###### By Robert M. Hazen, Ph.D., George Mason University

## James Maxwell’s four equations for the very first time provided a complete description of electromagnetism, and it also told us that light is a form of electromagnetism. But there’s more: the introduction to the concept of the electromagnetic wave, which had very profound consequences for science.

### Transferring Energy

The first law of thermodynamics states that waves provide a kind of energy. You can transfer energy from one place to another without moving mass. So, a wave in the surface of the ocean, or a sound wave, a sound traveling to you, a seismic wave in the earth—you’re not moving lots of mass, you’re just moving the energy through mass. Waves always transmit energy through a medium.

It could be solid, it could be liquid, it could be a gas. And for many decades scientists assumed that light also had to travel through a medium, a massless medium they called the ether. We now realize that electromagnetic waves can travel through absolute vacuum. It’s a strange concept, but that’s what light does, and we just sort of have to accept that that’s the way it behaves.

This is a transcript from the video seriesThe Joy of Science. Watch it now, on Wondrium.

### Describing Waves

In describing waves, we can use four different variables. The first is the wavelength. That’s just the length from one wave crest to another. You also have something called amplitude; that’s the height of the wave. A third variable is the frequency, and that’s how many beats per second you have. You could have fairly low frequencies, or you could have quite high frequencies, the number of beats per second.

The number of beats per second also in some cases is related to the length of the wave. This is true for light as well. And finally, you have the speed of the wave, the velocity of the wave. Those are the four variables of any wave: the length, the amplitude, the frequency, and the velocity.

Learn more about electromagnetism.

### Wave Variables

There’s a simple equation that relates three of these variables. Wavelength, velocity, and frequency are related as follows: Velocity is equal to the wavelength times the frequency (v = λf). In other words, velocity is in meters per second. That equals the length of each wave in meters times the number of waves that pass by each second. And we can do a simple calculation.

For example, imagine that you have a wave that’s two meters long, and it travels at six meters per second. Well, you can apply this equation. Velocity equals wavelength times frequency (v = λf). So, if you want to solve, for example, the frequency, frequency equals velocity divided by the wavelength (f = v/λ).

In this case, we know the velocity is six meters per second, the wavelength is two meters. So, the frequency then, six meters per second divided by two meters, is three cycles per second, three waves per second pass by. And you can manipulate this equation any way you want to make this kind of calculation.

### Applying Wave Theory

The basic concepts of how waves travel is easily applied to electromagnetic waves. First, the only restriction placed by Maxwell’s equation on the waves is that they travel at a fixed speed in a vacuum. That’s often referred to as the letter c. For example, in the famous Einstein equation E=mc^{2}, c is the speed of light—about 300,000 kilometers per second.

An important point about light is that its shorter wavelengths, that its higher frequencies, carry more energy per wave. The highest energy electromagnetic radiation therefore has the shortest wavelength.

### A Fixed Velocity

There’s no restriction on wavelength or on frequency. Know, however, that velocity for these waves is fixed. Wavelength and frequency then are dependent on each other. The wavelength is equal to the speed of light divided by frequency for electromagnetic waves. The frequency is equal to the speed of light divided by wavelength for electromagnetic waves. There’s an inverse relationship here.

Now, let’s understand the very special nature of the electromagnetic wave. Consider a single charged particle, produced by running a comb through your hair. The comb now has a charge. Think about what happens if you wiggle this comb. There are electric charges that are moving back and forth in space. And these electric charges exert a force on every other electrically charged object in the universe, including every electron that’s around.

Every electron everywhere—in the air, in solids, in your own body. The idea is that as the electrons in the comb are moved back and forth, they exert slightly varying forces on electrons in the air and other places, and these forces travel outward simply by the movement of charged particles that are affecting other charged particles all around.

Learn more about magnetism and static electricity.

### Self-Propagating Wave

This is really just a consequence of Coulomb’s law that says that every charged particle exerts a force on every other. Built into Maxwell’s equations is this interaction, and Maxwell discovered that the information that one electron wiggles travels to other electrons at the speed of 186,000 miles per second: that’s the speed of light.

Now think about the effect of an electron wiggling back and forth. That motion in effect is a tiny varying electric current, and a varying electric current also has to produce a magnetic field. But a varying magnetic field has to produce an electric current, so the mere process of wiggling an electron with a charge on it creates a magnetic field that creates an electric field, that creates a magnetic field simultaneously back and forth intertwined, and that’s this electromagnetic radiation that radiates out in all directions.

It’s not just an electric field, it’s not just a magnetic field, it’s intertwined. And these are like waves of light that travel out from every charged object that wiggles. That’s how you produce electromagnetic radiation; it is the complex intertwined electromagnetic wave traveling through everything around it.

### Common Questions about Electromagnetic Waves and Electromagnetic Radiation

**Q: What are the variables used to describe waves?**In describing waves, we can use four different variables: the length, the amplitude, the frequency, and the velocity.

**Q: How are wavelength, velocity, and frequency related?**Wavelength, velocity, and frequency of waves are related as follows: Velocity is equal to the wavelength times the frequency.

**Q: What is the only restriction placed by Maxwell’s equation on electromagnetic waves?**The only restriction placed by Maxwell’s equation on electromagnetic waves is that they travel at a fixed speed in a vacuum. This is the speed of light, of about 300,000 kilometers per second.

**Q: How is an electromagnetic wave created?**

An electron wiggling back and forth is a tiny varying electric current, and a varying electric current also has to produce a magnetic field, which has to produce an electric current, and so on. The mere process of wiggling an electron with a charge on it creates a magnetic field that creates an electric field, that creates a magnetic field simultaneously back and forth intertwined, and that’s electromagnetic radiation.