Waves: A Few Explanations and Orders of Magnitude

by | May 13, 2019

At the dawn of a hyperconnected twenty-first century, the impression of being permanently subjected to emissions generated by a multitude of electronic devices is legitimate, as is feeling a certain level of anxiety as a result. Although no firm consensus has yet been reached regarding how dangerous these waves really are, their physical characteristics have been the object of extensive research by scientists for more than a century. The following article  does not intend to demonstrate that waves are harmless, since that debate lies beyond the scope of physics. Its sole purpose is to demystify the theory of waves, particularly electromagnetic waves that are used in most telecommunication technologies, in order to allow its readers to better understand the effect of those waves on their daily lives.

This article was written by Marie Chupeau (PhD in physics and Data Scientist at Magic LEMP).
We are very grateful for her contribution.

1) What is a wave?

 

Let us start by broadly defining what a wave is. A wave is a disturbance that propagates through matter or space? The nature of any given wave may vary greatly. In the case of water waves (oceans or ripples caused by a stone falling in a body of water), the disturbance is the water elevation, which alternates between crests and troughs. In the case of a string instrument, the disturbance is the distance between the stretched string and its position of rest. When football supporters create a stadium wave, the disturbance is simply the fact that they raise their arms. For a sound, whatever its source, the disturbance is the local compression of air. For a seismic wave, the disturbance is the local compression of the earth’s surface and its subsoil. Finally, in the case of light, the disturbance is an electromagnetic field, that is to say the ability to set in motion electrically charged objects. We will explore these types of waves in greater detail in section II.

Wave propagation is simply the way the disturbance travels from the source of the wave at a certain speed, which depends on the type of wave (from a few meters per second for a stadium wave, or 300 meters per second for sound moving through air, to 300,000 kilometers per second for light). When a lamp is turned on, the light is instantly visible (in 10 billionths of a second!) from the other end of the room because light moves extremely fast. On the other hand, the sound emitted by a timbale from the back of the orchestra will take 50 milliseconds to reach the conductor, standing about fifteen meters away. This time lapse is perfectly audible, which is why musicians farther back are traditionally asked to play slightly ahead of the beat.

Waves can take different forms, but the most basic is the sine wave depicted below. The sine wave alternates between crests and troughs, similarly to ocean waves.

 The sine wave is defined by two fundamental parameters: its wavelength, meaning the distance between consecutive crests, and its frequency, meaning the number of crests that pass a fixed point in a given amount of time. These two variables are not independent as their product is equal to the wave propagation speed. The higher the frequency, the shorter the wavelength, and vice versa.

2) What is an electromagnetic wave?

 

Let us now dive into the main subject of this article – electromagnetic waves. These types of waves are trickier to understand than other waves mentioned above, such as sound or water waves, since the propagated disturbance is mostly invisible to the naked eye. Indeed, we are only able to perceive a tiny fraction of these waves, which we know as visible light.

The range of frequencies and wavelengths of electromagnetic waves is represented in the following spectrum. Electromagnetic radiation visible to the human eye is represented by the rainbow on the bottom axis.

If we can only see a tiny fraction of all known waves, what other types of waves make up the rest of the electromagnetic radiation spectrum? The slideshow below gives a brief overview of the different types of electromagnetic waves.

Gamma rays

Gamma rays are not common on Earth as they are mostly absorbed by the atmosphere, and are used in advanced imaging technologies. Gamma rays are the form of electromagnetic radiation with the highest frequencies.

X-rays

X-rays are also absorbed by the Earth’s atmosphere. They are commonly used in radiography.

Ultraviolet

Ultraviolet radiation is almost completely blocked by the Earth’s atmosphere. It is nevertheless responsible for skin tans.

The Visible Spectrum

Visible light mostly passes through the Earth’s atmosphere unhindered. It is essential to life on Earth, particularly via the process of photosynthesis.

Infrared

Infrared radiation is moderately absorbed by the Earth’s atmosphere. This type of radiation is used in numerous technologies, such as thermal cameras, vitroceramic stove tops, remote controls, etc.

Microwaves

Partly blocked by the Earth’s atmosphere, microwaves are located between infrared and radio waves on the electromagnetic spectrum. They are used in the eponymous microwave oven.

Radio waves

A large range of radio wave frequencies are not absorbed by the Earth’s atmosphere, and they are extensively used in telecommunication technologies.

3) It’s all a question of energy

 

Another type of parameter that is primordial for understanding electromagnetic waves is energy, or power (energy per unit of time). Both energy and power are directly related to the amplitude of the wave. Using the previous example of the water wave, the amplitude corresponds to the distance between the crests and the troughs of the wave. The larger the amplitude, the more energy and power a wave has.

However, a wave cannot be solely characterized by measuring its power; indeed, a measurement of its frequency is also necessary. In fact, the higher the frequency (or inversely, the smaller its wavelength), the more energy each basic grain of light – or photon – will carry. So the higher the photon’s frequency, the higher its energy. In the spectrum shown above, you can see that gamma rays are the most energetic forms of electromagnetic waves, whereas radio waves are the least energetic.

