# How the Doppler Effect Works

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If you like riddles, you'll like this one: How can a musician playing a single note on a horn change that note without changing the way he or she plays that note? At first, you might think this is a trick question. Clearly, the musician must do something to change the pitch, right? Wrong. If the musician plays the same note while moving toward or away from a stationary listener, the note heard by the listener will indeed change -- even if the musician does nothing different.

Dutch scientist Christoph Hendrik Diederik Buys Ballot conducted this very experiment in 1845. He assembled a group of horn players and placed ­them in an open cart attached to a locomotive. Then ­he had the engineer start up the locomotive so it could carry the cart, complete with the horn players, back and forth along the track. As they were being pulled, the musicians played a single note on their horns. Ballot stationed himself beside the track and listened carefully, both as the train approached and receded. And the notes he heard were different than the notes being played by the musicians.

Although unusual, Ballot's experiment demonstrated clearly one of the most important wave phenomena known to scientists. The phenomenon is called the Doppler effect after Austrian mathematician Christian Johann Doppler, who first predicted this odd behavior of sound in 1842. Today, scientists know that the Doppler effect applies to all types of waves, including water, sound and light. They also have a good idea why the Doppler effect occurs. And they've incorporated its principles into a variety of useful tools and gadgets.

In this article, we'll examine everything Doppler: the man, the science and the technologies. But first we have to lay some groundwork. Because the Doppler effect is a phenomenon associated with waves, let's start by covering some basics about the two basic types of waves -- light and sound.­

## Wave Basics

When most people think of waves, they think of water waves. But light and sound also travel as waves. A light wave, like a water wave, is an example of a transverse wave, which causes a disturbance in a medium perpendicular to the direction of the advancing wave. In the diagram below, you can also see how transverse waves form crests and troughs.

The distance between any two crests (or any two troughs) is the wavelength, while the height of a crest (or the depth of a trough) is the amplitude. Frequency refers to the number of crests or troughs that pass a fixed point per second. The frequency of a light wave determines its color, with higher frequencies producing colors on the blue and violet end of the spectrum and lower frequencies producing colors on the red end of the spectrum.

Sound waves are not transverse waves. They are longitudinal waves, created by some type of mechanical vibration that produces a series of compressions and rarefactions in a medium. Take a woodwind instrument, such as a clarinet. When you blow into a clarinet, a thin reed begins to vibrate. The vibrating reed first pushes against air molecules (the medium), then pulls away. This results in an area where all of the air molecules are pressed together and, right beside it, an area where air molecules are spread far apart. As these compressions and rarefactions propagate from one point to another, they form a longitudinal wave, with the disturbance in the medium moving in the same direction as the wave itself.

If you study the diagram of the wave above, you'll see that longitudinal waves have the same basic characteristics as transverse waves. They have wavelength (the distance between two compressions), amplitude (the amount the medium is compressed) and frequency (the number of compressions that pass a fixed point per second). The amplitude of a sound wave determines its intensity, or loudness. The frequency of a sound wave determines its pitch, with higher frequencies producing higher notes. For example, the open sixth string of a guitar vibrates at a frequency of 82.407 hertz (cycles per second) and produces a lower pitch. The open first string vibrates at a frequency of 329.63 hertz and produces a higher pitch.

As we'll see in the next section, the Doppler effect is directly related to the frequency of a wave, whether it's made of water, light or sound.

## Wave Frequency

Let's begin our dissection of the Doppler effect by considering a source that creates waves in water at a certain frequency. This source produces a series of wave fronts, with each moving outward in a sphere centered on the source. The distance between wave crests -- the wavelength -- will remain the same all the way around the sphere. An observer in front of the wave source will see the waves equally spaced as they approach. So will an observer located behind the wave source.

Now let's consider a situation where the source is not stationary, but is moving to the right as it produces waves. Because the source is moving, it begins to catch up to the wave crests on one side while it moves away from the crests on the opposite side. An observer located in front of the source will see the crests all bunched up. An observer located behind the source will see the waves all stretched out. Remember, the frequency equals the number of waves that pass a specific point per second, so the observer in front actually sees a higher frequency than the observer in back of the source.

The scenario above describes waves formed in water, but it also applies to sound waves and light waves. Sound waves are heard, not seen, so the observer will hear the bunched-up waves as a higher-pitched sound, the stretched-out waves as a lower-pitched sound. For example, consider a car traveling down a highway between two observers, as shown below. The roar of the engine and friction between the tires and the road surface create a noise -- vroom -- that can be heard by both observers and by the driver.

To the driver, this noise will not change. But the observer located in front of the car will hear a higher-pitched noise. Why? Because the sound waves compress as the vehicle approaches the observer located in front. This increases the frequency of the wave, and the pitch of the vroom rises. The observer located behind the car will hear a lower-pitched noise because the sound waves stretch out as the car recedes. This decreases the frequency of the wave, and the pitch of the vroom falls.

