Hi. It’s Mr. Andersen and this is AP Physics essentials video 107. It is on wave speed.
If you spend any time in a thunderstorm you know that the light reaches you much quicker
than the sound does. And so if it is far away there will be a big gap in those two waves
arrival time. But as it gets closer and closer and closer, the time between those two waves
arriving, the lightning and then the thunder is going to get closer and closer and closer.
Okay, that was pretty close. And so waves transfer energy through oscillations. Since
we are talking about wave speed, what is the speed remember it is a distance we travel
over a given period of time. Now how do we measure distance when it comes to waves? That
is going to be the wavelength or lambda. How do we measure time when it comes to waves?
That is going to the period. So if we simply divide the wavelength by the period, we now
have calculated the wave speed. Now the wave speed is going to depend on the medium. In
other words what it is in. For example sound is going to go much faster in water than it
does in air. So the medium determines that. But there is an established relationship between
the velocity of the wave and then the lambda divided by time or the lambda divided by the
period. Now lots of times since the frequency is the reciprocal of the period of time, and
so instead of being written like that it will be written like this, v equals lambda f. In
other words the velocity or the speed of the wave is lambda or the wavelength times the
frequency. And so let’s take a look at that wave speed for a second. And so we will just
do this qualitatively. So what I am going to do is start some waves in this simulation.
And then I am going to play around with the tension. And watch what happens as I make
it less tense and then more tense. I could also affect how much of it is being dampened
by the medium itself. And so you can see that I can play around with the medium itself and
I can vary the speed of the waves. So let’s just look at one for a second. So we are going
to keep that tension the same, but we are sending one wave down. And we will stop it
right when it gets to 6 centimeters. And so now we have watched the wave move. So we are
going to try to calculate wave speed in a couple of different ways. So it has moved
a set distance from here to here. And again I had the clock running. So it took 1.6 seconds
for it to make it there. And so if I want to figure out its wave speed one way to do
it is to simply measure distance divided by time. So what is the distance? In this case
we moved 0.060 meters per 1.6 seconds. You can see I converted that to meters. And so
what is going to be the wave speed just watching the wave go? It is going to be around 0.038
meters per second. Now we also know that you could calculate it in a different way. And
so velocity equals lambda times frequency. And so we could calculate lambda. Lambda is
going to be the wavelength. So let’s figure out what the wavelength is. So from here to
here it is 1, 2, like 2.5 centimeters. And also on this simulation it is telling us what
the frequency is. And so if I know the frequency and I know the wavelength, I know the velocity.
And let’s make sure that that matches. So my wavelength is 0.025 meters. My frequency
is 1.5 hertz. And so it is going to be 0.038 meters per second. So same thing. We could
then try to change the make-up of the material or the matter through which the wave is moving.
So let’s start it now. So we have increased tension. So it went faster. You can see the
time is less. So it is 0.96 seconds. So we could calculate the distance we moved, again
that is 0.060 meters per 0.96 seconds. So that is one way. So we could get a velocity
that is fast. It is much faster than it was before. So as we increase tension we increase
the speed. But we could also use V equals lambda F. And so what is our lambda? What
is our wavelength? It is going to be that distance. And what is our frequency, 1.5.
And so we could say it is going to be the same value. And so those are two ways we could
calculate the speed of the wave. Now what happens if we totally decrease the tension?
There is no tension inside there? Oh, you can see that it is going really, really slow.
And so I am not going to keep going because this one would take forever. And so as we
increase the tension inside the material you can see we are increasing the speed. So here
is some speed of sound. So this is in air, 331 meters per second. In water it is much
faster. And in steel, if you were to just hit steel and then listen to it really far
down it is going to way faster then it would inside the air itself. Now let’s say we
keep the medium the same. Let’s say we keep the tension in everything the same, what is
going to be the relationship between the wavelength and the frequency of the wave. And so let’s
just start it going. And what I am going to do is vary the frequency. And so as I increase
frequency, what happens to the wavelength? You can see it decreases. As I now decrease
frequency what is happening to the wavelength? No you can see the wavelength is increasing.
So again the medium determines the speed of the wave. But then there is this relationship
between the wavelength and the frequency. Lots of times you will be given problems like
this. So for example we are given this picture. You can see the distance between the waves
is 23 meters. We know the velocity of the waves is 2.8 meters per second. So could you
calculate the wave frequency? So here is my equation. So V equals lambda f. I plug in
what I know. In this case I know the velocity and I know the wavelength. And I could solve
for a frequency of 0.12 hertz. Or you could try this problem. Now I am giving you the
period. Let’s say it is 3.5 seconds you are watching it. And that is how much time
it takes for the boat to move up and down. And you could also measure the wavelength.
And so could you calculate wave speed? Well give it a try. And then include your answer
in the video description down below. And so did you learn to design an experiment to determine
the relationship between the wave speed, the wave length, the frequency and relate those
to everyday examples, like lightning? I hope so. And I hope that was helpful.