you're here: any ways to support
       | your work?
        
         | primarydonkey wrote:
         | You can support him on Patreon:
         | 
         | https://www.patreon.com/ciechanowski
        
       | krinchan wrote:
       | I appreciate the mention and demonstration of Fourier Transforms.
       | It makes a lot of previous sound codec discussions click a bit
       | more now.
        
       | sgraaf wrote:
       | Bartosz' blog posts are in a league of their own.
       | 
       | They way he is able to explain complex subjects by starting from
       | first principles, gently adding more and more layers, with
       | beautiful, custom-made figures and animations is truly,
       | literally, awesome.
       | 
       | I strongly recommend supporting the author via his Patreon if you
       | enjoy his blog posts.
        
         | armchairhacker wrote:
         | The article on mechanical watches had so much depth and such
         | good explanations I thought he was a mechanical watch engineer
         | or enthusiast who happened to also have web design, 3d
         | animation, and writing skills
        
         | [deleted]
        
         | behnamoh wrote:
         | This is how school must be. I'd rather pay people like him to
         | create interactive content than pay the school to teach my kids
         | useless material in dry, rigid ways.
        
         | russellbeattie wrote:
         | These are amazing - from the design to the interactive demos to
         | the writing. I think "digital monograph" is almost a more apt
         | description than "blog post". I've written tons of blog posts
         | and they have almost nothing in common with what he's doing.
         | 8,000 well written words plus formatting and links plus 50 or
         | so embedded demos is really an astounding amount of work. What
         | I appreciate most is the use of the medium itself. Imagine if
         | the standard format for academic papers was updated from the
         | black and white two-column format used for a half century to
         | something like this?
        
       | Scarlxd wrote:
       | The resources were awesome! Everyone should check this out!
        
       | mfwit wrote:
       | Incredible stuff as always from Bartosz.
        
       | anderspitman wrote:
       | I was 20 minutes into this before I realized the interactive bits
       | were automatically turning themselves off and on based on which
       | one was visible in the viewport. That seems obvious, but the fact
       | that it worked so intuitively and without bugs on my system says
       | a great deal. This is what master UX design looks like.
        
         | lelandfe wrote:
         | That it all worked perfectly on my phone is testament to a
         | _ton_ of testing.
        
         | mixmastamyk wrote:
         | It's a few lines of standard JavaScript. Nice touch used by
         | many sites, not difficult.
        
           | behnamoh wrote:
           | > not difficult.
           | 
           | And yet, not so common especially on popular websites with
           | $$$ development costs.
        
             | mixmastamyk wrote:
             | Someone has to care enough to notice, often the case.
        
       | woliveirajr wrote:
       | > at room temperature the average velocity of a particle is a
       | staggering 460 m/s so to make the particles visible I'm showing
       | their motion significantly slowed down
       | 
       | Isn't 460 m/s the speed of the shock waves?
       | 
       | I mean, it you make some "air particle" move, it'll hit a nearby
       | particle, and so on, and this wave has a speed of 460 m/s. In a
       | solid object (wood, for example) the particles are close together
       | and the speed will be greater. If you remove air particles it'll
       | decrease the pressure and the speed will be slower...
        
         | pqn wrote:
         | Speed of sound isn't too directly affected by air pressure I
         | think (holding all else constant):
         | https://physics.stackexchange.com/a/146207
        
         | jcims wrote:
         | Yes, IIUC basically that's the point where the local particle
         | speed is no longer sufficient to clear the leading edge of the
         | wave.
        
       | jcims wrote:
       | I love it when I'm halfway through something and take a second to
       | pause and wonder why someone put so much effort into it, and them
       | I appreciate that they did. This is amazing.
       | 
       | One thing that surprised me the first time I learned it is how
       | 'dense' air is under normal circumstances. The 'mean free path'
       | is the mean distance that a particle travels before changing
       | velocity (typ due to collision). The mean free path of
       | atmospheric air at standard pressure is ~65 nanometers, with
       | ~2x10^19 (20 billion billion) molecules per cubic _centimeter_
       | experiencing about 10^33 collisions per second. This is roughly
       | the volume of an adult 's ear canal.
        
