Doppler Shift: Definition & Formulas

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  • 0:04 What is the Doppler Effect?
  • 0:57 Doppler Effect Equation
  • 1:25 Applying the Equation
  • 5:13 Lesson Summary
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Lesson Transcript
Instructor: Amanda Robb

Amanda holds a Masters in Science from Tufts Medical School in Cellular and Molecular Physiology. She has taught high school Biology and Physics for 8 years.

In this lesson, we're going to be learning about a property of sound waves called the doppler effect. By the end of the lesson you'll understand what the doppler shift is and how to calculate it in different situations.

What Is the Doppler Effect?

What happens when an ambulance speeds past you? How does the sound of the siren change? It does get louder as it approaches, but another characteristic of sound changes also. The pitch is higher when it moves towards you (think a whining noise), and lower when it moves away (think a deep voice). This change in pitch has to do with the frequency of the waves, or how many waves pass through an area per unit time.

In the case of the ambulance, you are standing still and the ambulance is approaching you. Since the sound waves are moving towards you, they are compressed and the frequency increases, and thus you hear a higher pitch. However, when the ambulance moves away from you, the sound waves are spread further apart and the frequency gets lower, so you hear a lower pitch. This change in sound wave frequency due to movement is called the Doppler shift, also known as the Doppler effect.

Doppler Effect Equation

The Doppler effect is not all theoretical though. We can use the Doppler effect equation to calculate both the velocity of the source and observer, the original frequency of the sound waves and the observed frequency of the sound waves.

Doppler effect equation
Doppler effect equation

Using the Equation in Different Scenarios

While there is only one Doppler effect equation, the equation changes in different situations depending on the velocities of the observer or the source of the sound. Let's look at how we can apply the Doppler effect equation in different situations.

Apply the Equation

1. Source Moving Towards the Observer at Rest

Imagine our ambulance again. In this scenario, you are standing still and the ambulance is moving towards you. Let's look back to our equation. The velocity of the observer is zero, so vo is equal to zero. Plugging this into the equation above, we get the equation when a source is moving towards an observer at rest:

Equation for when a source moves towards an observer at rest
Doppler effect

2. Source Moving Away from the Observer at Rest

Now, imagine the ambulance has passed you. The ambulance is traveling at 25m/s, but you are still stationary. The frequency of the sound emitted by the ambulance is 1,000Hz, and the sound waves travel with a velocity of 343m/s. Since your velocity is zero, we can eliminate vo again from the equation. But this time, the ambulance is moving away from you, so its velocity is negative to indicate the direction. Inserting our numbers into the equation gets us:

A source moving away from the observer creates a lower perceived frequency of sound waves
Doppler effect

The frequency perceived by the observer is less than the actual frequency emitted by the siren, just as we expect from the Doppler effect.

3. Observer Moving Toward a Stationary Source

Now imagine riding in a car towards a loud block party. As you move towards the speakers, the sound waves get closer together and the frequency increases. In this case, you are moving, but the source is not. So, vs will be equal to zero, and we get the following equation:

Doppler effect equation for an observer moving towards a stationary source
Doppler effect

4. Observer Moving Away From a Stationary Source

You pass the loud party and are on your way to a more serene setting. Now you're moving away from the sound waves, and the frequency decreases. So, since you're moving away, your velocity becomes negative. So, instead of adding vo, we now subtract, since vo is negative.

Doppler effect equation for an observer moving away from a stationary source
Doppler effect

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