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Nothing like listening to the sound of ocean waves
to learn about the nature of waves.
Waves crashing onto the beach are obvious ones,
but we're just scratching the surface
of what waves are all about.
Think about it.
What are all the different waves you know?
Look up.
Light waves from the sun. That's another wave.
Sound waves from music, voices, laughter.
Waves move in a sine curve.
They have a defined harmonic rhythm.
So, the swinging of a pendulum,
the repeated up and down of a yo-yo or jumping rope,
are all examples of wave motion.
Waves even help us understand earthquakes.
More on that later.
To talk about waves, it's good to know certain key words.
Through the power of video, let's freeze a wave.
The crest is a wave's high point.
The trough is its low point.
To write a wavelength, you use the lambda symbol.
This is a lambda.
One wavelength is measured from the crest to crest,
or trough to trough.
On a graph, let's start from the point of origin
and go to where it touches the x-axis the third time.
That's also one wavelength.
Like ocean waves, other waves don't stand still either.
They move.
If you measure how many wavelengths
pass a certain point,
or count the number of crests that pass by per second,
that's its frequency.
A longer wave will have fewer crests,
which means a lower frequency compared to a shorter wave
moving at the same speed.
The period is the time it takes for a complete wave cycle
to happen from one crest to the next.
So, appropriately, period is written T.
One over a wave's frequency equals its period, T.
And one over period equals frequency, f.
They're reciprocal.
So,
What's the period for the Earth to go around the sun?
About 365 days, right?
And what is the period of the Earth's rotation
spinning around its axis one complete time?
About 24 hours.
If you think about all the different waves,
you can already figure out
there are a lot of factors
influencing the period of a wave.
Here's a wave you probably never realized.
Pendulums make waves, too.
If I move this pendulum,
the period of the wave is how long it takes
to go from one side to the other
and back to its original position.
In this case, the period is in seconds.
Now, if I swing it with a little more force,
the pendulum moves faster, over a longer distance.
So the period stays the same.
With a lighter tap, it moves more slowly,
over a shorter distance.
So, again, the period stays the same.
When the pendulum is at rest,
it's at its equilibrium.
The rhythm and motion varies
depending on the length of the pendulum.
Okay, if I shorten the string, what happens to the wave?
The periodic motion changes.
It swings more quickly, so a faster period.
If I add more length, it swings more slowly,
and the period is much longer.
The formula for the pendulum's period
is T, in seconds, equals two times pi
times the square root of the fraction length, L,
in meters, divided by the acceleration of gravity, g,
which is in meters per seconds square.
So, you can see, in this equation,
gravity affects the pendulum as well.
Gravity is always pulling the pendulum
back to its equilibrium.
The force of gravity on the pendulum
depends upon the pendulum's altitude
or its distance from the center of the earth.
For example, on the moon, gravity is much less,
which means the acceleration is slower,
and the period is much longer than it is on Earth.
By the way, if you add weight to the pendulum,
it doesn't change the period of its wave.
Weight is not a factor.
And some waves, like a pendulum,
have a rhythmic or harmonic motion,
which is a repetition of the wave with the same frequency.
So, think of a wave as a vibration,
a disturbance that moves through space,
and a wavelength shows a wave's complete cycle.
Looking at a wave on a graph,
the x-axis is the wave's equilibrium position
where its height is zero.
A cosine wave is the same as a sine wave,
except it's shifted.
The peak begins higher on the y-axis
instead of the midpoint, like a sine wave does.
The amplitude of a wave is measured from the x-axis
to the peak or crest,
or from the x-axis to the trough.
The distance from the resting point
or equilibrium position to the maximum or minimum intensity.
And, again, the period is the length of time
it takes for a wavelength to pass a point
or to complete a cycle.
And frequency is the number of those cycles
that pass a point in a second.
Most waves that we think about are mechanical waves,
which means they need a medium in which to travel.
Now, what's not a mechanical wave?
Electromagnetic waves, which include radio,
visible light, and x-rays.
They don't need a medium.
They can travel in the void of space just fine.
That's why we can see light from stars
and can pick up radio waves from them.
Now, how fast is a wave moving?
The speed of mechanical waves depends on the medium
they're traveling through.
Sound waves travel more than four times faster in water
than in air.
The velocity of a wave is written with the letter v,
and calculated by multiplying the wave's frequency,
small f, times the wavelength.
There are two ways waves can move.
Can you guess?
Longitudinally and transversely.
Longitudinal waves are compression waves.
They move in the same direction
as the force that creates them.
As these waves move,
they stretch and compress matter or particles in their path.
Here's an example.
When all the coils of this slinky
are equidistant from each other,
this slinky is at rest.
That's its equilibrium position.
Now, let's add a little force.
I'll push one end of the slinky.
Watch what happens to the coils
as the wave passes through.
The coils compress,
which means they get closer to each other
compared to when they were at rest, right?
And they get farther apart here.
Now, think of it like this.
Where they're farthest apart,
you can think that they are more rare
than in other parts of the slinky.
That's called rarefaction.
So, as I keep adding the same force...
with the same rhythmic beat,
the compressed coils move down the length of the slinky.
Check it out.
Compression.
We have created a longitudinal wave.
You'll see in other segments
that sound waves move like this, too.
So, what is the amplitude of these slinky longitudinal waves?
The amplitude is the distance
from the equilibrium position coils at rest
to the maximum or minimum intensity.
The second type of wave is a transverse wave,
which we can also show with a slinky.
They look like sine waves.
Okay, with what you know about waves,
let's go underground because with earthquakes,
you get both transverse and longitudinal waves
of varying magnitudes.
And you've seen the devastation they can cause.
These waves can pack a powerful punch.
When plates in the earth shift,
they create seismic waves.
They're what scientists monitor
to locate the epicenter of the earthquake.
Seismic waves come in two varieties, P and S waves.
P waves, where P stands for primary,
are longitudinal and move quickly through the earth.
S waves are secondary waves.
They're transverse waves.
They travel more slowly and can be very destructive.
Springs make waves, too.
Pull on a spring...
and you can see there's a harmonic action from rest
to bouncing down, and up, and down, and up.
Each spring has a different ability to restore itself.
To bounce back to its equilibrium position.
That's called the spring constant.
The force required to pull the spring
away from its rest position is given by the equation
F equals negative k times x,
where F is the force, k is the spring constant,
and x is the displacement from the rest position.
The negative sign is there
because the force opposes the motion of the spring
getting back to its rest position.
The potential energy of the spring at rest is zero,
but the potential energy of a stretched spring
is one half kx squared.
Here's how to figure out the energy in a spring
that oscillates and has a wavelike motion.
You should know the spring constant,
which describes how stiff or strong the spring is.
The higher the spring constant,
the more force it takes to stretch or compress it.
Every spring has a spring constant,
and it's not always the same for every spring.
Springs are different
because they do not apply constant forces.
The more a spring is stretched,
the greater the force pulls back on you.
So, are you getting the gist of all this wave action?
Just look around you,
and you'll see that waves are everywhere.
Just dive right in.
For more practice problems, lab activities,
and note-taking guides,
check out the "Physics in Motion" toolkit.