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  • So, I've had a lot of requests to find out how I made the sound of hydrogen

  • for the sound of hydrogen video; so this week I figured I would do a little tutorial

  • to show how you actually create that sound.

  • I'm gonna be using Mathematica but you can use any software that can synthesize sounds.

  • In Mathematica the sound synthesizing command is just called play

  • So you can play a sine wave at, say, 440 Hz.

  • So play from a time of 0 to, say, 3 seconds

  • and it sounds like sine wave.

  • [Beep Sound]

  • Uh, we can also play, say in 880, which is an octave higher

  • [Higher Beep Sound]

  • And if you want you can do crazy things like, uh,

  • playing sine of t^2.

  • [Whoop Sound]

  • Or even the sine of the sine of t^2

  • [Squiggle Sound]

  • So thats a lot of fun.

  • But we're interested in maybe some more slightly realistic sounds.

  • So we will

  • instead of just playing the single sine wave

  • that sounds like:

  • [Beep Sound]

  • Pretty boring.

  • You might want to simulate, uh,

  • an instrument string.

  • So I'll do a sum

  • over sine waves

  • using the harmonic series

  • so we just multiply the frequency inside by n

  • and the sum from n = 1 to 10 maybe

  • and add that up.

  • [Loud, Strong Buzz Sound]

  • That's kind of an annoying sound, because violin strings and guitar strings actually

  • the higher harmonics are quieter than the lower harmonics.

  • So if we

  • modulate the amplitude of each of these sine waves by something like 1/n

  • [Muffled Strong Buzz Sound]

  • we make it a slightly nicer sound.

  • Also, we can set the sample rate

  • to be something a little bit more appropriate. It starts off default as 8000, uh, hertz

  • but maybe you want to speed something like 16- or 32-...000 Hz.

  • That'll make the sound a little bit higher fidelity.

  • [Muffled, Weaker Buzz Sound]

  • So that's basically the sound of a really crappily synthesized violin.

  • For the sound of hydrogen now ----

  • Uh, we need to use the Rydberg Formula instead of the normal harmonic series

  • The Rydberg Formula is : ( 1 / n1 ^ 2 ) - ( 1 / n2 ^ 2 )

  • You could look this up online and see the basic physics behind it

  • But basically, this gives you

  • the spectral lines of hydrogen.

  • And depending on what n1 is,

  • you can get different series, like the Lyman series, the Balmer series...

  • So, for the Lyman series we'll play

  • the Sum ( Sin (1 - 1/n^2)...

  • ... x 2π t

  • Also, times, say, 440, and we'll up-modulate it to an A

  • and then we'll add that up from n = 2... because that's where the Lyman Series starts...

  • ... to, say, 10...

  • You can go all the way to infinity if you want, but it'll take your computer a long time.

  • And time, again, from say 0 to 3 seconds

  • Play that.

  • [Squiggly Sounds in a Pipe]

  • And it doesn't sound too shabby,

  • a lot like our sound of hydrogen from the video.

  • But, if we want to,

  • we can add in another series.

  • So, instead of just the Lyman Series,

  • we can have the Balmer Series, which is:

  • 1/(2)^2, which is 1/4,

  • and then n here has to be n+1,

  • because we start at 3 rather than 2.

  • Now if we play that, we'll get a lot more bass.

  • [Deeper Squiggly Sounds in a Pipe]

  • Sounds closer to our original sound of hydrogen.

  • But what I actually did for the video was I went to the NIST website,

  • and the NIST Atomic Spectra Database,

  • and got the actual spectrum of hydrogen

  • obtained from, you know, experimental results rather than just using the Rydberg formula.

  • So this is the exact spectrum that we see for hydrogen

  • and actually the amplitude as well ----

  • How bright each of the lines are

  • and I downloaded it.

  • It's free.

  • Now you could download that data;

  • You kinda have to mess around with it to get it to look

  • anything intelligible.

  • But I brought it back to Mathematica,

  • and normalized it,

  • and then you plug that in,

  • and

  • [Higher Squiggly Sounds in a Pipe]

  • you get the sound of hydrogen.

  • [High Squiggly Sounds in a Pipe continues]

  • So I hope that you've enjoyed this tutorial,

  • and go and use your

  • math software to do fun stuff like make crazy sounds.

  • [Sounds Similar to Retro Shooting Video Games]

  • [Sound Gets Faster]

  • [Static Sound]

  • [Sound Fades]

So, I've had a lot of requests to find out how I made the sound of hydrogen

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教程:創造氫氣的聲音 (Tutorial: creating the sound of hydrogen)

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    林宜悉 發佈於 2021 年 01 月 14 日
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