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The Doppler Effect

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**What is the Doppler effect?**

You’ve heard the Doppler effect before. Maybe you were listening to the siren of an ambulance and heard the frequency change as the vehicle passed you. This change in frequency is the Doppler effect, but why does it happen? Let’s explore this phenomenon with some animations. Please click on the link below and WATCH the simulation. Don’t play with it yet!! Continue through the power point.

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**Observer and Source Are Stationary**

The Doppler effect is related to the frequency of the sound heard by an observer compared to the frequency of the sound the source actually produces. fs = frequency produced by the source fo = frequency heard by the observer How does fs compare to fo when the source and observer are stationary? Look at the simulation to answer this question. DON’T PUSH ANY BUTTONS YET! Compare the rate at which the crests (green) and troughs (yellow) are being created to the rate at which the observer is hearing them.

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**Observer and Source Are Stationary**

Without movement there is no Doppler Effect fo = fs

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**Observer Stationary, Source Moving**

How does fo compare to fs when the source is moving towards the observer? How does fo compare to fs when the source is moving away from the observer? Use the simulation to answer these two questions. Click on the “Source approaches” button. In your notes, write down your observations and try to justify why the frequency changes in the way it does.

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**Observer Stationary, Source Moving**

How does fo compare to fs when the source is moving towards the observer? fo > fs The speed at which the wave crests move remains constant. The frequency is larger because the wavelength decreases since the source moves in the direction the wave is moving, not allowing as much space between crests. Note: The source is moving to the left. If the source is moving towards the observer, the wavelength is small, the waves look “bunched” up.

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**Observer Stationary, Source Moving**

How does fo compare to fs when the source is moving away from the observer? fo < fs The speed at which the wave crests move remains constant. The frequency is smaller because the wavelength increases since the source moves in the opposite direction the wave is moving, resulting in lots of space between crests. Note: The source is moving to the left. If the source is away from the observer, the wavelength is big, the waves look like they are spread apart.

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**Observer Moving, Source Stationary**

How does fo compare to fs when the observer is moving towards the source? How does fo compare to fs when the observer is moving away from the source? Use the simulation to answer these two questions. Click on the “Observer approaches” button. In your notes, write down your observations and try to justify why the frequency changes in the way it does.

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**Observer Moving, Source Stationary**

How does fo compare to fs when the observer is moving towards the source? fo > fs The frequency is larger because the time between hitting crests decreases since after hitting one crest the observer moves towards the source, hitting another crest sooner than they would if they were stationary.

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**Observer Moving, Source Stationary**

How does fo compare to fs when the observer is moving away from the source? fo < fs The frequency is smaller because the time between hitting crests increases. After one crest overtakes them, the observer moves away from the source and the next crest takes longer to overtake them than if they were stationary.

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**What does the fo depend on?**

We know that the frequency increases if the source is moving towards the observer or the observer is moving towards the source. What does the value of fo depend on? You can now play with the simulation for a few minutes. Note that you can reset the animation and then make either the source or the observer move by grabbing onto it and moving it in a particular direction. You will see an arrow pop up – the bigger the arrow, the faster it will move.

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**What does the fo depend on?**

You should have noticed that the larger the speed of the source or observer, the larger the resulting frequency change. What would happen if the observer was moving away from the source, but the source was moving toward the observer? Try to come up with a general trend for whether an observer hears a higher or lower frequency, no matter who is moving and in which direction.

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**What does the fo depend on?**

No matter which direction the source and observer are moving: If the observer and the source are getting closer to one another, fo > fs If the observer and the source are getting further away from one another, fo < fs

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**The Doppler Effect Equation!!**

𝑓 𝑜 = 𝑓 𝑠 𝑣± 𝑣 𝑜 𝑣∓ 𝑣 𝑠 Where: fo = frequency the observer hears fs = frequency the source produces vo = speed of the observer vs = speed of the source v = speed of sound Note: If both the observer and the source are moving, you CANNOT consider one of the speeds to be zero and use a relative speed for the other.

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**The Doppler Effect Equation!!**

𝑓 𝑜 = 𝑓 𝑠 𝑣± 𝑣 𝑜 𝑣∓ 𝑣 𝑠 EEK!! What do the ± and ∓ symbols mean?!?! You will pick either + or – depending on which direction the source/observer are moving. In the next few slides, we will use an example to figure out how to use this equation.

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Example 1 A police car is at rest with its siren on. Imagine that the siren plays a single tone of frequency 550 Hz. You are in your truck, moving toward the car at a speed of 18 m/s. (A) Is the frequency you hear greater than, equal to or less than 550 Hz? Greater than!! The source and object are moving toward each other.

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Example 1 A police car is at rest with its siren on. Imagine that the siren plays a single tone of frequency 550 Hz. You are in your truck, moving toward the car at a speed of 18 m/s. Find the frequency you hear. fs = 550 Hz vo = 18 m/s vs = 0 v = 340 m/s fo = ? 𝑓 𝑜 = 𝑓 𝑠 𝑣± 𝑣 𝑜 𝑣∓ 𝑣 𝑠 𝑓 𝑜 = 𝑓 𝑠 𝑣± 𝑣 𝑜 𝑣 𝑓 𝑜 = 𝑓 𝑠 𝑣+ 𝑣 𝑜 𝑣 𝑓 𝑜 = 𝑓 𝑜 =580 𝐻𝑧 vs = 0 so we are left with this. We know that the frequency increases, so we must be using the + sign.

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**The Doppler Effect Equation!!**

Moving toward 𝑓 𝑜 = 𝑓 𝑠 𝑣± 𝑣 𝑜 𝑣∓ 𝑣 𝑠 Top term: 𝑣± 𝑣 𝑜 (+) is used when the observer is moving toward the source (-) is used when the observer is moving away from the source Bottom term: 𝑣∓ 𝑣 𝑠 (-) is used when the source is moving toward the observer (+) is used when the source is moving away from the observer The top sign is used for “moving toward” The bottom sign is used for “moving away”. Moving away

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