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]