Phantastic Phun with Phascinating Physics #1: Redshift and the Doppler Effect

Over the years, very few things have brought more joy into my life than science. An understanding of some of the principles of physics in particular has enriched my life and answered questions I’ve long wondered about in a very satisfying way. So, I would like to share with you a number of things that I’ve learned over the years that I find particularly fascinating. This will be the first of many installments to come, and I’ve decided to start with two related topics. The Doppler Effect is something that most of us probably experience in some way on a daily basis although we may not be aware of it or understand exactly what’s happening. I’d like to share with you a detailed explanation of the Doppler Effect, and how it led to one of the most significant cosmological discoveries of the twentieth century: the effect known as “Redshift”. If you’re already familiar with the inner workings of both of these concepts, you may want to skip this blog entry as I’m just going to yak about these two subjects for a bit without talking about anything else.

The way most people experience the Doppler Effect is in the presence of some sort of motorized vehicle. A train blasting its horn is a particularly good example. As the train approaches, the horn sounds at one consistent pitch (or frequency), but as the train passes and the engine moves away down the track, the pitch of the horn seems to get lower in frequency. This is the Doppler Effect in action. The horn isn’t actually changing in pitch; it’s blowing at one steady frequency. The interesting thing is that the horn’s actual pitch is lower than it sounds as the train approaches, and higher than it sounds as the train fades into the distance. To understand what’s happening, first we need to understand some of the basic properties of sound.

Sound and Waves

All sound is vibration. Vibration by an object causes the air (or other medium) to vibrate, and that air upon reaching a human ear causes the ear drum to vibrate. That vibration is then interpreted by the brain, and the sound is registered. It’s amazing to think that all the different sounds that you hear in your daily life are just different vibrations of air entering your ears. Classical music, an airplane engine and a crackling fire are all making sound the same way: by vibrating the air. What makes them sound different to your ear is that each of those sound sources vibrates the air in a slightly different way. To describe the differences in vibration is a subject for some other time however, so we’ll just try to stick to a basic type of vibration that we can use as an example.

Let’s say that you and I are in a concert hall together, and I’m on stage at my drum kit which has been miked up through the huge sound system. The room is silent, until I hit my bass drum once. In this setting, the vibration created by the speakers is often something you can actually feel in your chest. What you’re feeling is in fact the air being pushed (vibrated) by the speakers, and that specific type of vibration is registered by your ears as a deep, low thud.

To understand what’s actually happening to the air, see Figure 1.
Here you can see the speaker on the left pushing molecules of air. Where you see the highest concentration of molecules (dots) is where the air has been compressed most severely by the speaker’s vibration. Just like a wave on the ocean, this compression pushes the air in front of it, which pushes the air in front of it, and so on and so on until the compression “wave” hits your ear drum and you hear a loud thud.

Now, to make a few things easier to understand, I’m going to show you a very rough graph of this compression wave (see Figure 2). (I promise not to let this get too dry; or at least no more so than necessary!)
Here you can see the degree to which the air molecules are compressed on the vertical axis, and time on the horizontal axis. As you can see, the compression of the air starts at zero just before the compression wave hits. As the wave hits, the compression of air molecules increases rapidly until it reaches a maximum peak, which we call a “crest”. After the “crest” hits, the air compression starts to subside, but what’s interesting is that the wave leaves behind it a pocket of lower air density, or negative compression.

To understand this, imagine you drop a heavy, flat rock into a calm pond. As the rock passes through the surface of the water it pushes down on the water under itself, compressing that water. Also, as the rock passes below the surface it leaves only air behind it for a split second until the water rushes back from all sides over the top of the rock, creating a big splash which takes a few moments to calm down. What we’re interested in right now is the pocket of air traveling behind the rock because for that split second there’s very little water above the rock, and compressed water below the rock.This represents (in this case with water instead of air) the region of LOW compression which we call rarefaction. Basically, you can just think of the word “rarefaction” as the opposite of compression, or negative compression if you like. The point of this long winded example is to show that one wave is made up of both one region of compression and one region of rarefaction before everything can begin returning to normal.