         | moritonal wrote:
         | Whilst I imagine he'd produce content regardless of income, he
         | does have a slightly successful Patreon. To encourage this
         | effort, consider supporting him in some form, if you don't.
        
           | jcims wrote:
           | Nice callout. Done.
        
         | jarenmf wrote:
         | I was able to reach 10^-7 mbar with a good vacuum system and I
         | though I would have few thousand molecules, turns out there is
         | a billion (10^9) molecules per cubic centimeter at that vacuum
         | level.
        
           | jcims wrote:
           | And yet somehow, as far as we know, the energy of every
           | molecular collision is faithfully preserved during a
           | supernova, when effectively the entire volume of a star
           | collapses into its core in less then a second.
           | 
           | Reality is very strange.
        
       | mortenjorck wrote:
       | Ordinarily, I follow the HN best practice of clicking through to
       | a link first rather than upvoting based solely on the headline
       | and domain.
       | 
       | Seeing there's a new Bartosz Ciechanowski explainer might be my
       | one exception to this rule.
        
         | giarc wrote:
         | https://news.ycombinator.com/from?site=ciechanow.ski
         | 
         | A link to all the HN submissions from ciechanow.ski
        
         | sebmellen wrote:
         | I did the same. The minute I saw it on the homepage, upvote.
        
         | green-eclipse wrote:
         | I'm a simple man. I see ciechanow.ski and I upvote.
        
           | symlinkk wrote:
           | Reddit: Orange Edition
        
       | meta-level wrote:
       | Bartosz, you have to choose another name, I just upvoted by
       | reflex, when I saw it's you again
        
       | hiidrew wrote:
       | Quick babe wake up, new Ciechanowski intractable dropped.
        
       | aidenn0 wrote:
       | When I started playing around with square/triangle waves, I
       | couldn't help but hear
       | https://www.youtube.com/watch?v=uyMKWJ5e1kg
        
       | igtztorrero wrote:
        
       | lagrange77 wrote:
       | This guy!
        
       | patel011393 wrote:
       | As an educational psychologist, there's a lot to love here and I
       | catalog posts like these as examples of expert exposition.
       | 
       | One suggest to Bartosz: breaking one long essay into many smaller
       | pages or hiding content until the viewer has indicated
       | understanding of previous steps will be even more useful (see:
       | https://tigyog.app/d/H7XOvXvC_x/r/goedel-s-first-incompleten...).
       | 
       | Explorable models are a great way to increase engagement and
       | understanding. Beyond that, I would supplement this with highly
       | frequent comprehension questions to check for learning. I bet
       | you'd find a way to make it fun and approachable.
        
       | naillo wrote:
       | Nothing really to say about this other than excellent work again
       | and this really inspires me to make amazing web-based material in
       | ways I haven't really experienced since the ~2012 era.
        
       | mNovak wrote:
       | I'm really curious to know how he selects the topic of each
       | article; the archive has quite a range!
       | 
       | This is the type of blog I aspire to make, one day
        
       | nonrandomstring wrote:
       | +1 for the recommendation for "The Scientist and Engineer's Guide
       | to Digital Signal Processing" by Steven W. Smith. I spoke to
       | Steven many years ago about his putting all of the book PDFs
       | online for free and since then have recommended at least 5
       | university libraries to buy it because the students could get
       | free copies of a great book that can be referenced in the
       | library.
       | 
       | FWIW the The Scientist and Engineer's Guide doesn't actually
       | cover a lot on sound. It starts in a particular DSP way with
       | frequency domain definitions and convolution - and I actually
       | think Steven's background is in medial imaging, though I could be
       | mistaken.
        
         | voidhorse wrote:
         | I'm actually reading through it right now after trying out a
         | few other DSP resources. It is by far the clearest and most
         | approachable, without sacrificing much depth at all. It's a
         | great book.
        
           | anigbrowl wrote:
           | It's the best. I learned DSP from that ~20 years ago and
           | still use those mental models whenever I need to think
           | through a problem. A good book like that is a friend for
           | life.
        
