In our discussion of periodic motion,
we first introduced sound and the basic sound properties
and how to measure those properties and how they're discussed.
We're ready to move now to sound dynamics.
The first thing we'll discuss with the sound dynamics
is the idea of a beat frequency.
A beat frequency arises when we have two different waves of sound
or two waves of any kind really and we're adding them together.
So what happens if both of these waves,
maybe one of a different frequency than another,
maybe they have different amplitudes than another,
maybe they're two different instruments playing at the same time.
What happens to the frequency if we add these two waves together?
In other words, as these pressure waves are moving through the air.
How do they interact with each other
and what is the result that we end up hearing?
First of all, just mathematically,
if we were plotting waves like these two.
The way you would add them
is very simply to add them as you might expect.
You might take at a particular point,
like where we have these dots lined up here.
At a particular point on the x-axis,
you can see the amplitude of these waves.
To add the waves, you just add those two amplitudes
and so for this point, for example, we could take these two positions,
add them up and we get something a little bit bigger
than either one of those positions.
What we do if we have two different waves,
maybe these two top points as we have listed here is
if we add them point by point going along the wave
in a way I just described.
In some places the waves will both be positive
and they will add constructively,
and by constructive interference,
we mean that they're both going in the same direction
and in other places because they're oscillating at different frequencies,
they will be destructive.
In other words, one might be positive and one might be negative
and they will cancel each other out.
We call that destructive interference.
By putting these two together,
the constructive interference from when they're adding constructively
and the destructive interference from when they're adding negatively.
We get these different beats as we call them
and you can see this in the bottom graph here.
So the different beats of the wave
correspond to the times when they become constructive
and then the times they become destructive reaching these antinodes.
So you can see their constructive waves
create this positive amplitude beats.
The destructive waves create this zero points.
And now aside from these two independent and different waves,
we now have a third wave which has its own frequency just in its amplitude.
So you see the envelope of this wave.
So the total shape if you will of the overall green wave as it's going up
and then down and then up and down,
inside with this, this would correspond to its getting louder and then quieter
and then louder and quieter and we call this a beat frequency.
The beat frequency which is the frequency
with which this bigger amplitudes occur,
is the difference between the two frequencies that you were adding together.
So if these two upper waves that we've drawn,
these two upper sound waves had frequencies f1 and f2.
The frequency of the beats would be the difference between those
and because we don't want negative frequency,
we're just talking about the actual frequency difference between the two.
We also take the absolute value as you can see here.
This phenomenon is actually used,
for example by anybody playing an instrument,
if they're trying to tune, for example, a violin.
If they want two strings to sound exactly the same.
They could make sure that they're playing them the same
and they play it and then they,
if those frequencies are different they will hear a beat frequency.
The sort of oscillation, this louder and quieter, louder and quieter
and they can tune until that beat frequency goes away
and so there's a very physical basis for this
that you can very readily imagine.
Two frequencies may be played by two instruments
or may be two strings on the same instrument,
creating this louder and quieter phenomenon
which again will have a frequency of the difference between
the frequencies of the two different things being played.