Hello everyone and welcome back. So in the last few videos, we saw how to find the direction of electromagnetic waves. But some problems like the one we're going to work out down below will ask us for the direction and also ask us to relate the speed of the waves with the magnitudes of the fields that make it up. So what I want to do in this video is I want to talk to you about the speed of electromagnetic waves, and I'm going to show you some very important equations you need to know to solve problems. Let's go ahead and take a look here.
Remember that all waves travel at certain speeds, and it really just depended on their type and also the environment that they travel through. For example, with mechanical waves, we had waves on strings, we also had ocean waves through water, and we had sound waves through air, and all of them had different speeds. So actually, what I first want to point out is the difference between mechanical and electromagnetic waves. Because mechanical waves did require a medium, they did require some type of material to travel through, right? So our waves on strings needed the string, you have to have that. Now, ocean waves require water to travel and sound waves require air to travel through. Without any air, there would be no sound. And that's different from electromagnetic waves because electromagnetic waves do not require a medium. For example, things like visible light from the sun or radio waves or even x-rays don't require a material to travel through. So basically, it means that these waves can freely travel through the vacuum of space. They don't need air or water or anything like that.
Now, let's move on here because for mechanical waves, the speed did depend on the properties of the medium itself. For example, with waves on strings, we saw this equation here. I'm not going to write it outright, which is the V string equation, which really just depended on the tension on the string divided by the mass and length of the string. So I'm just going to make up some numbers here really quick here. If I was ripping the string up and down with a tension of 10 Newtons, and let's say the speed of the wave was 5 meters per second, then if I flicked it harder and basically flicked it with a tension of 40 Newtons, let's say, then the wave speed would double. It would double to 10 meters per second.
Now, let's look at electromagnetic waves, because electromagnetic waves, the speed also does depend on the medium, but there's a very important distinction here. Which is that basically in your homeworks and your tests and things like that, most of your problems are going to involve electromagnetic waves that are traveling in a vacuum. So unless you are explicitly told otherwise, you can always assume that this is true. You can always assume that waves are traveling in a vacuum here. And that's really important because that means that the speed is going to be the same. In fact, we give this speed a letter, it's the letter c, and it is always equal to 3.0×108m/s. This is a universal constant, that is super important known as the speed of light in a vacuum. What it means is that all electromagnetic waves, whether it's visible light or x-rays or radio waves or whatever, they will always travel at this speed here as long as they are in a vacuum. So what that means is that this electromagnetic wave not only is traveling in this direction as we saw from the last video, but it's traveling with a speed equal to c, which is just 3×108m/s.
Now, before we get into our example, I have one last thing to show you, which is that this speed here is also related to the magnitudes of the electric and magnetic fields that make it up. And the equation for that is that c is equal to e divided by b. So in other words, what happens here is that the ratio of the field of the magnitude of the electric field to the magnetic field at any point is always equal to 'c'. This equation here is really important because basically what it means here is that if you have e divided by b, you should get 3×108m/s