The Doppler Effect

Mr. Donovan, from you I learned about the Doppler Effect (I’ll never forget your truck going by, horn full blast), I learned that blue bounces best, and I learned that I wanted to teach and I learned that the best learning happens when a student feels respected- and that there needs to be a little humor, too (now I know it was for the both of us- teaching is hard!) Thanks- these are fun to read. I see some familiar names I haven’t seen in a long time!

CC (former student)

My response:

I am so happy that I asked this question. You now know intimately that humor is not only important, it’s essential. Can you imagine your classroom without it? Humor can be an expression of joy. And we want nothing else than our kids to know that joy in their learning. I could not be happier that you chose to become a teacher. And I know your students, both current and former, that completely agree!

More about the Doppler Effect:

What was that car horn really teaching? This was one of my favorite demonstrations to do in a physics or astronomy class. Officially, the Doppler Effect is defined as the apparent change in frequency of a wave caused by relative motion between the source of the wave and the observer. It happens with all waves- sound, light, water, … It was described by the Austrian mathematician/physicist Christian Doppler in 1842 in Űber das farbige Licht der Doppelsterne (On the Colored Light of the Double Stars). He proposed that the light from stars would appear different depending on if they were moving towards or away from us. The tools and the supporting knowledge weren’t available yet for him to prove this at the time. But he was right!

Probably the most common experience you have with the Doppler Effect is when an ambulance goes by with its siren on. As it approaches you the sound of the siren is at a higher pitch than when it is going away from you. It can also be easily heard if a train rushes through the station when you are standing on the platform. You will hear something like, NEEEEEEEEE-OOOOOOO-OOOOWWWWWWW!

This is not an effect of the sound getting louder. While that does happen, it is actually a change in frequency that you hear. Sound travels in waves, specifically longitudinal waves. They come from a vibration, a stop and go, where the air is forced close together (compression) and then spread out (rarefaction) compared to air that doesn’t have the sound going through it. This vibration happens over and over, and when the air makes it to your ears you hear the sound. The more frequently the vibration is made, the higher the pitch you hear. The frequency is measured in units called hertz (Hz). This would be how many compressions hit your ear per second. The more often they hit per second, the higher the sound. The less often they hit, the lower the sound.

As the emitter of a sound approaches you like a car horn, the compressions stack up. They reach your ears at a higher frequency than they would if the source of the sound wasn’t moving. A typical car horn might have a standing frequency of 500 Hz. That is close to the note B4 on a piano, just below high C. When a car blaring its horn is coming towards you at 30 mph (13.4 m/s) you will not hear it at 500 Hz. You will hear something more like 520 Hz. While that is still a little below high C, it is an easily heard difference to most people. The sound heard by you is not the sound actually emitted by the car. You perceive it at a higher pitch. And if the car horn is moving at 30 mph away from you, the sound you hear will be 480 Hz- closer to B_flat4.

Mathematically,

(for a receding source)

There are speeds of waves (v) and their frequencies (f)in this equation. There is nothing that talks specifically about sound waves only. This equation fits for all types of waves. Most interestingly- light. 

Light is described as having a wavelength. It is a transverse wave, not longitudinal like sound. This means that instead of compressions and rarefactions along the motion of the wave, light’s changes are in amplitude in a series of crests and troughs. But still, how frequently these oscillations hit your eye is called frequency, still measured in Hz. Red light has a frequency of 4.3 X 10¹⁴ Hz while blue light has a higher frequency of 6.5 X 10¹⁴ Hz. 

There are many applications using the Doppler Effect with light. 

• Doppler radar in police speed guns use microwave or infrared light. Once the light hits your car it is reflected back with a shift towards the blue end (a higher frequency). 
• It is used in medical exams to measure blood flow with the light being scattered by red blood cells. I saw this first hand when my wife was pregnant with our second child! The sonogram was able to show us blood flowing in and out of his heart while in utero. It was incredible!
• Self-driving cars use LIDAR (light detection and ranging). 
• You can determine the rotation rate of a planet like Jupiter. The light on one edge will be shifted a little bit to a higher frequency as the edge is turning towards you and the other edge to a lower frequency as it moves away from you. That is called blueshifting and redshiftting. 

This is a wonderful tool when studying astronomy as the only information we can get from them is the light that reaches us. If something emitting light is moving towards us, we see it shifted to the blue part of the spectrum. If it is moving away from us, it is called redshifted. 

By 1912, Vesto Slipher, an astronomer at the Lowell Observatory in Flagstaff, AZ was able to measure a redshift from twenty-five different spiral nebulae (what we now call other galaxies). The spectrum that hydrogen normally makes was shifted to a lower frequency. What was amazing is that they were all redshifted and the speeds calculated for them could be hundreds of miles per second. One mile per second is about the speed a high-velocity rifle bullet is going. These spiral nebulae are traveling incredibly fast, away from us.

In the mid 1920s, Edwin Hubble, an astronomer at The Mount Wilson Observatory in Pasadena, CA was able to measure the distance to some of the closer spiral nebulae. He determined they were a lot farther away from us than was currently thought. The majority of astronomers at the time considered these objects to be relatively close, only thousands or hundreds of thousands of light years from us (Space is big!). Hubble measured the Andromeda Nebula (now called the Andromeda Galaxy) distance to us to be 2.5 million light years away! And that is the closest one. These spiral nebulae that are all redshifted are also incredible distances away. That is why we call them galaxies now. Space is really REALLY big!!

Hubble then took his data of distances and compared it to Slipher’s speed data. He discovered that the further a galaxy is from us, the greater the redshift. Galaxies that are far away are moving away from us at an apparently faster rate. Picture these galaxies being raisins in a loaf of raisin bread. As the dough is cooking the raisins will move further away from each other, and the further the raisins are from each other, it appears the faster they move from each other.

Hubble took this and applied it to a very simple equation.

speed = distance/time

v = dt

Or better yet, 

t = dv

Hubble wrote it as v = H₀d. H₀ ~ 1/t. Basically, t = the age of the universe. This isn’t exactly true as the universe didn’t have to, and most likely didn’t, expand at a constant rate. And the gravitational effects that arose once matter formed also have to be taken into account.

This is the beginning of the support for the Big Bang Theory. Our universe is expanding. That is true. And if it is bigger today than it was yesterday, how big was it a million years ago? A billion years ago? It has been determined that 13.8 billion years ago the universe was a singularity. This is supported by Hubble’s work, but not by it alone. Measurements of the Cosmic Microwave Background Radiation, general relativity, the amount of matter and energy measured in our universe; these are all things that support the current understanding of a 13.8 billion year old universe. 

So how do you get people to understand the Big Bang? Let them actuallyhear it! Just do what I used to do. Have the students stand safely on the side of the road and drive past them with your pickup truck’s horn blaring. As you fly by they will hear the  NEEEEEEEEE-OOOOOOO-OOOOWWWWWWW. So will the neighbors and the math classes that are closest to the road. Now they apply their first hand experience to the creation of our universe.

That’s what that truck horn demonstration really was — not just a frequency shift, but a reminder that the universe is dynamic and follows the same rules everywhere. They are the same whether witnessed in a train going by, a radar gun measuring a fast ball, or even the universe expanding.