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## NetLogo Models Library:Sample Models/Chemistry & Physics/Waves/Unverified

Note: This model is unverified. It has not yet been tested and polished as thoroughly as our other models.

# Doppler

 If you download the NetLogo application, this model is included. You can also Try running it in NetLogo Web

## WHAT IS IT?

This model demonstrates the Doppler effect, the apparent change in the frequency of a wave emitted by a source moving relative to an observer.

When the source of a wave moves towards you, the perceived frequency of the wave increases; when the source moves away from you, the perceived frequency decreases. This phenomena can be observed when a car passes you while the driver honks his horn. The pitch of the sound you hear is higher as the car approaches you and lower when the car is moving away.

In this model, a plane flies above an observer. Yellow circles represent the peaks of sound waves emitted by the plane.

## HOW TO USE IT

Press the SETUP button to create a plane and a person. Press GO to start the plane moving. Adjust the PLANE-SPEED slider to control the speed of the plane. There is also a convenient button that sets the plane speed to exactly the speed of sound. The SHOW-AMPLITUDES? switch lets you see the strength of the sound wave on each patch of air.

## THINGS TO NOTICE

Set the speed to zero. When the plane is not moving, the wavelength (the distance between the peaks of each wave) is the same on both sides of the plane. As you increase the speed of the plane, the waves bunch together in front of the plane and spread apart behind the plane. So when the plane is moving towards the person, the wavelength is shorter, so the perceived frequency of the sound is higher. When the plane is moving away from the person, the wavelength is longer, so the perceived frequency of the sound is lower.

When the plane is travelling at the speed of sound (Mach 1, approximately 757mph), notice how all the sound waves overlap at one point. At this point of intersection, the constructive interference of the wave peaks creates a loud bang called a SONIC BOOM.

## THINGS TO TRY

Set the plane speed to the speed of sound, 757 miles per hour (Mach 1). Notice that the peaks of the sound waves in front of the plane bunch up completely. Look at the SIGNAL plot when the plane passes the person at the speed of sound? When happens to the perceived amplitude of the sound heard by the person? This phenomena results from a shock wave -- the constructive interference of a large number of wave peaks -- and creates a very loud sound called a sonic boom.

Turn on the SHOW-AMPLITUDES? switch and adjust the plane speed to watch the constructive interference in action as the plane speed approaches Mach 1.

Increase the plane speed beyond the speed of sound. What happens to the shape of the shock wave? What does the person hear?

## EXTENDING THE MODEL

Add a second plot that displays the relative frequency heard by the person. Improve the first plot to interpolate the signal data and display the amplitude between signal peaks.

In this model, only the plane is in motion. Add controls to move the person as well.

Use the NetLogo extensions API to write a Java extension that plays a sound at a given amplitude and frequency. Have the person generate the sound he hears so you can listen to the Doppler effect in action.

## NETLOGO FEATURES

This model is a vertical cylinder, the plane, moving in the x direction wraps around the world, but the sound waves exit the system when they reach the top or the bottom of the world.

The listener stands at the origin, which is off-center.

## HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

Please cite the NetLogo software as: