### Video Transcript

Which of the following formulas correctly shows the relation between the frequency, the speed, and the wavelength π of a wave? Number one: π is equal to π over π. Number two: π is equal to π minus π. Number three: π is equal to π plus π. Number four: π is equal to π over π. And number five: π is equal to ππ.

Now this is an important equation to remember. We need to memorize this. So what weβll go through in this video is the answer. And then a way of checking that weβve got it right. So first of all, the answer: itβs number five. π is equal to ππ. Obviously, this is something we need to know. But there is a way of checking it, like we mentioned earlier.

What we can do is use something known as dimensional analysis. Basically, what it means is to compare the units of each thing on the left-hand side to the units of everything on the right-hand side. And the idea is, is because weβve got an equation, thereβs an equal sign in it, then the units of the left-hand side must be equal to the units on the right-hand side because the two things are equal. So carry on watching if youβre feeling a bit brave.

Letβs start with the left-hand side. Weβve got speed π. We can recall that speed is defined as a distance divided by time. Itβs basically the amount of distance travelled in a unit of time. And we can look at the units of distance and time. We know that distance is measured in meters. And time is measured in seconds. So the units of speed are meters per second.

Next, letβs look at π, the wavelength. Well, π is a wavelength. It measures a distance. Therefore, it has units of meters.

And finally, letβs go on to frequency. Now this one is a bit more tricky because frequency is usually measured in hertz. But we can also recall that frequency is defined as one divided by the time period of a wave. This time period is defined as the time taken for an entire cycle of a wave to travel past one point in space. Basically, thereβs a wave travelling to the right. And imagine that weβre standing here. Well, the time period is how long itβll take an entire cycle, thatβs all of this until this point here, to travel past where weβre standing. Or, in other words, how long it takes for this point to get to where weβre standing. But remember, we donβt have to start on the peak of a wave. We could always start on the trough, or anywhere else on the way for that matter.

So the time period of the wave is however long it takes the next adjacent, equivalent point, which is this trough here in this case, to travel to where weβre standing. And frequency is simply one divided by this time period. So for frequency, weβve got one divided by the units of time which happens to be one divided by seconds.

Now, if we take our final answer, π is equal to ππ , then we can compare the units. On the left-hand side, weβve got the units of speed which happens to be meters per second. And on the right-hand side, weβve got frequency which is one divided by seconds multiplied by π which happens to be meters. And of course, the right-hand side simplifies slightly to give us meters per second. Therefore, the units on both sides of the equation are equal. And our final answer is: π is equal to ππ.