# How can I simply define electromagnetic waves

## Electromagnetic waves

In this post you can find out what **electromagnetic waves** are what use they have and get to know important formulas.

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### Electromagnetic waves explained simply

The name **Electromagnetic waves** has two components, "electromagnetic" and "waves". With "waves" you are given the indication that something periodically oscillates up and down. The addition "electromagnetic" tells you that this "something" is electrical and magnetic fields.

So this means that electromagnetic waves (also **electromagnetic radiation **called) describe the periodic swings up and down of electric and magnetic fields. The fields do not oscillate up and down arbitrarily, but are coupled with each other so that the electric field is perpendicular to the magnetic field.

The reason you can see something is because of electromagnetic waves (in the form of light). The reason you can talk on the phone is because of electromagnetic waves (in the form of microwaves). The reason that you can surf the Internet is because of electromagnetic waves (also in the form of microwaves or in the form of radio waves). So you see that electromagnetic waves are essential for our life.

### What are electromagnetic waves?

In this section we will first explain to you what you can imagine by a wave in general and how it is characterized. We then combine this knowledge with electric and magnetic fields to explain electromagnetic waves and their properties.

### Waves in general

When you think of waves, you are probably imagining something swinging up and down. In the case of a rope wave, for example, this is the rope, in the case of water waves, the water. The wave does not swing up and down arbitrarily, but with a very specific pattern. So if you take a photo of a water wave and then wait a certain time to take another photo of the wave, the two pictures will look almost identical. The difference is that the pattern moved in the time interval between the first and second photo. Instead of "pattern" you will often find the term "**Disorder**„.

Under one **wave** you can imagine a disturbance in a medium moving with a fixed shape and constant speed.

The interested reader will find a mathematical description of this definition at the end of the article.

### Electric and magnetic field

So a wave is a kind of disturbance that propagates with a solid shape. In electromagnetic waves, this disturbance consists of electric and magnetic fields. The emphasis here is on "and". You cannot have an electromagnetic wave where only the electric field swings up and down, but the magnetic field remains unchanged and vice versa. This is where the term "electromagnetic" comes from.

You can do that under an electromagnetic wave **periodic interaction** from electrical **and** understand magnetic fields.

Do you notice how the term "medium" does not appear in this definition while it did in the definition of a general wave? This is due to one of the most distinctive properties of electromagnetic waves, which we will explain to you in the next subsection.

### Electromagnetic waves properties

There are a number of properties that electromagnetic waves have. In this subsection we list the most important properties and what they mean.

**Propagation medium:**While rope waves or water waves need a medium in order to be able to propagate, electromagnetic waves can also propagate in a vacuum. Electromagnetic waves can not only propagate in a vacuum, but also in gases such as air, in liquids such as water or in solids such as glass fibers. This variety of propagation media makes it possible to use electromagnetic waves for many technological and non-technological applications.**Propagation speed:**Electromagnetic waves propagate in a vacuum at a speed of about out. That is also the speed with which light travels. This finding was a first indication that light is electromagnetic radiation.**Type of propagation:**If you looked in the direction of the electromagnetic wave and could see, for example, the oscillation of the electric field, you would find that the electric field oscillates perpendicular to the direction in which the wave propagates. Electromagnetic waves are therefore**Transverse waves**. Due to this property, electromagnetic radiation can be polarized. The magnetic field is always perpendicular to the electric field.**Colour:**Every electromagnetic wave has a wavelength. The wavelength and frequency of the wave can be transformed into one another (see next section). A certain color corresponds to a certain wavelength (therefore also to a certain frequency). This relationship between wavelength and color is illustrated by the**electromagnetic spectrum**illustrated.

### Electromagnetic waves formulas and conversion

In this section we will show you how you can convert between the values of wavelength, frequency and energy of an electromagnetic wave.

### Wavelength-frequency and energy-frequency relation

If we use the wavelength and the frequency with , then applies

.

Here is the speed of light. This relationship also applies to waves that are not involved but with speed spread. The wavelength gives you that **spatial distance** between two wave crests or wave troughs. The reciprocal of the frequency gives you that **time interval** between two wave crests or wave troughs. Therefore the wavelength has the unit meter and the frequency is the unit .

Between the energy the wave and its frequency the relationship applies

,

in which is Planck's quantum of action.

If we take the first relation and transform it to the frequency, we get

.

Let us now replace the frequency in the second relation by , we get

.

### conversion

This connects all three sizes. So if you have given one of the three sizes, you can work out the other two. For example, if you know the wavelength, you can use the formula

calculate the frequency and use the formula

the energy.

With such transformations, always make sure that the units fit. Energy has the unit joule (), so we expect the combination also has the unit joule. The has the unit , the wavelength the unit and Plank's quantum of action is unity . The expression thus owns the unity

,

as requested.

### Supplement: mathematical description of a wave

The **Strength of the disorder** (in the case of a water wave or a rope wave, this corresponds to the deflection of the particles) at a certain point depends both on the point itself and on the time. For example, if you take the first photo of the water wave, the time is constant, but the displacement of the water particles changes as you move along the photo. Similarly, if you stand and wait at a certain point, the displacement changes. As a function, therefore, the magnitude of the disturbance is a function of location and time

.

Let us name the pattern of the wave . For every point in time is a function of the location . At the time the disturbance has exactly the shape of the pattern , that is, it applies

.

Let us assume that the wave moves with the speed of propagation spreads to the right. After a time will then move each point along the pattern around the track have moved to the right. Mathematically, there will be a shift to the right along the -Axis represented by a subtraction. The disorder at a time therefore has the following form

.

The subtraction is the mathematical notation for having all points along the pattern around the track moved to the right. The following picture is intended to illustrate this idea.

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