ElectroMagnetic Waves

Copyright © Karl Dahlke, 2023

Take a magnet in your hand and move it back and forth once per second. This sends out an invisible electromagnetic wave, also called an em wave, with a frequency of 1 hertz, 1 Hz, one oscillation per second. You can't see this wave, but you can detect it, if you have another magnet in your house. (This experiment is well worth performing if you have two magnets at hand.) Call the first magnet A, the magnet you are moving back and forth with your hand. Call the second magnet B, and hold it a few centimeters from A. You will feel A tugging on B, back and forth back and forth, at a frequency of 1 hertz. You may allow B to move, under the influence of A, or you may hold B steady, but either way, you can feel the wave. Hold the magnets farther apart and you can still feel the wave, though it is weaker, just as sound, heat, light, or any other force weakens with distance.

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If you don't have a second magnet in the house, any object made of iron or steel will do. A metal bolt will ride the wave, though the effect isn't as strong as a second magnet.

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Now move magnet A back and forth 4 times a second, which is as fast as the human hand can go, (unless you are Neil Peart). Magnet B wiggles in response, 4 times a second. B is riding the em wave produced by A, with a frequency of 4 Hz.

The more you think about this, the more amazing it becomes. What is waving? When you strike the side of a bell, the sound reaches your ears through the air; the air is waving. The side of the bell vibrates, and presses in and out on the air around it, and the air vibrates, and carries the sound to your ear, where the eardrum vibrates in sync with the air and the bell. Nerves detect the vibrations in your ear drum and pass it along to your brain, which then "hears" the sound of the bell. If you did this under water you would still hear the bell, though the sound has different characteristics. Perhaps you have heard voices and sounds when swimming under water. In a vacuum you wouldn't hear the bell at all, because there is nothing to carry the sound.

As a matter of intuition, we have the feeling that air is not carrying the em wave. Granted, you can't do this experiment at home, but other people have performed it in the laboratory - they have created a vacuum and moved one magnet, and watched the second magnet move in response. The action is the same. It does not require air or any medium.

How fast does this em wave travel? We know the speed of sound, about 700 miles an hour. You've seen it in a thunder storm - the lightning flashes, and then the thunder reaches your ears several seconds later. The delay is longer when the lightning is far away. The thunder travels a mile every 5 seconds, so you can count seconds and then divide by 5 to measure the distance to the lightning. All good, but how fast does the em wave travel? We probably can't answer that question until we understand what is waving, and how the wave propagates.

These were the most important questions of the late 1800's. They were pursued, at the time, out of scientific curiosity, but they underpin every piece of technology we enjoy today. We can't even get electricity from the power station to our homes without a deep understanding of electromagnetic waves.

Maxwell's Equations

In 1861, James Clark Maxwell published a set of equations that explains what is waving, and even how fast it propagates. The math is beautiful, but beyond the scope of this book.

When a magnetic field changes, e.g. when you move a magnet back and forth, or spin it, it creates an electric field. And when an electric field changes, e.g. when electricity moves through a wire, it creates a magnetic field. Each field, as it changes, induces the other. Electric begets magnetic begets electric begets magnetic, and thus it propagates through empty space. No medium is required.

After some experiments inspired by his equations, Maxwell computed the speed of the em wave; it was exactly the speed of light. In an epiphany, he realized that light was an em wave. There was a deep connection between light, electricity, and magnetism.

Maxwell didn't know the frequencies, but we know them now, so let's illustrate with a thought experiment, which is completely impractical. Hold magnet A in your hand and vibrate it back and forth 440 trillion times a second. This isn't possible but pretend like it is. The magnet is emitting red light. Do this in a dark room and imagine seeing the red glow as you wiggle the magnet back and forth 440 trillion times a second. 440THz is the deepest red, the first color you can see, while 484 THz is a bright red-orange. (THz is terahertz or trillions of hertz or trillions of vibrations per second.) Thus 440 to 484 THz is the range of frequencies of em radiation that registers as red to the human eye. Here are the colors and their ranges. Boundaries are somewhat arbitrary and subjective. Individuals may perceive and classify colors differently, and some can see farther into the spectrum than others.

