Let's do a quick example using the wave velocity
that we just introduced as an important equation.
Suppose we had light and we know that light's velocity is a number called the c.
And we'll talk a little bit more about light in particular later.
But this number c is equal to 3 times 10 to the 8th meters per second.
So obviously a very fast speed.
If we have a particular wave of light with a particular frequency of 500 nanometers,
can we find the frequency of the light using our wave velocity equation?
So go ahead and give this a try
and see if you can find the wave velocity if you, or sorry,
the frequency of this light if you know the wave velocity
as well as the wave frequency.
We're gonna do that here as well.
It should look something like this.
This isn't too long a problem
because all we have to do is recognize that the wave velocity
is equal to the wavelength times the frequency.
Since in this problem what we're solving for is the frequency of our wave,
all we need to do is rearrange.
We have frequency equals velocity divided by wavelength
and then all we have to do is plugin these two properties,
the velocity of the wave and the wavelength.
The velocity and the speed of light is this number c
that's given to us in this problem and then the wavelength is also given to us.
So let's put in the numbers, we have 3 times 10 to the 8th meters per second
divided by and here's where we have to be careful.
We have 500 nanometers but a nanometer is 10 to the minus 9th meters
and we have to always watch these units.
So we want meters down here because we have meters up here
and if we want units of frequency,
we're going to need units of 1 over seconds
and that's what we'll have here when we finish.
So this is just 3 divided by 500
and then we'll do our unit analysis of, or sorry,
the powers of 10 analysis, the scientific notation analysis separately.
We have a minus 9 down here.
So putting it up here we have a 9 plus 8th,
which is times 10 to the 17th and since again,
we make sure our units cancelled properly.
This is units of 1 over seconds.
So careful this isn't 1 over 5 or anything this is an s.
So we just have to simplify this.
So this is 3 over 5 times 10 to the 15th
and 1 over seconds is our unit of hertz.
So we can maybe rewrite this one more time
as 0.6 times 10 to the 15th hertz.
Now we need to be careful with our notation here
because this is often represented in a completely different way.
First of all, with scientific notation we would move the decimal place
over one more time anyways but often when it comes to light,
you'll see things written this way.
I could write 600 and then instead of times 10 to the 12th
which would be the number of powers of 10 we would need if wrote 600.
We could use that 10 to the 12th as a terahertz.
So this abbreviation T,
this stands for tera and we talked about some of these prefixes
and especially when we're talking about things
like light with very, very high frequencies you might run into numbers
like these with very, very big prefixes.
So be aware of that as we go forward.
So this is a very simple example of how you could use the wave velocity equation
that we just introduced and compare the wave frequency with wavelength,
with the wave speed.
In some cases, you'll know the speed which we do in this case
and you'll have to compare the wavelength and the frequency.
In other cases, there'll be different variables that you'll know.
So maybe you might have to solve for the velocity or do something else.
So be aware of what you're looking for
as you're using the wave velocity equation,
but this is a good basic example.