Let’s look at a naïve example that illustrates the importance of the subtlety between total energy and elementary energy. Imagine that you are being thrown, continuously and at a given speed, one ping pong ball per second. This stream of ping pong balls has a certain power value. Now let’s spread this power differently by throwing tennis balls, again continuously and at the same speed as before. Since a tennis ball weighs about fifteen times more than a ping pong ball, it will have to be thrown fifteen times less often to retain the same power value, that is to say once every fifteen seconds.
After a minute, you will have received the same amount of energy from these two streams of balls, since they will have the same power value, but it doesn’t take much to imagine that receiving a ping pong ball every second and a tennis ball every fifteen seconds will not feel the same at all!

4) What happens to an electromagnetic wave as it propagates?

 

Unless it is being channeled, a wave, irrespective of its nature, will weaken as it propagates. The vast majority of the time, electromagnetic waves propagate all around their source and their amplitude therefore decreases as the distance from the source increases. For example, think of the ripple that is formed when a stone falls into a body of water. The height of those small waves decreases the further they travel from the point of impact.

Likewise, the greater the distance between yourself and someone you are trying to communicate with, the louder you will have to speak for them to hear you. This is because the distance has weakened the sound of your voice. The same goes for light. You may be blinded by a candle flame if you look at it from very up close, but not if you are standing one meter away. This attenuation, which is called geometric, depends solely on the wave’s propagation, and not on its nature, power or frequency. As an indication, a wave located one meter from its source sees its power attenuated by a factor of about twelve. Once it reaches a distance of two meters, its power will have been attenuated by a factor of fifty, and so on. This attenuation factor increases exponentially with distance, and it explains why using headphones when talking on the telephone will greatly reduce wave exposure compared to holding the phone to one’s ear.

Another factor that causes the attenuation of a wave’s amplitude is when it passes through a medium that absorbs it. For example, as mentioned above, the Earth’s atmosphere absorbs a significant proportion of radiation coming from space. Another example would be that there is often no network reception in underground car parks.

5) What generates electromagnetic waves?

 

The answer may surprise you: absolutely everything that surrounds us emits electromagnetic radiation. Every object emits a radiation which depends first and foremost on its temperature. The higher the temperature, the lower the wavelength at peak emission.

This is a process that you will already be familiar with – think, for example, of a piece of iron that is being heated in a flame. It turns from a dull gray at room temperature, to glowing red and yellow as its temperature gradually rises, before finally turning bright white. At room temperature, a body will mostly emit radiation in the infrared region of the spectrum, which is invisible to the naked eye but visible on an infrared camera. As its temperature rises, the body’s emissions will move towards the smaller wavelengths, eventually reaching the visible range.

There are other mechanisms for emitting electromagnetic radiation, such as those found in radio antennas. However, thermal radiation (which depends on a body’s temperature) has the effect of bathing us in a continuous halo of electromagnetic radiation. Do you enjoy the heat of the sun warming your body? Or the look of your tanned skin? Have you ever felt the heat radiating off another person’s body without actually touching them? All of these phenomena are caused by natural electromagnetic radiation emitted either by the sun or by another living being.

6) Orders of magnitude

 

Orders of magnitude help us compare the differences in energies generated by electromagnetic radiation that surrounds us, whether natural or artificial.

  • The primary source of electromagnetic radiation in our lives is, of course, the sun. After being filtered through the Earth’s atmosphere, the energy generated by solar radiation reaches ​​about 500 W/m2.
  • Next in line is the human body, whose surface temperature is about 68°F and emits around 450 W/m2 from a very close distance.
  • Finally, let’s have a look at the radiation emitted by iPads and other similar devices (see the following document for more detailed information). According to the manufacturer’s website, the specific absorption rate (SAR; the rate at which the body absorbs radiant energy) does not exceed 1 W/kg, or about 100 W/m2, across all its products. This is significantly less than solar radiation or radiation generated by all surrounding objects at room temperature.

In addition, this technical documentation explicitly states that SAR is tested for use against the body. However, as explained in section IV, a freely propagating electromagnetic wave attenuates as it moves further away from its source. Therefore, if an iPad is placed on a desk about one meter away, the radiant energy absorbed by the body will be ten times less than having the device used against the body.

 

To sum up, we first saw any mention of the general term “waves” in relation to the field of telecommunications actually refers to electromagnetic waves. These electromagnetic waves are mostly invisible to the naked eye, except if they are on the visible spectrum. We also learned that light and radiofrequency waves share the same nature, even though the properties of electromagnetic waves depend on their frequency.

Any heated body (including at room temperature) emits electromagnetic waves, with the sun being the primary source of electromagnetic radiation on Earth. Even a human body emits more radiation than an iPad at full power.

The distance from the source of the electromagnetic wave has a strong impact on the radiant power that is received. By moving even one meter away from the source (for example by placing an iPad on a holder), the radiant power will decrease by about 12 times compared to direct contact with the source. It should also be noted that even when in direct contact with an iPad, the radiant power that is received is still lower than the regulatory limits for power emissions.

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