Why then does a hot iron glow red? Heat is molecular motion, i.e. rapid and chaotic vibrations at the atomic level. Electrons jostle with the heat, and create moving electric fields. (If you know quantum mechanics, then you know I am oversimplifying this considerably - but it's a good first approximation.) They don't move all as one, and they don't move in exactly the same way, but they move about an average excitation, according to the temperature of the metal, and they radiate em waves in the red band of the spectrum, along with infrared, which we feel as heat. Review the discussion of the iron rod, and the colors it produces as it gets hotter. More heat means the atomic particles are moving faster, and the radiation has ever higher frequencies.

Radio Waves

It may seem counterintuitive, but It is surprisingly easy to push electricity through a wire, back and forth, a million times a second. It isn't done by a spinning wheel, or anything mechanical, but by an oscillating circuit, based on a capacitor. We knew how to do this by the early 1900's. I'll call the wire an antenna. As electric charge moves back and forth within the antenna, it creates an electromagnetic wave, with a frequency of one million hertz, or 1 megahertz, or 1 MHz.

Far away, perhaps miles away, the wave induces a trickle of current, back and forth, in another wire, which I will also call an antenna. This antenna should be aligned with the first, and for maximal effect, it should be attached to a resonance circuit, tuned to the same frequency. When the transmitter is turned on, an em wave travels through the air, along with trees and houses and other nonmetallic objects, and induces a current of the same frequency in the receiver. Turn the transmitter off, and a few microseconds later, current stops flowing in the receiver.

The first application was, as you might guess, wireless communication. Thus the receiver was called a wireless. For 40 years, telegraph lines crisscrossed the country, carrying news, messages, and even basic financial transactions. Now, instead of a wire, morse code could be sent across a span of 20 miles, through the air, even through the buildings of a city or the trees of a forest. Turn the transmitter on for 0.1 seconds for a dot, and 0.3 seconds for a dash. An operator at one end, and an operator at the other, both fluent in morse code, and both equipped with a transmitter and a receiver, could send messages back and forth.

The next step wasn't far away. A microphone converts sound into variations in the current, the current that is pushed back and forth in the antenna. If you sing middle c into the microphone, the current varies in strength 261 times a second. Realize it is still oscillating a million times a second, that is the carrier wave; but it gets stronger and weaker 261 times a second. Thus the wave that spreads out across the city grows stronger and weaker 261 times a second. It's amplitude changes with the sound, thus amplitude modulation, or AM.

A receiver locks on to this signal, at 1 MHz, and that signal comes in stronger and weaker 261 times a second. This current feeds into an ear piece or a loud speaker and the listener hears middle c. Sound is transmitted by radio, just as it was transmitted by light in an earlier chapter. A radio wave can carry the sound, just as light can carry the sound, but the radio wave is more practical when broadcasting to the masses, since it passes ghost-like through buildings and trees, and is not overwhelmed by the sun, or even the light in your bedroom.

The signal spreads out in all directions from the radio station, like the spokes of a wheel. These are the radii of a circle, thus we call them radio waves. They "radiate" away from the antenna in all directions.

In 1915, my grandfather listened to KDKA Pitsburgh, one of the first stations on the air. His house didn't have electricity; nor did most houses at that time. And batteries were not available at the local store. How did his radio get its power?

Answer: from the radio wave itself. A crystal radio set requires no power source, thus they were popular at the time. Using a dial, you could tune in the the desired frequency, according to the radio station (s) in your aria, whence the wave induced a tiny current in your crystal set. This current grew stronger and weaker, back and forth, according to the sound that was carried by the wave. The current ran directly through an earphone, which was placed in your ear. This works because human hearing is exquisitely sensitive, at least in young people. Also, there was very little background noise in 1915. No traffic, no lawn mowers, no television, no tablets, no phones. Just the occasional bird, or perhaps some crickets. Thus my grandfather could tune in to KDKA, and hear some music, or perhaps the news, as the Great War was unfolding overseas.