         | belkarx wrote:
         | The book is amazing: http://www.dspguide.com/ (link for the
         | lazy)
        
         | WhitneyLand wrote:
         | Wow. Such a profound insight could not get published for 15
         | years because others couldn't grasp it. Including Lagrange!
         | 
         | It's an uncomfortable reminder of how essential reputation and
         | credibility are in the machinery of science.
         | 
         |  _"The paper contained the controversial claim that any
         | continuous periodic signal could be represented as the sum of
         | properly chosen sinusoidal waves. Among the reviewers were two
         | of history 's most famous mathematicians, Joseph Louis Lagrange
         | (1736-1813), and Pierre Simon de Laplace (1749-1827). While
         | Laplace and the other reviewers voted to publish the paper,
         | Lagrange adamantly protested. For nearly 50 years, Lagrange had
         | insisted that such an approach could not be used to represent
         | signals with corners, i.e., discontinuous slopes, such as in
         | square waves. The Institut de France bowed to the prestige of
         | Lagrange, and rejected Fourier's work. It was only after
         | Lagrange died that the paper was finally published, some 15
         | years later."_
         | 
         | from chapter 8 http://www.dspguide.com/ch8/1.htm
        
           | comboy wrote:
           | > Lagrange had insisted that such an approach could not be
           | used to represent signals with corners, i.e., discontinuous
           | slopes, such as in square waves.
           | 
           | Isn't that true though? You can only approximate it, right?
        
             | AceJohnny2 wrote:
             | In practice, yes you can only approximate it, because in
             | theory it requires an infinite series of sinusoidal waves.
             | But since maths is all about the theory, Laplace's
             | objections were silly. (though I admit I don't know what
             | the state of acceptance of infinite series was at that
             | time)
             | 
             | Also, it's fine to cut off the infinite series of
             | sinusoidal waves because all physical systems cut off
             | around a given frequency, for example human hearing around
             | ~20kHz.
        
               | armadsen wrote:
               | Also, in practice, there's no such thing as a truly sharp
               | corner, which makes sense intuitively based on the math,
               | I think. But real systems have inertia, friction, stray
               | resistance/capacitance/inductance, etc. so you can't have
               | a truly perfect square wave in a physical or electrical
               | system in the real world.
        
               | tuatoru wrote:
               | * Lagrange's objections
        
               | AceJohnny2 wrote:
               | whoops! thanks. Too late to edit.
        
             | anigbrowl wrote:
             | Corners in signals are like limits in calculus or
             | irrational numbers in arithmetic. Once you accept them as
             | an abstraction that you can't touch them directly all the
             | anxiety dissipates.
        
             | retrac wrote:
             | In the same sense that a circle does not exist, because you
             | can only approximate it with an arbitrary number of
             | points/lines. But an infinite number of points the same
             | distance from the origin is a good definition of a circle.
             | In a similar way, an infinite set of sine waves
             | approximating a square wave _is_ a square wave,
             | mathematically speaking.
        
         | SonOfLilit wrote:
         | It's one of my favorite technical books. So simply explained,
         | so full of engineering wisdom.
        
         | rectang wrote:
         | I have this conviction that I ought to be able to code up crude
         | audio DSP processors before I understand the totality of the
         | theory.
         | 
         | For example, every DFT/FFT explanation seems to start with
         | complex numbers. I wish there was a resource that was
         | programming focused, starting with "Step 1: Process this
         | artificially created periodic signal by multiplying it by sine
         | waves of frequencies from from 1 to N. There are our bins! Step
         | 2: OK, for real world signals we need phase, so _now_ let 's
         | talk about complex numbers."
         | 
         | I've been studying math for a while trying to build up the
         | prerequisites for writing audio DSP code. I have this sneaking
         | suspicion that at the end what I want to achieve won't be as
         | hard as DSP resources imply. At least there will be parts that
         | I could have done with hardly any theory at all. But because of
         | the way these resources are written, I have to consume massive
         | amounts of theory first.
         | 
         | (For background, I've worked as a mastering engineer and have
         | done a fair amount of audio production, so I know intimately
         | what the tools ought to do.)
        