Now, back to sound in the air and Figure 2. We’ve talked about the crest of the wave, and now we see the region of low compression, which we call a trough. So now that you understand both the crest and the trough, there are three more properties of waves that we need to understand before moving on to the Doppler Effect itself. The first is speed. Since we’re talking about sound here, we can see that all sound travels at the speed of sound (I know that’s a bit of a silly statement, but it does help to clarify a few things), and so all of the sound waves coming from my bass drum that we might discuss are going to travel at the same speed. The second property is called wavelength. This is really just what it sounds like. It is the length of physical space between the start of the wave’s crest and the end of its trough. Depending on the size of the wave in question, it’s just measured in meters, centimeters, yards, inches, or sometimes even kilometers or miles. The last property we’re going to discuss right now is called frequency. We use the word “frequent” often enough in every day life to know what it means, and really it doesn’t mean anything terribly different here. In every day life, “frequency” just refers to how often something happens, and in the case of sound, the “something” in question is your ear being hit by a wave crest. (We generally refer to being hit by the crests because remember that this is the region of HIGH compression that you feel in your chest and which slams into your ear drum to initiate vibration). It’s worth noting that frequency is measured in units called Hertz (abbreviated Hz), which really just means “cycles per second”, or for our purposes here, complete waves per second. All of this of course is really just a fancy way of saying “how often something happens”.

Now, here’s a very important concept. If you picture water waves on the ocean, and we assume for the moment that they’re going to all travel at the same speed: what happens to frequency as wavelength is increased? Or, put another way, if you’re standing neck deep in the water at the beach and waves are hitting you in the face one after another: if the distance between wave crests gets larger, will you get hit in the face more or less frequently? If you think about it, or go and try it out, you’ll probably realize the fundamental concept that (assuming the speed of the waves doesn’t change) as wavelength increases, frequency decreases. Likewise, as frequency increases, wavelength decreases. (See Figures 3 and 4). This concept is very important, and crucial to understanding how the Doppler Effect works.

The Doppler Effect

Now we’re ready to take on the Doppler Effect. To do so, let’s return to the example from the beginning of this ramble where we talked about a train going by while blowing its horn. I don’t know much about train horns, but it’s safe to assume that the horn is something like a glorified version of your car horn. It beeps at a certain pitch (or frequency – eh, eh?), and if the horn is working properly, it always beeps at the same pitch. Depending on your particular style of driving, you may be intimately familiar with the sound of your own car horn. If you could stand in front of the train while it was blowing its horn and wasn’t moving, you would hear the sound of its horn exactly the way it really does sound. Something interesting happens though as soon as the train starts moving towards you. First of all, you get off the train tracks. Less importantly, but more interestingly, something happens to the sound of the horn. It seems to get higher in pitch. Let’s have a look at why.

(Although I just hinted at it in the above paragraph, it’s important to point out that the words “pitch” and “frequency” can be used somewhat interchangeably; frequency is just a little more specific. The same thing that you would describe as being high in pitch can also be described as being high in frequency. Try it yourself. Go find someone, and right in their face sing a high note and then a low note. You’ve just changed the frequency with which your lungs and vocal chords are vibrating the air. You just made the face of the person in front of you get hit by wave crests less frequently when you sang the low note than when you sang the high note. Now, if you haven’t been punched in the nose yet, you might also want to reflect on the fact that the wavelength of your low note was longer than that of your high note).

Now, there’s a very important distinction between the train horn and my bass drum from the earlier example that we now need to consider. When I hit my bass drum, it was a relatively short lived sound. It was one quick hit, and then it was over. The train however is blowing its horn constantly. This does not mean that the whole blast of the horn consists of one incredibly long wave, but rather one continuously emitted type of wave See Figure 5.

