The Doppler Effect

By Danny Keck

One major area of interest in science this century is waves. Waves have always been around and are easy to see in things like water. In the past few centuries though the wave property has been assigned to more and more things such as sound and light. It has become more and more important to find out the properties of waves. One of these properties, which when it was discovered caused a major effect on physics and astronomy, is the Doppler effect.

The Doppler effect was first stated by Austrian physicist and mathematician Christian Johann Doppler. Doppler was a professor at the Technical Institute of Prague and later the Polytechnicum in Vienna. In 1842 he published a paper on the color effect of double stars. It was in this paper that Doppler explained the principle that is now called the Doppler effect.

The Doppler effect is a characteristic of waves. It is "the change in the frequency of a wave observed at a receiver whenever the source or the receiver is moving relative to each other or to the carrier of the wave, the medium" (McGraw-Hill 389). If the source of waves and the receiver of waves are both relatively stationary, the receiver will detect the same frequency as the source emits. However, if one or the other is moving, the detected frequency will be different than the emitted frequency.

The existence was first verified by C. H. D. Buys-Ballot in 1845 using experiments with a moving train. Today it is easy to notice the effects of a Doppler shift. If you are going down a highway and a car passes you, the pitch of the noise will be much higher when it is coming toward you than when it goes away. (Sometimes this is referred to as an auditory illusion). This holds true with any high speed object going past something. This is because pitch depends on frequency and frequency is affected by the Doppler effect.

Consider a sound source moving to the right, towards a stationary object. The source will emit waves in circles around the point that the source was at the time it emitted the sound waves. Although the frequency of the emitted waves is constant, because the source is moving the waves in the direction of movement will be crowded together. The wavelength is shortened, making the frequency higher. Likewise the frequency will appear lower if an source is moving away from the receiver.

The Doppler effect for sound with concern to linear motion can be described using this equation:

fo = fs(s + vo/s - vs)

where o is the received frequency, s is the source's emitted frequency, vo is the speed of the observer, vs is the speed of the source, and s is the speed of sound. The Doppler effect exists as long as the relative speed between the source and the receiver is less than the speed of sound. If the relative speed is greater than the speed of sound then no sound will be heard at all. If both objects are moving at the same speed in the same direction, the detected frequency will be equal to the source frequency.

The Doppler effect occurs in all wave motion, whether it be electromagnetic or mechanical. So therefore it works for both sound and light. The Doppler effect for light was first observed by J. Stark in 1905. Experiments showed that the speed of light is constant, which supported both Einstein's theory of Relativity but also the Doppler effect.

The Doppler effect for light is analogous to that for sound. While different frequencies of sound produce different pitches, different frequencies of light can produce different colors. Visible light goes through these frequencies in order from least to greatest: red, orange, yellow, green, blue, and violet. If an object is moving toward the receiver, the light emitted from it will appear to the receiver to be shifted toward the blue direction of the light spectrum. This is called a blueshift. If the source is moving away from the receiver, then, a redshift is seen.

Theoretically this always happens; however at low speed this color change is basically impossible to detect. At high speeds, however, the Doppler shift becomes detectable. Scientists can use this phenomenon to help measure the relative speed and distance of remote galaxies and stars. We detect higher energy light from objects moving towards us than those moving away (of course according to relativity you could say we are moving towards or away from them and mean the same thing).

Using the Doppler effect in this way is very useful to astronomers. Finding the relative speed and distance of heavenly objects is useful in calculating not only what all is out there, but also the nature and age of the universe itself. In the 1920's and 1930's Edwin Hubble used Doppler's effect to judge the speeds of galaxies. He saw that the light of a distant galaxy was always redshifted - and therefore deduced that the universe was expanding. Scientists continue to try to find out more and more about the universe using Doppler and other effects.

The Doppler effect is often applied with laser beams. By reflecting a laser off an object and noting the shift in frequency, the speed of the object, such as a speeding car, can be derived. When working with radar the Doppler shift in hertz is equal to 3.4 o vr where o is the frequency of the radar in gigahertz and vr is the radial velocity of the object in knots. Radar systems find the amount of Doppler effect. Using this and the radar frequency, the velocity of the object can be found.

Another way radar can be used in conjunction with the Doppler effect allows scientist to "see" objects using radar. Because objects have shape, lasers pointing at them will hit at different times on the same object. In a process called Synthetic Aperture Radar, scientists note the different Doppler effects caused by different areas of an object. Using this data a model or image of the object can be created. This image actually is similar to an optical photograph.

Similar to radar is sonar, which instead of a light wave used to gather information, is a sound wave used for the same purpose. Ultrasonic waves used in sonar are 20 kilohertz, which is higher than humans can hear. Under the water sonar beams are aimed at submarines and other objects. By noting the Doppler effect of the returning wave, the speed of the objects is determined. Other sonar applications include measuring the flow of liquids such as blood in arteries, and some burglar alarms.

The Doppler effect can now be used to locate one's self on earth with far more accuracy than previous methods. Satellites orbit the earth emitting radio signals of a constant frequency. Depending on the location and speed of the satellite in relation to an observer standing on earth, the observer will detect different Doppler shifts from the normal frequency. Because the satellite orbits a known track in space, the observer can use the Doppler shift to determine precisely his position on the planet.

The Doppler shift has many other practical applications. The shifting of light from the sun can be measured to calculate the temperature and turbulence of the sun's surface. Antennas bounce waves off plasmas in space, and, by analyzing the Doppler shifts, scientists determine the plasma's velocity, temperature, density, electric field, and types of ions. Physicians use the Doppler effect in ultrasounds when they examine fetuses. When bats use sound to find prey, they are utilizing the Doppler effect.

It has been noted that redshifts occur from the Doppler Effect. There is also a gravitational, or "Einsteinian" redshift. This was described in Relativity. Light passing through a gravitational field will appear to lose energy. More gravity causes a greater redshift. Although the causes would seem to be different it could be argued that they are similar phenomena if not the same because Einstein said that gravity and acceleration are the same thing. To go any further into this topic would lead to a confusing discussion of relativity.

This then is the Doppler effect, a phenomenon that follows logically from the nature of waves. When the waves are all crowded together then naturally they have a higher frequency; this causes them to be received as more energetic. The discovery of this effect and that of redshifts have been very important to the development of relativity and astronomy.

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