Light waves are perceived as color, so the observer will sense the bunched-up waves as a bluer color, the stretched-out waves as a redder color. For example, consider an astronomer observing a galaxy through a telescope. If the galaxy is rushing toward Earth, the light waves it produces will bunch up as it approaches the astronomer's telescope. This increases the frequency of the wave, which shifts the colors of its spectral output toward the blue. If the galaxy is rushing away from Earth, the light waves it produces will spread apart as it recedes from the astronomer's telescope. This decreases the frequency of the wave, which shifts the colors of its spectral output toward the red.

As you can imagine, astronomers routinely take advantage of the Doppler effect to measure the speed at­ which planets, stars and galaxies are moving. But its usefulness isn't limited to outer space. Doppler's discovery is integral to several applications right here on Earth.

## Practical Applications of the Doppler Effect

In the 160 years or so since Doppler first described the wave phenomenon that would cement his place in history, several practical applications of the Doppler effect have emerged to serve society. In all of these applications, the same basic thing is happening: A stationary transmitter shoots waves at a moving object. The waves hit the object and bounce back. The transmitter (now a receiver) detects the frequency of the returned waves. Based on the amount of the Doppler shift, the speed of the object can be determined. Let's look at a few specific examples.

The handheld radar guns used by police to check for speeding vehicles rely on the Doppler effect. Here's how they work:

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1. A police officer takes a position on the side of the road.
2. The officer aims his radar gun at an approaching vehicle. The gun sends out a burst of radio waves at a particular frequency.
3. The radio waves strike the vehicle and bounce back toward the radar gun.
4. The radar gun measures the frequency of the returning waves. Because the car is moving toward the gun, the frequency of the returning waves will be higher than the frequency of the waves initially transmitted by the gun. The faster the car's speed, the higher the frequency of the returning wave.
5. The difference between the emitted frequency and the reflected frequency is used to determine the speed of the vehicle. A computer inside the gun performs the calculation instantly and displays a speed to the officer.

Meteorologists use a similar principle to read weather events. In this case, the stationary transmitter is located in a weather station and the moving object being studied is a storm system. This is what happens:

1. Radio waves are emitted from a weather station at a specific frequency.
2. The waves are large enough to interact with clouds and other atmospheric objects. The waves strike objects and bounce back toward the station.
3. If the clouds or precipitation are moving away from the station, the frequency of the waves reflected back decreases. If the clouds or precipitation are moving toward the station, the frequency of the waves reflected back increases.
4. Computers in the radar electronically convert Doppler shift data about the reflected radio waves into pictures showing wind speeds and direction.

Doppler images are not the same as reflectivity images. Reflectivity images also rely on radar, but they are not based on changes in wave frequency. Instead, a weather station sends out a beam of energy, then measures how much of that beam is reflected back. This data is used to form the precipitation intensity images we see all the time on weather maps, where blue is light precipitation and red is heavy precipitation.

Doppler Echocardiogram

A traditional echocardiogram uses sound waves to produce images of the heart. In this procedure, a radiologist uses a transducer to transmit and receive ultrasound waves, which are reflected when they reach the edge of two structures with different densities. The image produced by an echocardiogram shows the edges of heart structures, but it cannot measure the speed of blood flowing through the heart. Doppler techniques must be incorporated to provide this additional information. In a Doppler echocardiogram, sound waves of a certain frequency are transmitted into the heart. The sound waves bounce off blood cells moving through the heart and blood vessels. The movement of these cells, either toward or away from the transmitted waves, results in a frequency shift that can be measured. This helps cardiologists determine the speed and direction of blood flow in the heart.

## Name Recognition

Christian Doppler
Imagno/Hulton Archive/Getty Images

In 1992, Austria marked the 150th anniversary of the discovery of the Doppler effect by releasing a stamp featuring the thin face of Christian Johann Doppler. Although Doppler never could have imagined such a tribute, he did grasp the significance of his work from the very beginning. In the 1842 paper that first described the phenomenon, Doppler offered this prediction: "It is almost to be accepted with certainty that [the Doppler effect] will in the not too distant future offer astronomers a welcome means to determine the movements and distances of such stars which, because of their unmeasurable distances from us and the consequent smallness of the parallactic angles, until this moment hardly presented the hope of such measurements and determinations."

The "not too distant future" ended up being almost 100 years, which is how long it took for the Doppler effect to have a major impact on cosmology, meteorology and medicine. But it certainly made an impact and made Doppler one of the most recognized names in the history of science.

For more ­information on the Doppler effect and related topics, visit the links on the next page.

### Sources

• Barnes-Svarney, Patricia, ed. The New York Public Library Science Desk Reference, Macmillan. New York, 1995.
• "Christian Johann Doppler: the man behind the effect," British Journal of Radiology 75 (2002). 615-619.http://bjr.birjournals.org/cgi/content/full/75/895/615
• The Doppler Effect and Sonic Booms http://www.kettering.edu/~drussell/Demos/doppler/doppler.html
• Doppler Radar on USA Today Web Site http://www.usatoday.com/weather/wdoppler.htm
• Doppler Ultrasound on the Mayo Clinic Web Site http://www.mayoclinic.com/health/doppler-ultrasound/AN00511
• Engelbert, Phyllis, and Dupuis, Diane L. The Handy Space Answer Book. Visible Ink Press, Michigan. 1998.
• Gundersen, Erik.The Handy Physics Answer Book. Visible Ink Press, Michigan, 1999.