Our previous diagrams all dealt with stationary objects; but now we’ve got to deal with a moving train. Keep in mind that the train is continuously blowing its horn as it starts moving. I’m going to use just a few numbers here, but don’t let them freak you out. It’s not necessary to understand the math right now, just the results. Let’s say for the sake of simplicity that when it was stationary, the distance between wave crests was 10 centimeters. At the speed of sound, that would mean that the horn has a frequency of about 3,420Hz, depending on the air temperature. All that means is that your ear would get hit by 3,420 wave crests every second. What’s very important to realize is that while the wavelength and frequency of the sound being emitted by the train’s horn remain constant (just like your car horn always sounds the same to you while you’re in the car, regardless of how fast you’re going), as the train starts moving, it’s ever so slightly closer to you (the bystander observing the train) when it releases the second wave than it was when it released the first wave. At very low speeds, such as that of a train just beginning to accelerate, this change in the train’s position hardly makes a detectable difference. However at higher speeds the difference begins to become pronounced. For example, if the train were moving at 100 kilometers per hour it would be 0.81cm closer to you when it released the second wave than it was when it released the first. That means that the distance between wave crests (the wavelength) seems to your ear to have been reduced by 0.81cm. (Remember that when wavelength decreases, frequency increases). What this means in terms of what you hear is that the train’s horn will seem to have a frequency of 3,681.38Hz. It’s not necessary to understand right now anything more about these numbers than the fact that to you the bystander the frequency of an approaching train’s horn will be higher than that of a stationary train. (See Figure 6 for an overhead view of a stationary train vs. a moving train radiating sound waves out in all directions. The circles represent wave crests).

Now, the train isn’t going to go on approaching you forever. Eventually it’s going to go by. Now we have the opposite effect. As the train is rolling away from you down the tracks, it’s slightly farther away from you each time it releases a sound wave (See Figure 6). Assuming the train has held a constant speed, now the horn is going to seem to have a frequency of 3,163.74Hz. Again, it’s not important to understand any more about these numbers than that the frequency of a retreating train’s horn will be lower than either that of a stationary train or an approaching train. If you are standing near the tracks as all of this goes down, there will be a brief period between the time when the train’s horn is mostly heading directly towards you and the time when the train’s horn is mostly heading directly away from you during which the train’s horn will be barely moving relative to you. Can you guess when? It will be when the horn is directly next to you. In this split second, the horn isn’t moving towards or away from you; it’s just blasting away right next to your ear, relatively motionless, probably prompting you to cover your ears. This is why the sound of the horn holds a relatively high pitch for a while at first as it is approaching you, and then the pitch seems to rapidly fall off as the train blows by, finally settling on a pitch much lower than the one you heard at first.

Congratulations, you now understand how the Doppler Effect works (I hope). If you’d like to experience it for yourself in a controlled way and at your own convenience, you’ll need a friend who can drive a car to assist you. Go stand out next to a road (not ON the road) with at least a reasonable speed limit (say, no less than 50km/h or 30 mph) and send your friend out in the car to drive past you. As your friend approaches, have him/her lay on the horn and hold it while maintaining a constant speed until he/she is well past you. You’ll hear the Doppler Effect in action for yourself.

So how does any of this tie in to cosmology or some concept called Redshift? I’m glad you asked!

Light

Like sound, light is a type of vibration. It is however a totally different type of vibration from sound in that it doesn’t require a medium through which to travel. Basically all I mean by that is that while sound needs some sort of substance like air or water (or about a million other substances) to vibrate and thus make itself heard, light can travel through the empty vacuum of space (as well as air and water and others). This is because while sound is just moving physical objects (ie molecules of one substance or another), light is pure energy, and has comparatively little interaction with physical objects. Just for your own curiosity, we call sound waves “mechanical waves” while light waves are “electromagnetic waves”. Light waves do however have many of the same properties we discussed with sound waves. Light waves have wavelengths and frequencies and speed, although the speed involved with light is much, much higher than the speed of sound. Again, just for your own curiosity, while the speed of sound through the air is a sluggish 330 meters per second plus or minus 5/9 times the air temperature in degrees Centigrade, light whips along at almost 300,000,000 meters per second, regardless of the air temperature. Basically this means that the speed of light is about 877,193 times faster than the speed of sound!

When we normally think of light, what we’re actually thinking about is a small sliver of what is called the “electromagnetic spectrum”: the only type of radiation that’s visible to the human eye. The word radiation often carries with it a negative connotation. When we think of radiation we think of something invisible but very harmful in large doses. Perhaps we think of ultra-violet radiation, or microwaves, or even X-rays or radar. It can be interesting to consider that all of these forms of radiation aren’t really any different from the light we’re used to seeing except that they have a different wavelength and consequently a different frequency (recall again the relationship between frequency and wavelength). All of these forms of radiation, visible light included, travel at (big surprise) the speed of light! Imagine that. Sound travels at the speed of sound and light travels at the speed of light. Where do we come up with these names? Anyway, visible light is harmless, but some other frequencies can be quite harmful. The types of electromagnetic radiation, in order of from highest frequency to lowest frequency, are as follows: Cosmic Rays, Gamma Rays, X-Rays, Ultraviolet, Visible Light (Violet through Red), Infrared, Microwaves, and Radio Waves.

