Hi. It’s Mr. Andersen. And this is AP Physics essentials video 117. It is on beats. Beats
Hi. It’s Mr. Andersen. And this is AP Physics essentials video 117. It is on beats. Beats

are changes in amplitude when you have two wavelengths that have a frequency that is
are changes in amplitude when you have two wavelengths that have a frequency that is

very close together. And you can actually play around with this if you are connected
very close together. And you can actually play around with this if you are connected

to the internet. And so I will put a link to this down below. But is you go to this
to the internet. And so I will put a link to this down below. But is you go to this

website right here and you launch it, what you can do is you can play a tone. And so
website right here and you launch it, what you can do is you can play a tone. And so

what I am going to do is play one that is at 440 Hertz. I am then going to launch another
what I am going to do is play one that is at 440 Hertz. I am then going to launch another

tab. And in that tab I am going to briefly change what note I am playing. So that is
tab. And in that tab I am going to briefly change what note I am playing. So that is

440 Hertz. That is also 440 Hertz. But listen what happens when I change one. Those are
440 Hertz. That is also 440 Hertz. But listen what happens when I change one. Those are

beats. Now they are gone. Now as I go above it you can hear the beats again. And as I
beats. Now they are gone. Now as I go above it you can hear the beats again. And as I

bring them back to the same value, then it goes away. Now when would this be useful?
bring them back to the same value, then it goes away. Now when would this be useful?

Well let’s say you are tuning your guitar. What you can do is tune one of the strings.
Well let’s say you are tuning your guitar. What you can do is tune one of the strings.

So make sure you tune that to a tuner or piano or something like that. Once you have that,
So make sure you tune that to a tuner or piano or something like that. Once you have that,

then you can play another string, you have to move up on the fret, but play another string.
then you can play another string, you have to move up on the fret, but play another string.

And if it is close you will hear the beats. And if it is exactly the same you can adjust
And if it is close you will hear the beats. And if it is exactly the same you can adjust

the one, then the beats will go away. And then you can move on to the next string, and
the one, then the beats will go away. And then you can move on to the next string, and

the next string and the next string. And so waves, when they come together, will interact.
the next string and the next string. And so waves, when they come together, will interact.

And as they interact they cause interference. Now the interference can be constructive,
And as they interact they cause interference. Now the interference can be constructive,

sometimes building up the wave or the summation of the waves. And sometimes it is destructive.
sometimes building up the wave or the summation of the waves. And sometimes it is destructive.

It is tearing it down. But if those waves are very similar in frequency, what you get
It is tearing it down. But if those waves are very similar in frequency, what you get

are these beats. And beats are going to be amplitude changes. In other words the volume
are these beats. And beats are going to be amplitude changes. In other words the volume

is going to go up and down and up and down due to this constructive and destructive interference.
is going to go up and down and up and down due to this constructive and destructive interference.

Now it is really easy to calculate the frequency of the beats. All you do is, the frequency
Now it is really easy to calculate the frequency of the beats. All you do is, the frequency

of the beat equals the absolute value of the difference between the two frequencies. So
of the beat equals the absolute value of the difference between the two frequencies. So

if I know frequency one and two I simply subtract one and it is the value, the absolute value
if I know frequency one and two I simply subtract one and it is the value, the absolute value

of those. And so again in review, if you do not know what constructive and destructive
of those. And so again in review, if you do not know what constructive and destructive

interference are, if we have two waves that are perfectly the same frequency and they
interference are, if we have two waves that are perfectly the same frequency and they

are right next to each other, what we will get is constructive interference. If they
are right next to each other, what we will get is constructive interference. If they

are out of phase with one another we will have destructive interference. But if the
are out of phase with one another we will have destructive interference. But if the

frequencies are slightly off, and if we look at this animation down here, these are frequencies
frequencies are slightly off, and if we look at this animation down here, these are frequencies

that are close, but not exactly the same, what you get is as you have this constructive
that are close, but not exactly the same, what you get is as you have this constructive

and destructive interference you get the blue summation of those two waves and you can see
and destructive interference you get the blue summation of those two waves and you can see

that we are seeing these changes in the amplitude. In other words the amplitude is decreasing
that we are seeing these changes in the amplitude. In other words the amplitude is decreasing

and then it is increasing and then decreasing. Now if I could make those frequencies exactly
and then it is increasing and then decreasing. Now if I could make those frequencies exactly

the same, then the beats are simply going to go away. How do you calculate it? Again
the same, then the beats are simply going to go away. How do you calculate it? Again

it is frequency one minus frequency 2. Absolute value of. And let’s do a sample of that.
it is frequency one minus frequency 2. Absolute value of. And let’s do a sample of that.

So I am using audacity. It is a little music software. And so what I am going to do is
So I am using audacity. It is a little music software. And so what I am going to do is

I am going to generate some tones. And so I am going to generate a 440 Hertz tone. So
I am going to generate some tones. And so I am going to generate a 440 Hertz tone. So

that will be in one track. And then I am going to add another track down here and we are
that will be in one track. And then I am going to add another track down here and we are

going to generate another tone. So we will make this one slightly different. It is 444
going to generate another tone. So we will make this one slightly different. It is 444

Hertz. Like that. Now let me mute the bottom one and play the top. And now let me mute
Hertz. Like that. Now let me mute the bottom one and play the top. And now let me mute

the top and play the bottom. They sound almost the same. But let’s play them together now.
the top and play the bottom. They sound almost the same. But let’s play them together now.

So I will unmute them. So now you can hear those beats or those changes in the amplitude.
So I will unmute them. So now you can hear those beats or those changes in the amplitude.

Now let’s calculate what the frequency of the beats should be. So frequency of the beat
Now let’s calculate what the frequency of the beats should be. So frequency of the beat

is going to be f1 minus f2. And so what were the two frequencies? Well we had 440 and 444.
is going to be f1 minus f2. And so what were the two frequencies? Well we had 440 and 444.

And so if I put those two values in what is my frequency of the beat going to be? It is
And so if I put those two values in what is my frequency of the beat going to be? It is

simply going to be 4 Hertz. So now let’s check that with this model. And so what I
simply going to be 4 Hertz. So now let’s check that with this model. And so what I

am going to do is now mix these two together and we are making a single track of the two.
am going to do is now mix these two together and we are making a single track of the two.

And so let me get rid of those first two tracks. You can already see the beats. And now let’s
And so let me get rid of those first two tracks. You can already see the beats. And now let’s

check our numbers. So let’s look at 1 second in time. It is exactly 4 beats. The frequency
check our numbers. So let’s look at 1 second in time. It is exactly 4 beats. The frequency

of the beats equals the difference between the two frequencies. So did you learn to use
of the beats equals the difference between the two frequencies. So did you learn to use

a visual representation to explain how slightly different frequencies cause beats?
a visual representation to explain how slightly different frequencies cause beats?

I hope so. And I hope that was helpful.
I hope so. And I hope that was helpful.