# The Doppler Effect: Formula & Calculation

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• 0:03 What Is the Doppler Effect?
• 1:14 Doppler Effect and Light Waves
• 1:43 Calculating Observed…
• 2:12 Practice Problems
• 4:10 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

The Doppler effect causes wave frequencies to change when the source of the waves is moving. In this lesson, learn about the Doppler effect and how to calculate the frequency of sound produced by a moving source.

## What Is the Doppler Effect?

You're standing beside a busy road when you hear a motorcycle coming toward you. As it passes you, the sound of the engine seems to change. It seems to emit a lower-pitched sound after the motorcycle passes you and keeps moving away from you. What happened? Why did the motorcycle's engine seem to emit two different sounds when it was moving towards you and then away from you?

What you hear as the pitch of the sound is actually the frequency of the sound waves. If the sound waves are close together, you hear a high-frequency sound, and if they are farther apart, you hear a lower-frequency sound.

When sound waves are emitted by a moving source or when the observer of the sound is moving, the apparent frequency of the sound can change. This shift in frequency due to motion of the sound wave source or of the observer is called the Doppler effect.

When a source of sound waves, like the motorcycle, is moving towards you, the sound waves emitted become pushed closer and closer together. This means that when you hear the motorcycle coming towards you, you hear a higher-frequency noise than you would if the motorcycle was sitting still. After it passes you, the sound waves move farther apart, and you hear a lower-frequency sound.

## Doppler Effect and Light Waves

The Doppler effect affects all kinds of waves, not just sound waves. Light waves are affected by the Doppler effect, too! As a light-emitting object moves away from an observer, the frequency of the light waves becomes smaller, shifting the light towards the low-frequency, red end of the visible spectrum. Astronomers observed distant stars and could see that they were all red-shifted. This let them know that the stars were moving away from Earth and that the universe was expanding.

## Calculating Observed Sound Frequency

The frequency of sound heard by an observer can be affected by both the motion of the observer and the motion of the source of sound. You can calculate the observed sound frequency (f' ) using this equation:

## Practice Problems

Let's look at a few examples of how to apply the Doppler effect. In all of these problems, we'll assume that the speed of sound in air (v) is 350 m/s.

1. Arav is waiting for the bus when he hears a siren coming towards him. If the siren is emitting a sound with a frequency of 1500 Hz and is moving towards the bus stop at a velocity of 10 m/s, what frequency sound does Arav hear?

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