Cosmology

Cosmology, for anyone who doesn’t already know, is basically the study of the history of the Universe. Cosmologists attempt to figure out how the Universe came to be, what happened in the early Universe, what is happening out there now, and what will happen in the future. This can be a very difficult job, as you may imagine. Most scientists in most fields have the luxury of being able to closely examine the thing they wish to study. To pick it up, put it down, or subject it to a variety of tests. This is obviously not an option for the Universe as a whole. All cosmologists can really do is look, think, and calculate. The problem is that most of the Universe is pretty hard to see, with the exception of stars and the patterns they make. Cosmologists have used the light from these stars to try to figure out what’s going on out there.

One of the early problems of cosmology was to figure out how long the Universe has been around. Was the Universe always here? Will it always be here? Does it change with time, or is it completely static and constant? These are hard questions to answer from our little blue speck. The Universe is so incredibly big that if you could travel at the speed of light (given above), it would still take you over three years to reach the Sun’s nearest neighbor star. It would take you 120,000 years at the same speed to travel across our galaxy, and then there’s a whole Universe full of galaxies out there beyond ours. Quickly it becomes apparent just how difficult it is to take on any questions that concern the Universe as a whole!

Redshift

The way the above questions were answered was by studying the light being emitted by stars. The fusion reaction that powers the burning of the stars you see when you look at the sky at night is also responsible for creating almost all the elements that make up our planet. Amazingly enough, most of the chemical elements that make up your body were once part of a star shining light out into the blackness of the Universe. Astronomers realized that it was possible to detect the presence of different elements in an actively burning star by studying the spectrum of light it emits. What happens is that different elements have different indicators, signatures if you like, that show up when taking a reading of a given star’s spectrum. Basically there are certain narrow little frequencies in the star’s spectrum that stand out when a certain element is present. Here was actually an experiment we could perform here on Earth! By heating up some of these elements and taking a reading of the light spectra they give off, we were able to see matches. An interesting thing happened though: when looking at some galaxies and studying the light they gave off, scientists didn’t see quite exactly what they expected. They saw all the indicator frequencies that they expected, but they weren’t quite right. They were all uniformly shifted slightly over towards the red end of the light spectrum. It was a man named Edwin Hubble (yes, the guy for whom the telescope was named) who first realized that this was an indication that the galaxies scientists were studying were actually moving away from us. Remember from our discussion about the Doppler Effect that a train which is moving away from you will produce sound waves of a seemingly longer wavelength, and therefore lower frequency? The same thing was happening here, only with light! (Recall from the list above under the “Light” heading that the red end of the color spectrum has a lower frequency than the violet end). This effect was named (as you have no doubt guessed) “redshift”, and is really just a manifestation of the Doppler Effect on a grand scale. There are also some galaxies that have been found to have spectra that are “blueshifted”. Can you guess what this means these galaxies are doing? If you guessed that they’re moving towards us, you’re right. Again, this is because the light from a galaxy that is moving towards us will appear to have waves of a shorter wavelength and thus higher frequency than they really do. (I suppose that this effect might better have been called “violetshifting”, but that doesn’t have quite the same ring to it, eh?)

These discoveries eventually led cosmologists to conclude that the Universe is indeed expanding, and even helped (by working backwards) to estimate an approximate age for the Universe. There are a few different theories floating around on that one, but a middle of the road estimate puts the Universe at about 15 billion years old.

And so we come to the end of this very long diatribe about a couple of things that I find interesting. Who would have ever thought that the sound of a passing train might have helped anyone to figure out the age of the Universe? Or that the Doppler Effect could be applied to the light from distant galaxies? Anyway, I hope you’ve found these topics as interesting as I do, and if anyone has any questions, or if there’s anything that I haven’t made clear, I’d be delighted to answer and/or revise to alleviate any and all confusion.