Let's hear it.

[SOUND].

Okay.

In order to see that it's periodic, we can zoom into it,

and here we see the sinusoid oscillation, the periodic oscillation of a sine wave.

If we zoom even more, we are going to start seeing the samples

that are present in this signal, this discreet signal.

So we have generated this signal at 44,100 hertz, so

we'll have that many samples per second.

Okay, so the first thing we might want to do to understand

the concept of periodicity is to measure what is the period length.

Now the idea of periodic means that there is

a period that is repeating a cycle of the sound.

Okay, so this is a cycle of this sinusoid,

and in here we can see what is the length of this selection I made.

And it says that it's 0.002.

So that means 2 milliseconds.

If we go to the terminal and have Python in, we can use it as a calculator.

So we can convert this period length into frequency.

So the inverse of the period, so

1 over 0.002, will be our frequency.

And of course it gives us 500 hertzs.

500 hertzs is the frequency of this sinusoid.

Okay, another thing we might want to check is okay,

this period has a series of sample.

So, how many samples does one period of this sinusoid has?

Well, in order to compute that, what we should do is start with the sampling rate.

The sampling rate is 44,100.

And multiply by the duration of this period.

So we multiply by 0.002.

And it gives me 88.2,

which is the number of samples of a period.

Of course it should be an integer number.

So I guess it's going to be 88 samples in one period, okay?

Now let's generate another sinusoid but of a different frequency.

So let's maybe open a new file, okay?

And let's create another sinusoid.

But instead of 500 hertz, let's put, for example, 5000 hertz.

Okay, so this is the sinusoid of 5000 hertz.

We can hear it too.

[SOUND].

Clearly, much higher, and we can also zoom,

and to see the periodicity.

But here we already see that is not so nice, in fact

the samples are not really shaping a smooth sinus little function.

This is because there is less samples per period,

therefore we don't have a various most version.

So how many samples are in one period?

Well, not that many.

In fact, here we can even count them.

And it's one, two, three, four, five, six, seven, eight.

So in fact we have like eight, nine samples for one period.

Not exactly because they don't coincide, of course, with a period.

Of course it makes sense because if we had seen that

the frequency of Pythagorean had 88 sample in one period.

Now that we have 10 times the frequency, 5,000, the number of samples

will be 10 times less, so it's going to be around 8 or 9 samples, that's pretty good.

Of course, this relationship between the number of samples and

the frequency is a very important one, and related with the sampling rate.

The bigger the sampling rate, of course, more samples we'll have.

And for higher frequencies, we'll have more samples.

At 44,100, as we go up in frequency, and if we go even higher,

like 10,000 or even 15,000, the number of samples will be very less.

And therefore,

the shapes will not look like a sinusoid even though it's a sinusoid.