### Video Transcript

A wave is shown in the diagram. What is the wavelength of the wave
if its speed is 360 meters per second?

Okay, looking at this diagram, we
see a wave with the displacement of that wave plotted against time in seconds. We’re told that this wave has an
overall speed that is motion in the horizontal direction of 360 meters per
second. And based on this, plus the
information in our graph, we want to solve for the wave’s length.

Now, there’s a relationship that
ties together wavelength and wave speed, and it involves a third variable, wave
frequency. That relationship says that wave
speed 𝑠 is equal to wave frequency 𝑓 multiplied by wavelength 𝜆. In our case, though, it’s not wave
speed we want to solve for, but wavelength. So, let’s rearrange this equation
by dividing both sides by wave frequency.

When we do that, the frequency term
on the right-hand side cancels out and we see that the wavelength of the wave is
equal to the wave speed divided by the wave frequency. Since we’re given wave speed, we
want to solve for a wave frequency to ultimately figure out wavelength. Considering wave frequency, let’s
again take a look at our graph. If we start at the origin where the
wave’s displacement is zero, and zero time has elapsed. And then, we follow this wave along
through one complete cycle of the wave, we get to a time value of 0.5 seconds.

We can recall that wave frequency
is equal to the number of cycles a wave goes through as one second of time
elapses. So, as we’re seeing with this
particular wave, our wave frequency is equal to one cycle, since we go through one
cycle of the wave, in 0.5 seconds worth of time. And remember, we figured this out
by tracing out one complete cycle of our wave and seeing how much time it took to do
that.

Now, if we divide one by 0.5, then
that’s equal to two. So, we can write our wave frequency
as two cycles of the wave per second of time. And then, we can recall that one
hertz is defined as one cycle per second. Writing our wave frequency in terms
of this unit then, we would have two cycles per second, which is equal to two
hertz. This, then, is the value that we’ll
insert for 𝑓 in our equation to solve for wavelength 𝜆.

The wavelength of this wave then is
equal to the wave speed, 360 meters per second, divided by the wave frequency, two
hertz. And notice that if we replace the
units of hertz with units of inverse seconds, which is what a hertz is equivalent
to, then we have cancellation of the one-over-seconds unit in our numerator and
denominator. We’re left in the end with units
just of meters, units of distance, which is good since we’re calculating a
wavelength. And when we compute this fraction,
we find that it’s equal to 180 meters. That’s the wavelength of the
wave.