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# Doppler Effect for Waveforms

by Ron Kurtus

The Doppler Effect is the change in the observed wavelength or frequency of a waveform, as compared with that emitted from the source, when the source and/or observer are moving with respect to the wave medium.

Examples include hearing the change in pitch of a siren as an ambulance approaches you and observing the change in color—or red-shift—of a star that is moving in a direction away from the Earth.

This effect was named after Austrian scientist Christian Doppler, who discovered the phenomenon for light in 1842. Dutch chemist Buys Ballot verified the Doppler Effect for sound in 1845.

Questions you may have include:

• Why does the Doppler effect happen?
• How does it affect sound?
• How is the effect used in astronomy?

This lesson will answer those questions. Useful tool: Units Conversion

## What causes the Doppler Effect?

The Doppler Effect is caused when the source of a waveform—such as sound or light—sends out waves at a regular rate or frequency, but there is a constant relative motion between the source and observer, causing the observed frequency to change.

### Relationship between λ and f

The relationship between wavelength and frequency is seen from:

c = λf

where

• c is the constant speed of the waveform (such as sound or light)
• λ is the wavelength
• f is the frequency

Thus, when λ decreases, f increases and vice-versa.

Note: The speed of sound can vary according to conditions, but we assume nothing is changing, so that it is constant.

### If source is moving

If that source is moving with respect to a stationary observer, the speed of the waveform remains constant, but the distance between the emitted waves decreases in the direction that the source is moving and increases in the opposite direction.

Doppler effect caused by a moving source

The illustration shows how when the source of the waves moves to the right, the frequency of the waves in that direction is higher. The wavelength in the opposite direction is lower.

### If observer is moving

If you are moving toward a stationary source, you receive the waves at a faster rate than their emitted frequency. Thus the observed wavelength is shortened and the frequency is increased. Likewise, if you are moving away from the source, the observed wavelength is lengthened and the frequency is decreased.

Remember that motion is relative, so we really don't care whether the source or observer is moving. Instead, the concern is whether they are moving toward each other or away from each other.

### Reflection off moving object

If both the source of the waveform and the observer are stationary but the wave reflects off a moving object, it is as if the object was a moving source. The observed wavelength and frequency will change, according to the Doppler Effect.

This is the principle used in Doppler Radar.

## Sound waves

The Doppler effect is experienced when a source is moving and when the sound is reflected off a moving object.

(See Doppler Effect for Sound for information on calculating the effect.)

Note that the velocity of the source or moving object must be less than the speed of sound. A speeds equal to or greater than the speed of sound, a somewhat different effect takes place.

### Source is moving

When you hear the sound of an object moving toward you—such as a siren from and emergency vehicle—the pitch of that sound is higher than if the vehicle was standing still. Likewise, as the vehicle moves away from you, the siren would have a lower pitch.

### Reflected off moving object

If a stationary source sends out sound waves and they are reflected back off a moving object, the sound waves heard at the source will be a different pitch, according to the direction of the object. This is as if the moving object was sending out the sound waves. While sonar uses sound waves to measure the distance to an object, doppler sonar also measures the speed of the object.

## Electromagnetic waves

Astronomers use the Doppler effect to measure the velocities of the galaxies with respect to the Earth. Also, Doppler radar uses electromagnetic waves to measure the speed of vehicles and storms.

(See Doppler Effect Equations for Light for information on calculating the effect.)

### Measure velocity of galaxy

Most stars and galaxies have a high concentration of Hydrogen, which in turn has a specific spectrum of colors when it is extremely hot, such as on our Sun and in other stars. In measuring the wavelengths of the light from distant galaxies, it appears that the spectrum shifted slightly toward the red. This means that the wavelengths are longer than they should normally be, indicating the Doppler effect caused by a source of light moving away from the Earth.

This is called the red-shift. From the measurements, it can be calculated how fast the galaxies are moving away from us. It also shows that the Universe is expanding.

Galaxies and stars that are moving toward our Solar System would send out shorter wavelengths as a blue-shift.

Doppler radar sends out electromagnetic waves—usually in the microwave region—to calculate the velocity of moving objects by measuring the Doppler effect caused by reflection off the moving object.

Police use radar devices to send out an electromagnetic beam of a certain wavelength. When that waveform is reflected off a moving automobile, the motion causes the reflected wavelength to increase, thus allowing the doppler radar device to calculate the speed of the vehicle.

## Summary

The Doppler effect is the perceived change in frequency or wavelength caused when the source of the waveform is moving.

The wavelength appears shorter when the source is moving toward you and longer when the source is moving away. You can have heard the pitch of a siren sound higher as the vehicle moved toward you and then get lower as it moved away.

The Doppler effect is also used in astronomy to measure the motion of galaxies as they move away from the Earth.

Move with the flow

## Resources and references

Ron Kurtus' Credentials

### Websites

Waves, motion and frequency: the Doppler effect - Good overview with animations from Einstein Online

Wave Motion Resources

### Books

(Notice: The School for Champions may earn commissions from book purchases)

## Students and researchers

www.school-for-champions.com/science/
waves_doppler_effect.htm

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