           | cannam wrote:
           | > "Step 1: Process this artificially created periodic signal
           | by multiplying it by sine waves of frequencies from from 1 to
           | N. There are our bins! Step 2: OK, for real world signals we
           | need phase, so now let's talk about complex numbers."
           | 
           | Maybe the latter part could be prepped by resynthesising the
           | time-domain signal by summing the sines, and seeing that it
           | doesn't match the original. And it can't, not least because
           | all of the sines start at 0. But if you have cosines as well,
           | it can. Then refer to the geometrical relationship between
           | sine/cosine and phase.
           | 
           | A preliminary to the earlier part might be to multiply a
           | single long sinusoid by another one, and see what happens
           | when their frequencies do or don't match. (But there is a
           | whole well here about what it means for frequencies to
           | "match", which in the discrete world has to do with how long
           | the relevant part of the signal is.)
        
           | laszlokorte wrote:
           | I posted this as a submission a while ago but you might find
           | it helpful. While learning about signal processing my self I
           | built a collection of educational tools for visualizing some
           | concepts. [1]
           | 
           | Especially the fourier cube [2], the complex exponential [3],
           | the digital filter designer [4] and the signal generator [5]
           | might be helpful.
           | 
           | Additionally the matrix multiplier [6] has an option for
           | complex numbers that highlights the perspective that complex
           | numbers can be seen as just a subset of 2x2 matrices.
           | 
           | [1]: https://tools.laszlokorte.de/ [2]:
           | https://static.laszlokorte.de/fourier/ [3]:
           | https://static.laszlokorte.de/complex-exponential/ [4]:
           | https://static.laszlokorte.de/signal-transform/ [5]:
           | https://static.laszlokorte.de/signal-generator/ [6]:
           | https://static.laszlokorte.de/matrix-multiplication/
        
           | CamperBob2 wrote:
           | Your intuition is right, in that most of the heavy math is
           | simply unnecessary or irrelevant at the practical level.
           | Complex number notation doesn't fall into that category,
           | though. The notion of frequency is intimately tied to the
           | notion of vector rotation, and just as you can't represent
           | Cartesian translation without negative numbers, you can't
           | represent Cartesian rotation without complex ones.
           | 
           | The Smith book is definitely for you; also check out Rick
           | Lyons's books. Bo Pirkle and Julius O. Smith are good for
           | audio-specific theory and applications.
        
             | skybrian wrote:
             | Saying that you can't represent cartesian rotation without
             | complex numbers seems a bit much? You do need two numbers.
             | But you can teach a trigonometry class without complex
             | numbers, using either cartesian coordinates or polar
             | notation. And matrices do work.
        
           | skybrian wrote:
           | I've been writing notebooks about doing DSP and audio
           | processing in JavaScript. It might be a good place to crib
           | off of:
           | 
           | https://observablehq.com/collection/@skybrian/digital-
           | signal...
        
             | laszlokorte wrote:
             | Wow, thank you very much! Straight to the point and very
             | helpful, especially the web audio stuff.
        
       | rvba wrote:
       | I wish there was a post like this about fire.
       | 
       | On atomic level. Like atoms oscilating? How many photons are
       | emitted when say 5 carbon atoms connect with 5 oxyxen particles?
       | I tried searching and no avail.
        
       | 48cfu wrote:
       | Interesting topic
        
       | zebracanevra wrote:
       | Hmm, on Windows 10 Chrome/Firefox the demos with the movable ears
       | don't work very well when the position changes. Both browsers
       | output horrible audio in those sections.
       | 
       | edit: If I limit Firefox to 60fps (down from my display's 280hz)
       | then it seems to work fine.
        
       | bkallus wrote:
       | I haven't taken beyond high school physics, so this question is
       | probably obvious, but I haven't been able to find the answer
       | (probably don't know the right terms to search).
       | 
       | When I increased the slider that allows you to change the flow of
       | time for the gas in the cube, it really looked like
       | visualizations I've seen of increasing the temperature of a gas.
       | Is there a deeper relationship here? Could an observer tell the
       | difference between a cube $A$ of gas in which the flow rate of
       | time were doubled and a cube $B$ of gas with normal time passage,
       | but a correspondingly increased temperature? If so, what would
       | give it away?
        
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