 ## Subtitles section Play video

• 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

• [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

• It's free.

• 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]