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Frequency - Period

Teacher/Instructor Jonathan Osbourne
Jonathan Osbourne

PhD., University of Maryland
Published author

Jonathan is a published author and recently completed a book on physics and applied mathematics.

The frequency of a wave measures how often it passes a given point in a given length of time. A wave's period measures how long it takes for a wave to pass a given point in its entirety, from crest to crest. Frequency and period are basically measuring the same characteristic of a wave and can be related by the equation period = 1 / frequency. The frequency and periods of electromagnetic waves do not change and can be used to identify different types of waves.

Alright. Let's talk about frequency and period of a wave. Frequency and period are properties of periodic waves, kind of why they're called periodic waves, and so frequency is the number of waves that pass a given point in a certain amount of time. As you remember a periodic wave is a wave that hits again and again and again repeatedly and so the frequency characterizes how many times does it assault the medium in a given amount of time.

Period is kind of, kind of the opposite of that in some sense. It's how long does it take for one wave to assault the medium. Alright. So we've got a real simple way of thinking about period. So imagine that you're out in the ocean. Alright, you're on a boat in the ocean and you come to the crest of a wave. The period is how long it takes for you to go down and come back up to the next crest. So it's a real simple way of understanding what period means.

Alright. So let's go ahead and just do an example with frequency. Suppose that the frequency is 3 waves per second. And of course that makes sense if frequency's how many waves come in a given amount of time, then 3 waves per second would indicate that in one second, 3 waves come. Alright. We don't usually use waves per second as a unit, instead we use the unit hertz, which is named for our physicist who was actually the first guy to represent electromagnetic waves in 1887. Alright.

So we could say the frequency is 3 hertz. So what's the period? Well, let's see. If 3 waves come every second then how long does each wave take? Well, 3 waves per second, each one's going to take a third of a second. So that gives us actually a very very very general relationship between frequency and period. Frequency is equal to one over period. That is always true. It follows directly from the definitions of these quantities and that's always nice because that means I can always write it down and it will never be wrong. Alright.

So let's go ahead and look at some properties that are associated with this realtionship. Frequency times period equals one. So what that means is that if I increase the frequency, well jeez, that number's getting bigger, but the product got to stay the same, so the period's got to go down. So bigger frequency, smaller period. Conversely, smaller frequency, bigger period. Alright? Another thing that I've seen a lot of the tests ask, if I double the frequency what happens to the period? Well, that's really easy, because I've got a 2 here, doubling the frequency, but I need the product to remain the same. So I got to put a one half there. So if I double the frequency, I cut the period in half. Conversely, if I cut the frequency in half I double the period. Real real real simple but sometimes students don't notice how that goes and how easy it is until they've seen an example.

Alright. One other important property about frequency and period which will come up a lot later on in later studies of periodic waves is that period and frequncy can't change. And that's actually the wonderful thing about period and frequency. Because other properties of the wave will change. If I go like if I've got light coming in and it hits a piece of glass, a lot of its properties will change but its frequency and period can't. Why? Well, it's real simple. If you got 3 waves coming in per second, you got to have 3 waves going out per second. Because otherwise the waves are going to congregate at the boundary and the boundary can't take that. So frequency and period can be used to characterize a wave as it travels through whatever it's going to travel through. No matter what happens to it, frequency and period remain the same. And that's frequency and period.