[MUSIC]
Okay, right, we're gonna look now at the relationship between sound intensity and
sound pressure.
Intensity and pressure are two quantities that we use to assess sound.
Sound intensity, as we've learned in previous tutorials is watts per
meter squared, it's the amount of sound energy reaching the ear.
The other quantity that's important for sound is sound pressure.
And pressure basically is force per unit area, so
it's the amount of force that the sound is exerting on the eardrum per
meter squared of surface area of the eardrum.
There is a relationship between intensity and pressure.
The intensity is proportional to the pressure squared, okay?
So this is a relation between those two particular quantities.
And there is a relationship between intensity and
pressure in terms of equality.
The intensity is equal to the pressure squared,
divided by a parameter called rho times C.
Rho times C is called the acoustic impedance of the air.
So effectively, what we've got here is sound
traveling through the air to the ear, all right?
And it will actually be impeded as a result of the property and
the characteristics of the air.
Two important characteristics here is the density of the air, which is rho,
and that has a figure of about 1.2 kilograms per meter cubed.
And the parameter C is basically the velocity of sound in air and
that's typically around 340 meters per second.
So this figure here, or this product here of
rho times C is typically around 410, okay?
On the unit of combination of those units there.
The question arises now is what is the relationship
between sound intensity level and sound pressure level.
Is there a relationship between these two quantities?
If we know the intensity pressure squared over OC can we do anything about that?
Well let's first of all look at sound intensity level.
That's given by 10 log of I over I naught, okay?
We know that intensity is pressure squared over rho C.
So what we will do is substitute this relationship here into this formula here.
Also for eye note, eye note is remember is this reference value for
intensity and we can also write this, this P not squared over rho C.
So using the same arguments that we got here, we've just substituted
the reference intensity with a reference pressure there as well.
So you inserting this formula here and this formula here into this one.
We can therefore write it as formula that looks like this.
So in terms of intensity we have a pressure squared
over rho C divided by P not squared over rho C.
So that's the relationship that we've got.
So these two formulas into this one.
The rho Cs will cancel out which therefore leaves us with, sorry about this,
when you have to go this side here that leaves us with ten log of P over P not.
And is a square term in each of these terms here.
So we can take that square term and put it there.
So we've not changed the formulation here.
We've just taken the squared out and bracketed it all up.
Using the rules of logs we can take the two down to the front here so
it becomes 2 times 10 which is equal to 20, so
this gives you 20 log P over P not.
Now some of you will already recognize that,
that particular formula is the formula for sound pressure level.
So what we've actually shown, coming back to this opening statement we make,
what's the relationship between those two quantities,
we actually find that the relationship is that LI is actually equal to LP.
But bear in mind that this is only in terms of the decimal quantity okay?
Now that's a useful rule to remember, okay, because sound intensity levels,
sound pressure level are therefore interchangeable.
And that concludes that tutorial.