When more households received electricity in the 20's and 30's, plug-in radios became practical. The sound was amplified, and the entire family could listen to the broadcast.

Radio Stations

From the get-go, stations were licensed under call letters and a broadcast frequency. It remains so today. For example, WJR, in Detroit, is a radio station that broadcasts on 760, that is, 760 thousand hertz. This is just below a million hertz, and is within the AM radio band, which runs from 750 thousand Hz to 1.6 million Hz. WEXL announces itself as 1340, which is 1.340 megahertz, near the upper end of the AM band.

At the outset, stations on the east started with W, and stations on the west started with K, although the east-west line was somewhere in mid Pennsylvania. There wasn't a lot of radio out west. Thus my grandfather listened to KDKA. We soon realized this was a bit lopsided, and changed the dividing line to the Mississippi River. Stations east start with W, and stations west start with K. Canadian stations start with C, and stations in Mexico start with X. Military stations start with A or N. That is the convention in North America. I'm sure the other continents have their standards for radio and television stations and their call letters.

Frequency Modulation

Lightning produces em radiation at almost every frequency, including bursts in the megahertz range. Electric motors also produce unintended radio waves. As a result, AM radio was subject to static from many sources. A thunder storm within 5 miles filled the radio with crackles and static. ⛈ 📻 This wasn't a big concern for news or talk shows, but it detracted from the music.

The solution was frequency modulation - don't vary the strength of the carrier signal, vary its frequency. By the 1940's, FM radio was born. A new band was established for this purpose, 100 megahertz. The electrons moved back and forth in the antenna 100 times as fast as they did in the AM transmitter. But the increase in carrier frequency wasn't as important as the change in modulation. Suppose your radio station is WOMC, FM 104.3. That means its carrier frequency is 104.3 million cycles per second. Sing middle c into the microphone, as we did before. The carrier wave does not grow stronger or weaker with the sound. The power output, measured in watts, is constant. Instead, the frequency shifts down to 104.2 MHz, then up to 104.4 MHz, then back to baseline 104.3 Mhz, 261 times per second. A radio tracks the frequency shits, turns it into varying current, and passes it to the loud speaker, where the listener then hears middle c. Lightning might inject extra radio waves at this frequency, an extra boost of power, but it won't shift the frequency of the carrier wave. Steely Dan understood this technology, as their song, FM, has the refrain, “No static at all.”

A crystal radio cannot pick up an FM station. Remember that the signal is not processed in any way. When the wave is stronger, more current flows in the circuit, and the magnet in the ear piece is stronger, and the cone moves inward. The wave weakens and the cone moves out. The wave wiggles, weak and strong, with the sounds that the radio is broadcasting, and the cone in the ear piece moves in exactly the same way as the signal strength. this is amplitude modulation, or AM. However, in an FM broadcast, the strength of the signal does not vary, rather, the sound is encoded by wiggling the frequency of the carrier wave. A crystal set cannot pick up this signal and simply pass it to your ear. It has to be processed. The shifts in frequency have to become shifts in amplitude. This is easily done with a phase lock loop, but it does require active circuitry. You'll need a battery or wall power or some way to do it. Fortunately FM and transistors were coming out at about the same time, the late 40's. The transistor radio was just the ticket for people on the go. They could listen to their favorite AM or FM stations.

Electromagnetic Spectrum

Here is the em spectrum, from AM radio waves up to gamma rays. kHz is kilohertz, thousands of hertz. MHz is megahertz, millions of hertz. GHz is gigahertz, billions of hertz. THz is terahertz, trillions of hertz. PHz is petahertz, quadrillions of hertz. EHz is exahertz, quintillions of hertz.