Wave Speed

Alright. Let's talk about wave speed. And especially its relationship to frequency and wave length. That's really the most important thing that you'll see in this types of problems in introductory Physics.

Alright. Now, the motion of a wave since the wave is just something that's created by a disturbance and then just propagates of its own volition through the medium, the motion of the wave depends only on the properties of the medium itself. And that means that its speed can depend only on the medium. But that doesn't mean that it's independent of the wave length and the period. It does depend on the wave length and the period. Just through the standard formula. Speed is equal to distance divided by time. Now if I've got a periodic wave that's propagating through a medium, how far does it go? Well, if I'm talking about one of the disturbances, then the distance is equal to the wave length. How long does it take? Well, if I'm talking about one of the disturbances, the time is equal to the period. And that means that speed equals wavelength divided by period.

Now we can write this in a form that's more commonly seen just by taking this factor of [IB] and remembering that one over the period is equal to the frequency. So that means speed equals wave length times frequency. This equation is extremely common. you'll see it all the time in this unit in Physics. Alright. So let's see what this means.

If I'm talking about waves propagating through the same medium, then the speed has got to be constant. That means that the wave length times the frequency is constant. So that means that if the wavelength goes up, the frequency got to go down. Conversely. If the wavelength goes down then the frequency will go up. So long wavelength waves have very very very small frequencies whereas short wavelength waves, also like very fast and they've got high frequencies. Alright. Let's see how we can use this idea to solve some problems.

Procedure's fairly simple but I wanted to illustrate a couple of the common mistakes that people make. Alright. So number one very straight forward, a wave has a wavelength of two centimeters and a frequency of 300 hertz. What's its speed? Well, v equal lambda f. So I'm going to say, well alright, well v equal lambda f. So lambda is 2 centimeters, f is 300 hertz. So when I multiply 2 by 300, I get 600 but now what's the unit? Alright, well, if I just do this directly it will be centimeters. Hertz is waves per second. So this will be per second. But of course that's not SI. What I really should do is I should absorb this 100 into the sente and write the answer as 6 meters per second. And if I do that, no problem at all. And if I don't remember to do that and it's a free response problem, I'm fine. So long as I wrote it as centimeters per second, it's not wrong. Totally right. But if it's a multiple choice problem, chances are the answer's going to be given like that and I got to be able to recognize that.

Alright. Problem 2. A wave propagates through a medium with a wavelength of 20 milimeters. So now I want to know what's the wavelength of a wave that has twice the frequency. Alright. Now. I don't know what the speed is here. So I really can't, I can't get the frequency. So but the thing is I don't need to. Because I know that wavelength times frequency is constant. So I'm multiplying the frequency by 2. So what does that mean about the wavelength? Well, if the product's constant and I got a 2 here, I got to have a half here. So I'm going to multiply the wavelength by a half and a half of 20, 10. So there it goes. Alright? Now the idea is I didn't have to have numbers for everything. Often problems are given in that way in units like this, and so you just have to know how to set it up. It's not difficult but you just have to know how to do it and it just takes some practice. Alright.

So let's look at the last one. A wave with a 21 milimetre wavelength moves into a medium with one third the wave speed. Alright. Now, something's going on here. We're not in the same medium anymore. Alright. Now, we got to keep something in mind when we go into a different medium. Frequency can't change neither can period. Everything else all bets are off, frequency and period got to remain the same. As long as it's the same wave, frequency and period are the same. Everything else can change, alright?

So, goes into a medium with one third the wave speed and I want to know the new wavelength. Alright. Here's the idea. Speed equals wavelength times frequency. We said frequency can't change, the speed went down by a factor of 3. The frequency is the same. Can't change. So what does that mean about the wavelength? It means the wavelength got to go down by a factor of three because the wavelength is allowed to change. So as soon as we recognize that, the problem becomes easy. 21 divided by 3 is 7. And we're done. But we need to understand that simple fact. Now I've seen a lot of problems that are written even easier than this where it will say, what's the new frequency? It will give us frequencies instead or does the frequency go up, go down or remain the same? The frequency got to remain the same, because frequency can't change. And as son as we recognize that and that this equation is always true, wavelength and speed got to do the same thing.

Alright. That's wave speed.